title: RoboCop 3

text: The film was directed by Fred Dekker, a director primarily known for cult horror films ("Night of the Creeps", "The Monster Squad"). Comic author Frank Miller, who co-wrote "RoboCop 2", returned to write the screenplay for the film. Still optimistic that he could make an impression in Hollywood, Miller hoped that some of his ideas excised from "RoboCop 2" would make it into "RoboCop 3". Major themes of the plot were taken from Miller's original (rejected) draft of "RoboCop 2". Disillusioned after finding that his work was even more drastically altered, Miller left Hollywood until the 2005 adaptation of his work "Sin City". “[Working on "RoboCop 2" and "3"] I learned the same lesson,” Miller said in 2005. “Don’t be the writer. The director’s got the power. The screenplay is a fire hydrant, and there’s a row of dogs around the block waiting for it." Miller's original screenplay for "RoboCop 2", and source for major ideas in "RoboCop 3", was later turned into a nine-part comic book series called "Frank Miller's RoboCop". Boom Studios released an eight-part comic book series "Robocop: The Last Stand" which is based on Miller's original "Robocop 3" screenplay.


title: RoboCop 3

text: The star of the previous films, Peter Weller, did not reprise the role of RoboCop, as he was starring in "Naked Lunch." Robert John Burke was signed to play the cyborg character instead. The RoboCop suit Burke wore in the movie was originally built for "RoboCop 2" (1990). Burke often complained that wearing it was painful after a short time.


title: RoboCop 3

text: Recognizing that RoboCop's fan base consisted primarily of children, Orion Pictures cut down on the graphic violence that was seen as the defining characteristic of the first two films.


title: RoboCop 3

text: "RoboCop 3" went into production soon after "RoboCop 2" was complete. Initially scheduled for release in the summer of 1992, "RoboCop 3" would languish on the shelf until the following year as Orion Pictures went through bankruptcy and was bought out. Because of release delays, its tie-in video game was released prior to the film, and thus revealed the film's plot beforehand.


title: RoboCop 3

text: After "RoboCop 2"s score which was composed by Leonard Rosenman, the "RoboCop" original composer Basil Poledouris returned to compose the soundtrack score and brought back many of the RoboCop themes from the original film.


title: RoboCop 3

text: "RoboCop 3" opened at number one in Japan, grossing 147,695,744 yen ($1.3 million) in its opening week from 17 screens, and went on to gross over $10 million there. It also opened at number one in France with a gross of 9.6 million French franc ($1.7 million) from 317 screens. In the US, it grossed $4.3 million in its opening weekend from 1,796 theaters, placing third, ending its run with $10.6 million in the United States and Canada. Internationally, it grossed $36.3 million for a worldwide gross of $47 million, against an estimated $22 million production budget.


title: RoboCop 3

text: The film received negative reviews from critics, and is often considered to be the worst entry of the series. Rotten Tomatoes gives "RoboCop 3" a score of 6% based on 31 reviews, with an average score of 3.20/10. The website's critical consensus states, "This asinine sequel should be placed under arrest." Metacritic rates it 40 out of 100 based on 15 critic reviews, indicating "mixed or average reviews".


title: RoboCop 3

text: Richard Harrington from "The Washington Post" said the movie is "hardly riveting and often it's downright silly. The sets and effects betray their downsized budget."


title: RoboCop 3

text: "Chicago Sun Times" critic Roger Ebert gave the film one and a half stars, disputing the characters' longevity. "Why do they persist in making these retreads? Because "RoboCop" is a brand name, I guess, and this is this year's new model. It's an old tradition in Detroit to take an old design and slap on some fresh chrome."


title: RoboCop 3

text: David Nusair from Reel Film Reviews gave the film two and a half stars, stating, "The best one could hope for is a movie that's not an ordeal to sit through, and on that level, "RoboCop 3" certainly excels. When placed side-by-side with the original, the film doesn't quite hold up. But, at the very least, "RoboCop 3" works as a popcorn movie—something part two couldn't even manage."


title: RoboCop 3

text: Other points of criticism in this movie include curtailing the graphic violence of the first two films (deliberately done in order to be more family-friendly), less dark humor, and the absence of Peter Weller in the title role.


title: Lethwei

text: Lethwei (; : ) or Burmese boxing, is a full contact combat sport from Myanmar that uses stand-up striking including headbutts. Lethwei is considered to be one of the most brutal martial arts in the world, as the sport is practiced bareknuckle with only tape and gauze while fighters are allowed to strike with their fists, elbows, knees, and feet, and the use of headbutts is also permitted. Disallowed in most combat sports, headbutts are important weapons in a Lethwei fighter's arsenal, giving Lethwei its name of The Art of 9 Limbs, and deemed one of the bloodiest martial arts. A vast majority of Lethwei fighters originate from the Karen ethnicity.


title: Lethwei

text: The traditional martial arts of Myanmar are regrouped under the term called Thaing which includes bando, banshay, naban, shan gyi and Lethwei. According to researchers, thaing can be traced in its earliest form to the 12th century of the Pagan Kingdom dynasty.


title: Lethwei

text: In ancient times, matches were held for entertainment and were popular with every strata of society. Participation was opened to any male, whether king or commoner. At that time, matches took place in sandpits instead of rings. Boxers fought without protective equipment, only wrapping their hands in hemp or gauze. There were no draws, the fight went on until one of the participants was knocked out or could no longer continue. Back then, Burmese boxing champions would enter the ring and call for open challenges.


title: Lethwei

text: Traditional matches include "Flagship Tournament", which are still fought throughout Myanmar, especially during holidays or celebration festivals like Thingy an.


title: Lethwei

text: Myanma lethwei went through many years of suppression during the British colonial rule of Burma. The sport was revived under General Ne Win's nationalistic government Compared to Muay Thai, in Lethwei, punches are generally favoured over kicks because of their ability to draw blood easier.


title: Lethwei

text: In rural areas, having a skilled child fighter has been a way of escaping poverty. As of 2017, the minimum monthly wage in Myanmar was around $70 USD and children as young as ten years old could compete in Lethwei and can earn from $30 to $100.


title: Lethwei

text: In modern times, the sport is kept alive in Lower Burma in Mon State and Karen State where matches are held for events such as New Year's celebrations.


title: Lethwei

text: Kyar Ba Nyein, who participated in boxing at the 1952 Summer Olympics, pioneered modern Lethwei by setting in place modern rules and regulations. He travelled around Myanmar, especially the Mon and Karen states, where Lethwei is more actively practiced. After training with some of the fighters, Kyar Ba Nyein brought some to Mandalay and Yangon to compete in matches.


title: Lethwei

text: In 1996, the Myanmar Traditional Lethwei Federation (MTLF), a branch of the Myanmar's Ministry of Health and Sports, added the modern Lethwei rules for the occasion of the "Golden Belt Championship" in Yangon. The bouts, along with the undercard fights, were organized by the Ministry of Sport, Myanmar Traditional Lethwei Federation and KSM group. This marked a big addition to the art of Lethwei and potentially would make Burmese boxing more marketable internationally.


title: Lethwei

text: On July 18, 2015, ONE Championship held the first Lethwei fight its history inside a cage at the occasion of in Yangon, Myanmar. The fight showcased Burmese fighters Phyan Thway and Soe Htet Oo in a dark match and the result was a draw according to the traditional Lethwei rules.


title: Lethwei

text: In 2017, ONE Championship and World Lethwei Championship officially entered into a partnership to share athletes to fight in each other's organization. On June 30, 2017, ONE Championship held a Lethwei match at between Thway Thit Win Hlaing and Soe Htet Oo. Thway Thit Win Hlaing would end up winning a decision according to WLC point system.


title: Lethwei

text: In 2016, Myanmar's first international Lethwei promotion called World Lethwei Championship (WLC) launched its events using the modern Lethwei rules.


title: Lethwei

text: In 2019, the WLC marked history by broadcasting , the first Lethwei event, internationally live on UFC Fight Pass.


title: Lethwei

text: From 7 to 12 July 2001, twelve years after Burma changed its name to Myanmar, the first international event took place in Yangon with professional fighters from the United States facing Burmese fighters under full traditional Lethwei rules. The delegation of three American fighters brought by the IKF were Shannon Ritch, Albert Ramirez and Doug Evans. Ritch faced Ei Htee Kaw, Ramirez faced Saw Thei Myo, and Evans faced openweight Lethwei champion Wan Chai. All three Americans lost to the Burmese. A revenge match with American and European fighters was cancelled the last minute by Lethwei promoters and the military in 2003.


title: Lethwei

text: From 10 to 11 July 2004, the second event headlining foreigners took place with four Japanese fighters fighting against Burmese fighters. They were mixed martial arts fighters Akitoshi Tamura, Yoshitaro Niimi, Takeharu Yamamoto and Naruji Wakasugi. Tamura knocked out Aya Bo Sein in the second round and became the first foreigner to beat a Myanmar Lethwei practitioner in an official match. International matches continued with the exciting Cyrus Washington vs. Tun Tun Min trilogy.


title: Lethwei

text: In 2016, after having previously fought to an explosive draw, Dave Leduc and Tun Tun Min rematched at the "Air KBZ Aung Lan Championship" in Yangon, Myanmar. The rematch was sweetened by an added bonus: ownership of the Lethwei Openweight World Championship Belt. Leduc became the first non-Burmese fighter to win the Lethwei Golden Belt and become Lethwei world champion after defeating Tun Tun Min in the second round.


title: Lethwei

text: Following his title defence, Leduc said in an interview, "I have so much vision for this sport. I see Lethwei doing the same for Myanmar as what Muay Thai has done for Thailand."


title: Lethwei

text: On April 18, 2017, for his second title defense under traditional rules, Dave Leduc faced Turkish Australian challenger Adem Yilmaz at in Tokyo, Japan. This marked the first Lethwei World title fight headlining two non-Burmese in the sport's history and for the occasion, the Ambassador of Myanmar to Japan was present at the event held in the Korakuen Hall.


title: Lethwei

text: Due to the violent ruleset, Lethwei is difficult to sanction and is illegal in most countries outside of Myanmar. Even though headbutts are allowed in Lethwei, they are banned from most other combat sports including mixed martial arts, kickboxing, and Muay Thai. As of 2022, Myanmar Lethwei is only legal in the following countries: Myanmar, Japan, Singapore, Slovakia, Austria, Thailand, Taiwan, England, United States (Only the state of Wyoming), New Zealand and Poland.


title: Lethwei

text: Lethwei has been featured in media, including films, television, manga, anime. The combat sport gained worldwide attention after Dave Leduc defeated Tun Tun Min in 2016.


title: Lethwei

text: Lethwei has been featured in the popular Japanese manga series "Kengan Ashura". In the series, the Burmese Lethwei master named "Saw Paing", is so indestructible that an opponent shatters every bone in their hand trying to punch him.


title: Lethwei

text: The "lekkha moun" is the traditional gesture performed by Lethwei fighters to challenge their opponents with courage and respect. The lekkha moun is done by clapping 3 times with right palm to the triangle shaped hole formed while bending the left arm. The clapping hand must be in form of a cup, while the left hand must be placed under the right armpit. The lekkha moun is done at the beginning of the Lethwei yay and can also be done while fighting.


title: Lethwei

text: This invitation to fight is inspired from the birds of prey, like the eagle, as they flap their wings when flying and hunting.


title: Lethwei

text: The "Lethwei yay" could be described as a "fight dance". It is performed before the fight as a way to showcase the fighter's skills and as a victory dance after the fight. The lekkha moun is usually confused with the lethwei yay, but the lekkha moun is done along with the Lethwei yay.


title: Lethwei

text: Before modernisation, especially in colonial times, the pre-fight dance was more commonly referred to as han yay (ဟန်ရေး). Performed in accordance with the tempo of the traditional orchestra (ဆိုင်း), it incorporated a much more elaborate dance and show of skills. Boastful poetry was sometimes recited along with the dance.


title: Lethwei

text: Each bout can be booked as a 3, 4 or 5 round fight with 3 minutes per round and a 2-minute break in between rounds. Championship bouts are 5 round fights with 3 minutes per round and a 2-minute break between rounds.


title: Lethwei

text: The fighters are required to apply the wrapping in front of the fight officials, who will endorse the wraps.


title: Lethwei

text: The traditional rules, also known as "yoe yar" rules, come from the Burmese "Myanma yoe yar Latway", which means "Myanmar traditional boxing". Traditional matches are still fought throughout Myanmar, especially during festivals or celebrations like Thingyan. Traditional Lethwei is notorious for not having a scoring system and for its controversial rule of knock-out only to win.


title: Lethwei

text: At the end of the match, in the eventuality that there is no knockout or stoppage, if the two fighters are still standing, even if one fighter dominated the fight, the match is declared a draw. Fighters can win by incapacitating their rivals in a few different ways.


title: Lethwei

text: For Lethwei fighters, the traditional Lethwei Golden Belt is regarded as the highest and most prestigious award.


title: Lethwei

text: There is only one Golden Belt champion for each weight categories, with the Openweight class champion being considered the strongest fighter in Myanmar. The Openweight Champion is the equivalent of being pound-for-pound champion in the world of lethwei.


title: Lethwei

text: In 1996, for the inaugural Golden Belt Championship, the two-minute injury timeout was removed and judges were added ringside. This modified ruleset helped prevented the outcome of a draw and helped choose a winner to advance in the tournament. Former fighter Win Tun was the most successful fighter in Golden Belt Championship history, having won four Golden Belts. In recent years, the World Lethwei Championship, Myanmar's first international promotion, is the biggest proponent of the modern rules in order to follow the international safety and regulation for combat sports.


title: Lethwei

text: The knockout is still highly desired under this ruleset, but in the event that a bout goes the distance, judges will present a decision. The 3 judges score the bout based on aggression, number of significant strikes per round, damage and blood drawn. Fighters have a maximum of 3 knockdowns per round and 4 knockdowns in the entire fight before the fight is ruled a knockout.


title: Lethwei

text: Aside from punches, kicks, elbows and knee attacks, Burmese fighters also make use of head-butts, raking knuckle strikes and take downs.


title: Lethwei

text: The elbow can be used in several ways as a striking weapon: horizontal, diagonal-upwards, diagonal-downwards, uppercut, downward, backward-spinning and flying. They can be used as either a finishing move or as a way to cut the opponent's eyebrow to draw blood.


title: Lethwei

text: Elbows can be used to great effect as blocks or defenses against, for example, spring knees, side body knees, body kicks or punches. When well connected, an elbow strike can cause serious damage to the opponent, including cuts or even a knockout.


title: Lethwei

text: The foot-thrust is one of the techniques in Lethwei. It is used as a defensive technique to control distance or block attacks and as a way to set up attack. Foot-thrusts should be thrown quickly but with enough force to knock an opponent off balance.


title: Lethwei

text: Note - The Myanglish spelling and phonetics based spelling are two different things. The words used are phonetics based words which are more friendly and easy to pronounce for non-Myanmar speaking people. The phonetics wording is provided by Liger Paing from United Myanmar Bando Nation.


title: Digital art

text: Digital art refers to any artistic work or practice that uses digital technology as part of the creative or presentation process, or more specifically computational art that uses and engages with digital media.


title: Digital art

text: Since the 1960s, various names have been used to describe digital art, including computer art, multimedia art and new media art.


title: Digital art

text: John Whitney, a pioneer of computer graphics, developed the first computer-generated art in the early 1960s by utilizing mathematical operations to create art. In 1963, Ivan Sutherland invented the first user interactive computer-graphics interface known as Sketchpad.


title: Digital art

text: Andy Warhol created digital art using a Commodore Amiga where the computer was publicly introduced at the Lincoln Center, New York, in July 1985. An image of Debbie Harry was captured in monochrome from a video camera and digitized into a graphics program called ProPaint. Warhol manipulated the image by adding color by using flood fills.


title: Digital art

text: After some initial resistance, the impact of digital technology has transformed activities such as painting, literature, drawing, sculpture, and music/sound art, while new techniques, such as internet art, digital installation art, and virtual reality, have emerged.


title: Digital art

text: Digital art can be purely computer-generated (such as fractals and algorithmic art) or taken from other sources, such as a scanned photograph or an image drawn using vector graphics software using a mouse or graphics tablet. Artworks are considered digital paintings when created similarly to non-digital paintings but using software on a computer platform and digitally outputting the resulting image as painted on canvas.


title: Digital art

text: Amidst varied opinions on the pros and cons of digital technology on the arts, there seems to be a strong consensus within the digital art community that it has created a "vast expansion of the creative sphere", i.e., that it has greatly broadened the creative opportunities available to professional and non-professional artists alike.


title: Digital art

text: Whilst 2D and 3D digital art is beneficial as it allows the preservation of history that would otherwise have been destroyed by events like natural disasters and war, there is the issue of who should own these 3D scans - i.e., who should own the digital copyrights.


title: Digital art

text: Digital visual art consists of either 2D visual information displayed on an electronic visual display or information mathematically translated into 3D information viewed through perspective projection on an electronic visual display. The simplest is 2D computer graphics which reflect how you might draw using a pencil and a piece of paper. In this case, however, the image is on the computer screen, and the instrument you draw with might be a tablet stylus or a mouse. What is generated on your screen might appear to be drawn with a pencil, pen, or paintbrush. The second kind is 3D computer graphics, where the screen becomes a window into a virtual environment, where you arrange objects to be "photographed" by the computer. Typically 2D computer graphics use raster graphics as their primary means of source data representations, whereas 3D computer graphics use vector graphics in the creation of immersive virtual reality installations. A possible third paradigm is to generate art in 2D or 3D entirely through the execution of algorithms coded into computer programs. This can be considered the native art form of the computer, and an introduction to the history of which is available in an interview with computer art pioneer Frieder Nake. Fractal art, Datamoshing, algorithmic art, and real-time generative art are examples.


title: Digital art

text: 3D graphics are created via the process of designing imagery from geometric shapes, polygons, or NURBS curves to create three-dimensional objects and scenes for use in various media such as film, television, print, rapid prototyping, games/simulations, and special visual effects.


title: Digital art

text: There are many software programs for doing this. The technology can enable collaboration, lending itself to sharing and augmenting by a creative effort similar to the open source movement and the creative commons in which users can collaborate on a project to create art.


title: Digital art

text: Pop surrealist artist Ray Caesar works in Maya (a 3D modeling software used for digital animation), using it to create his figures as well as the virtual realms in which they exist.


title: Digital art

text: Computer-generated animations are animations created with a computer from digital models created by 3D artists or procedurally generated. The term is usually applied to works created entirely with a computer. Movies make heavy use of computer-generated graphics; they are called computer-generated imagery (CGI) in the film industry. In the 1990s and early 2000s, CGI advanced enough that, for the first time, it was possible to create realistic 3D computer animation, although films had been using extensive computer images since the mid-70s. A number of modern films have been noted for their heavy use of photo-realistic CGI.


title: Digital art

text: Digital painting mainly refers to the process of creating paintings on computer software based on computers or graphic tables. Through pixel simulation, digital brushes in digital software (see the software in Digital painting) can imitate traditional painting paints and tools, such as oil, acrylic acid, pastel, charcoal, and airbrush. Users of the software can also customize the pixel size to achieve a unique visual effect (customized brushes).


title: Digital art

text: Artists have used artificial intelligence to create artwork since at least the 1960s. Since their design in 2014, some artists have created artwork using a generative adversarial network (GAN), which is a machine learning framework that allows two "algorithms" to compete with each other and iterate. It is usually used to let the computer find the best solution by itself. It can be used to generate pictures that have visual effects similar to traditional fine art. The essential idea of image generators is that people can use text descriptions to let AI convert their text into visual picture content. Anyone can turn their language into a painting through a picture generator. And some artists can use image generators to generate their paintings instead of drawing from scratch, and then they use the generated paintings as a basis to improve them and finally create new digital paintings. This greatly reduces the threshold of painting and challenges the traditional definition of painting art.


title: Digital art

text: Generally, the user can set the input, and the input content includes detailed picture content that the user wants. For example, the content can be a scene's content, characters, weather, character relationships, specific items, etc. It can also include selecting a specific artist style, screen style, image pixel size, brightness, etc. Then picture generators will return several similar pictures generated according to the input (generally, 4 pictures are given now). After receiving the results generated by picture generators, the user can select one picture as a result he wants or let the generator redraw and return to new pictures.


title: Digital art

text: In addition, it is worth mentioning the whole process: it is also similar to the "generator" and "discriminator" modules in GANs.


title: Digital art

text: In 2018, the artificial intelligence art auction was held at Christie's auction house in New York. The auction price of artificial intelligence work, "Edmond de Bellamy" created by a collective in Paris named "Obvious" was $432500, far exceeding its original estimate.


title: Digital art

text: At the end of August 2022, a person named Allen Jason won the first prize in the Colorado State Fair's fine art competition through the digital artwork "Théâtre D'opéra Spatial" made from an AI picture generator Midjourney.


title: Digital art

text: In contemporary art, the term digital art is used primarily to describe visual art that is made with digital tools, and also is highly computational, and explicitly engages with digital technologies. Art historian Christiane Paul writes that it "is highly problematic to classify all art that makes use of digital technologies somewhere in its production and dissemination process as digital art since it makes it almost impossible to arrive at any unifying statement about the art form.


title: Digital art

text: Digital installation art constitutes a broad field of activity and incorporates many forms. Some resemble video installations, particularly large-scale works involving projections and live video capture. By using projection techniques that enhance an audience's impression of sensory envelopment, many digital installations attempt to create immersive environments. Others go even further and attempt to facilitate a complete immersion in virtual realms. This type of installation is generally site-specific, scalable, and without fixed dimensionality, meaning it can be reconfigured to accommodate different presentation spaces.


title: Digital art

text: Noah Wardrip-Fruin's "Screen" (2003) is an example of interactive digital installation art which makes use of a Cave Automatic Virtual Environment to create an interactive experience. Scott Snibbe's "Boundary Functions" is an example of augmented reality digital installation art, which response to people who enter the installation by drawing lines between people, indicating their personal space.


title: Digital art

text: Internet art is digital art that uses the specific characteristics of the internet and is exhibited on the internet.


title: Digital art

text: Blockchain, and more specifically NFTs, are associated with digital art since the NFTs craze of 2020 and 2021. While the technology received many critics and has many flaws related to plagiarism and fraud ("due to its almost completely unregulated nature"), auction houses like Sotheby's, Christie's and various museums and galleries in the world started collaborations and partnerships with digital artists, selling NFTs associated with digital artworks "(via NFT platforms)" and showcasing those artworks ("associated to the respective NFTs") both in virtual galleries and real life screens, monitors and TVs.


title: Digital art

text: Notable art theorists and historians in this field include Oliver Grau, Jon Ippolito, Christiane Paul, Frank Popper, Jasia Reichardt, Mario Costa, Christine Buci-Glucksmann, Dominique Moulon, Robert C. Morgan, Roy Ascott, Catherine Perret, Margot Lovejoy, Edmond Couchot, Fred Forest and Edward A. Shanken.


title: Digital art

text: In addition to the creation of original art, research methods that utilize AI have been generated to quantitatively analyze digital art collections. This has been made possible due to large-scale digitization of artwork in the past few decades. Although the main goal of digitization was to allow for accessibility and exploration of these collections, the use of AI in analyzing them has brought about new research perspectives.


title: Digital art

text: Two computational methods, close reading and distant viewing, are the typical approaches used to analyze digitized art. Close reading focuses on specific visual aspects of one piece. Some tasks performed by machines in close reading methods include computational artist authentication and analysis of brushstrokes or texture properties. In contrast, through distant viewing methods, the similarity across an entire collection for a specific feature can be statistically visualized. Common tasks relating to this method include automatic classification, object detection, multimodal tasks, knowledge discovery in art history, and computational aesthetics. Whereas distant viewing includes the analysis of large collections, close reading involves one piece of artwork.


title: RMS Empress of Ireland

text: RMS "Empress of Ireland" was a British-built ocean liner that sank near the mouth of the Saint Lawrence River in Canada following a collision in thick fog with the Norwegian collier in the early hours of 29 May 1914. Although the ship was equipped with watertight compartments and, in the aftermath of the "Titanic" disaster two years earlier, carried more than enough lifeboats for all aboard, she foundered in only 14 minutes. Of the 1,477 people on board, 1,012 died, making it the worst peacetime maritime disaster in Canadian history.


title: RMS Empress of Ireland

text: Fairfield Shipbuilding and Engineering built "Empress of Ireland" and her sister ship, , at Govan on the Clyde in Scotland. The liners were commissioned by Canadian Pacific Steamships or "CPR" for the North Atlantic route between Liverpool and Quebec City. The transcontinental "CPR" and its fleet of ocean liners constituted the company's self-proclaimed "World's Greatest Transportation System". "Empress of Ireland" had just begun her 96th voyage when she was lost.


title: RMS Empress of Ireland

text: The wreck of "Empress of Ireland" lies in of water, making it accessible to advanced divers. Many artifacts from the wreckage have been retrieved, some of which are on display in the Empress of Ireland Pavilion at the "Site historique maritime de la Pointe-au-Père" in Rimouski, Quebec, and at the Canadian Museum of Immigration at Pier 21 in Halifax, Nova Scotia. The Canadian government has passed legislation to protect the site.


title: RMS Empress of Ireland

text: "Empress of Ireland" was the second of a pair of ocean liners ordered by Canadian Pacific Steamships during their early years in operation on the North Atlantic. In 1903, Canadian Pacific officially entered the market for trans-Atlantic passenger travel between the United Kingdom and Canada. In February of that year, they had purchased Elder Dempster & Co, through which they obtained three ships from Elder's subsidiary, the Beaver Line. These ships were "Lake Champlain", "Lake Erie" and "Lake Manitoba", with "Lake Champlain" being the first to sail on the company's established route between Liverpool, England and Montreal, Quebec, the following April. The line proved to be successful on the North Atlantic trade, as in that first year, thirty-three westbound crossings were completed by those three ships, on which a combined total of 23,400 passengers traveled in third class, most of them immigrants bound for Canada.


title: RMS Empress of Ireland

text: In early 1904 work commenced at Fairfield Shipbuilding and Engineering in Glasgow, Scotland. The liners were designed by Francis Elgar and were specified to be twin screw liners with service speeds of . Both were of identical appearance, with two funnels and two masts, with equal passenger capacity of just over 1,500. In the early planning stages, their intended names were to have been "Empress of Germany" and "Empress of Austria", but were later changed respectively to "Empress of Britain" and "Empress of Ireland", following the implementation of a policy that any future Canadian Pacific ship named in the "Empress" format would be respectively named after a dependency or colony of the British Empire.


title: RMS Empress of Ireland

text: The ship's keel was laid down on 10 April 1905 for hull number 443 at Fairfield's berth number 4 next to her sister ship, , which was being built. "Empress of Ireland"s length was overall and between perpendiculars. The beam was and her depth was . "Empress of Ireland" had twin four-bladed propellers, each driven by a quadruple-expansion steam engine. Between them the two engines were rated at 3,168 NHP and gave her a service speed of . She had twin funnels and two masts.


title: RMS Empress of Ireland

text: "Empress of Ireland"s safety features included ten watertight bulkheads which divided the hull into eleven compartments which could be sealed off through the means of closing twenty-four watertight doors. All eleven bulkheads extended from the double bottom up to directly beneath the Shelter Deck, equivalent to three decks above the waterline. By design theory, the vessels could remain afloat with up to two adjacent compartments open to the sea. However, what would prove to be the fatal flaw in her design in 1914 was that, unlike aboard where the watertight doors could be closed by the means of a switch on the ship's bridge, the watertight doors aboard "Empress of Ireland" were required to be closed manually. Also, in the wake of the "Titanic" disaster, "Empress of Ireland", like many other liners, had her lifesaving equipment updated. When she first entered service in 1906, she had been equipped with standard wooden lifeboats, which in 1912 were replaced with sixteen steel lifeboats mounted in conventional radial davits, under which were stored another twenty-six wooden collapsible lifeboats, all of which combined had a capacity of 1,686 persons, 280 more than the ship was licensed to carry.


title: RMS Empress of Ireland

text: "Empress of Ireland" was launched on 27 January 1906. With her original configuration she required a crew of 373, and had berths for 1,542 passengers in four classes on seven decks.


title: RMS Empress of Ireland

text: "Empress of Ireland"s First Class accommodation, located amidships on the upper and lower promenade and shelter decks, could accommodate 310 passengers when fully booked. Their accommodation included access to the open boat deck and two enclosed promenade decks which wrapped the full exterior of the upper and lower promenade decks. Located on the upper promenade deck was the music room, with built-in sofas and a grand piano encircling one of the ships most notable features, the glass dome over the first class dining room. Also on this deck was the top landing of the first class main staircase, which as similarly seen aboard "Titanic", faced aft and extended down two decks to the entrance of the first class dining room. Located on the lower promenade deck was the First class library, situated at the forward end of the deck with windows overlooking the ship's bow. Amidships was the first class cafe, which was pierced by the two-story well above the first class dining room, while at the after end of the deck was the first class smoke room. One deck below on the shelter deck was the elegant first class dining room, which could seat 224 passengers in one sitting. In addition, a separate dining room for up to thirty first class children was located at the forward end of the deck. Finally, scattered across all three decks were arrays of two- and four-berth cabins.


title: RMS Empress of Ireland

text: The second class accommodation, in the stern on the lower Promenade, shelter, upper and main decks, could accommodate 150 more passengers than in first class, with a designed capacity for 468 in second class when fully booked. They were allotted open deck space at the after end of the lower promenade deck, extending from the after end of the superstructure to beneath the docking bridge at the end of the stern, while one deck below on the shelter deck was located additional deck space sheltered by the deck above. Also on the shelter deck were the second class smoke room, located at the aft end of the deck and designed in a similar but simpler fashion as what was seen in first class, with built-in sofas lining the outer walls and an adjacent bar. At the forward end of the deck, beneath the aft mast was the second class entrance, with a staircase running down two decks to the main deck. Aft of the main landing was the second class social hall, laid out in a fashion similar to the smoke room and provided with a piano, while forward of the entrance was the second class dining room, large enough to seat 256 passengers at one serving. On the starboard side of the upper deck and in the three compartments aft of the engine room casing on the main deck were an array of two and four berth cabins, designed to be interchangeable to both first class and third class. According to the ship's deck plans, cabins for 134 passengers on the upper deck were designed to be converted to first class cabins if needed, while the cabins for 234 passengers on the main deck could simultaneously be converted to be used for third class passengers if needed.


title: RMS Empress of Ireland

text: As for immigrants and lower-class travellers, "Empress of Ireland" was designed with accommodations which symbolised the dramatic shift in immigrant travel on the North Atlantic commonly seen between the turn of the 20th Century and the outbreak of the First World War, that being a general layout which included both the 'old' and 'new' steerage, which combined provided accommodations for 764 passengers at the forward end of the ship. Passengers travelling in these two classes had some shared public areas, including access to the forward well deck on the shelter deck, as well as a large open space on the Upper Deck very similar to the open space later seen aboard "Titanic". This open space, which spanned the full width of the ship and the length of two watertight compartments, included wooden benches lining the outer walls, and a large children's sandbox enclosed by a wooden fence. At the after end of this space were two smaller public rooms, side by side against the adjacent bulkhead. On the port side was the third class ladies' room, which included a piano, while across on the starboard side was the third class smoke room, complete with an adjacent bar. On the main and lower decks, the accommodations separated, with the 'new' steerage, more commonly referred to as third class, providing for 494 passengers, and the 'old' steerage providing for 270 passengers. Accommodation for Third class consisted of four sections of two, four and six berth cabins, three on the main deck and one on the lower deck, and defined by watertight bulkheads. Directly aft of the section on the main deck was the third class dining room, which was large enough to seat 300 passengers in one sitting. The old steerage consisted of three sections of open berths, one on the main deck and two on the lower deck, all forward of the third class sections. Each section consisted of two-tiered bunks, individual pantries and long wooden tables with benches.


title: RMS Empress of Ireland

text: Two months after "Empress of Britain" entered service, "Empress of Ireland" departed Liverpool for Quebec City on her maiden voyage on Thursday, 29 June 1906. The following morning she made port at Moville, a coastal town on the north coast of Ireland, to pick up a number of Irish immigrants before making for the open Atlantic. On her first trip across the Atlantic she carried 1,257 passengers, with 119 in First Class and 342 in Second Class, Third Class being booked well past capacity with 796, a large number of small children and infants among them. Seen as a foreshadowing of "Empress of Ireland"'s popularity with immigrants, Third Class was so heavily overbooked on her maiden voyage that at least 100 passengers who had booked passage aboard her had to be left behind in Liverpool to wait for the next ship.


title: RMS Empress of Ireland

text: On the afternoon of 6 July, "Empress of Ireland" arrived at the mouth of the Saint Lawrence River, calling at Pointe-au-Père to pick up a river pilot who would assist in guiding the ship down the final 300-kilometer stretch of the voyage to Quebec City. While off Rimouski, another small boat met "Empress of Ireland" to collect all Canadian-bound mail and drop off a group of people working to aid in preparing for the liner's arrival. These consisted of Canadian Pacific Railway (CPR) ticketing agents who would meet with all the passengers to arrange for their transportation by rail to their final destinations across Canada; Canadian immigration and customs officials who would inspect luggage and check passenger documents, and doctors to examine all passengers to check for any illnesses which would warrant quarantine at Grosse Isle, a process all but one of the ship's passengers passed through successfully. "Empress of Ireland" arrived in Quebec City early the following morning, where passengers disembarked and cargo was offloaded, and after a six-day turnaround she sailed on her first eastbound crossing back to Liverpool on 12 July.


title: RMS Empress of Ireland

text: Over the next eight years, "Empress of Ireland" completed the same process of transporting passengers and cargo between Britain and Canada, with alternating Canadian ports by season, terminating at Quebec City in May through October and at Halifax, Nova Scotia, and Saint John, New Brunswick, in November through April when the river was frozen over. By 1913 "Empress of Ireland" was equipped with wireless telegraphy, operating on the 300 and 600 metre wavelengths. Her call sign was MPL.


title: RMS Empress of Ireland

text: "Empress of Ireland"s final successful crossing ended when she arrived at Quebec City from Liverpool on 22 May 1914, by which time she'd transported 119,262 passengers westbound to Canada and another 67,838 eastbound to Britain.


title: RMS Empress of Ireland

text: "Empress of Ireland" departed Quebec City for Liverpool at 16:30 local time (EST) on 28 May 1914, manned by a crew of 420 and carrying 1,057 passengers, roughly two-thirds of her total capacity. In first class, the list of passengers was relatively small, with only eighty-seven booked passages. This small number did not however spare the inclusion of some rather notable figures from both sides of the Atlantic.


title: RMS Empress of Ireland

text: Second class saw a considerably larger booking at just over half capacity with 253 passengers, owed greatly to a large party of Salvation Army members and their families, numbering 170 in all, who were travelling to attend the 3rd International Salvation Army Congress in London.


title: RMS Empress of Ireland

text: Third class saw the largest booking, which with 717 passengers was nearly filled to capacity. This complement reflected greatly the typical mix of steerage travellers seen on eastbound crossings aboard "Empress of Ireland" and her running mates on the North Atlantic which paralleled that seen on westbound crossings from Liverpool. While on westbound crossings third class passengers were predominantly diverse mixes of immigrants, eastbound crossings saw equally diverse blends of former immigrants from both Canada and the United States returning to their native countries in Europe. Many were returning to visit relatives, while others were in the process of remigrating and resettling.


title: RMS Empress of Ireland

text: Henry George Kendall had been promoted to captain of "Empress of Ireland" at the beginning of the month, and it was his first trip down the Saint Lawrence River in command of her.


title: RMS Empress of Ireland

text: "Empress of Ireland" reached Pointe-au-Père in the early hours of 29 May 1914, where the pilot disembarked. She resumed a normal outward bound course of about N76E (076 degrees) and soon sighted the masthead lights of SS "Storstad", a Norwegian collier, on her starboard bow at a distance of several miles. Likewise, "Storstad", which was abreast of Métis Point and on a virtually reciprocal course of course of W. by S. (259 degrees), sighted "Empress of Ireland"s masthead lights. These first sightings were made in clear weather conditions, but fog soon enveloped the ships. The ships resorted to repeated use of their fog whistles. At 01:56 local time "Storstad" crashed into "Empress of Ireland"s starboard side at around midships. "Storstad" remained afloat, but "Empress of Ireland" was severely damaged. A gaping hole in her side caused the lower decks to flood at a rate alarming to the crew. Captain Kendall shouted to the crew of "Storstad" with a megaphone to keep her engines at full power and plug the hole, but "Empress of Ireland" continued her forward motion, and the current of the St. Lawrence shoved "Storstad" away after about five seconds, allowing 60,000 gallons of water to begin pouring into "Empress of Ireland".


title: RMS Empress of Ireland

text: "Empress of Ireland" lurched heavily to starboard and began settling by the stern. There was no time to shut the watertight doors. Water entered through open portholes, some only a few feet above the water line, and inundated passageways and cabins. Most of the passengers and crew located in the lower decks drowned quickly. Those berthed in the upper decks were awakened by the collision and immediately boarded lifeboats on the boat deck. Within a few minutes, the ship's list was so severe that the port lifeboats could not be launched. Some passengers attempted to do so but the lifeboats just crashed into the side of the ship, spilling their occupants into the frigid water. Five starboard lifeboats were launched successfully, while a sixth capsized during lowering.


title: RMS Empress of Ireland

text: The lights and power on "Empress of Ireland" eventually failed five or six minutes after the collision, plunging the ship into darkness. Ten or eleven minutes after the collision, the ship lurched violently onto her starboard side, allowing as many as 700 passengers and crew to crawl out of the portholes and decks onto her port side. The ship lay on her side for a minute or two, having seemingly run aground. A few minutes later at 02:10, about 14 minutes after the collision, the bow rose briefly out of the water and the ship finally sank. Hundreds of people were thrown into the near-freezing water. The disaster resulted in the deaths of 1,012 people.


title: RMS Empress of Ireland

text: As reported in the newspapers at the time, there was much confusion as to the cause of the collision with both parties claiming the other was at fault. As was noted at the subsequent inquiry, "If the testimony of both captains were to be believed, the collision happened as both vessels were stationary with their engines stopped". The witnesses from "Storstad" said they were approaching so as to pass red to red (port to port) while those from "Empress of Ireland" said they were approaching so as to pass green to green (starboard to starboard), but "the stories are irreconcilable".


title: RMS Empress of Ireland

text: Ultimately, the swift sinking and immense loss of life can be attributed to three factors: the location in which "Storstad" made contact, failure to close "Empress of Ireland"s watertight doors, and longitudinal bulkheads that exacerbated the list by inhibiting cross flooding. A contributing factor was open portholes. Surviving passengers and crew testified that some upper portholes were left open for ventilation. The International Convention for the Safety of Life at Sea (SOLAS) requires that any openable portholes be closed and locked before leaving port, but portholes were often left open in sheltered waters like the Saint Lawrence River where heavy seas were not expected. When "Empress of Ireland" began to list to starboard, water poured through the open portholes further increasing flooding.


title: RMS Empress of Ireland

text: There were only 465 survivors: 4 children (the other 134 children were lost), 41 women (the other 269 women were lost), 172 men (the other 437 men were lost), and 248 crew (the other 172 crew were lost). The fact that most passengers were asleep at the time of the sinking (most not even awakened by the collision) also contributed to the loss of life when they were drowned in their cabins, most of them from the starboard side where the collision happened.


title: RMS Empress of Ireland

text: The exact numbers of passengers and crew of the sunken ship who either died or were saved was not established until the inquiry. This was because of discrepancies in the names of the passengers shown on the manifest (particularly in regard to the continentals) and the names given by the survivors. As a consequence, initial reports in the newspapers were incomplete.


title: RMS Empress of Ireland

text: "Storstad", which remained afloat, lowered her own lifeboats and began to rescue the survivors in the water. The radio operator at Pointe-au-Père who picked up the emergency signal from "Empress of Ireland" notified two Canadian government steamers: the pilot boat "Eureka" at Pointe-au-Père Wharf, which left the wharf at full steam at 02:30; followed by the mail ship "Lady Evelyn" at Rimouski Wharf which left at 02:45. "Eureka" was first on the scene at 03:10 and rescued about 150 survivors from the water. She brought the survivors first to Pointe-au-Père, but was redirected to Rimouski Wharf where doctors and relief supplies were waiting. "Lady Evelyn" arrived at the site of sinking at 03:45. No survivors were left in the water but "Lady Evelyn" collected the 200 survivors rescued by "Storstad", as well as 133 bodies, and arrived to join "Eureka" at the Rimouski Wharf about 05:15. "Storstad" was damaged but not severely, so her captain continued on to Quebec.


title: RMS Empress of Ireland

text: One of the survivors was Captain Kendall, who was on the bridge at the time of the collision and quickly ordered the lifeboats to be launched. When "Empress of Ireland" lurched onto her side, he was thrown from the bridge into the water, and was taken down with her as she began to go under. Swimming to the surface, he clung to a wooden grate long enough for crew members aboard a nearby lifeboat to row over and pull him in. Immediately, Kendall took command of the small boat and began rescue operations. The lifeboat's crew successfully pulled in many people from the water, and when the boat was full, Kendall ordered the crew to row to the lights of "Storstad" so that the survivors could be dropped off. He and the crew made a few more trips between "Storstad" and the wreck site to search for more survivors. After an hour or two, Kendall gave up, since any survivors who were still in the water would have either succumbed to hypothermia or drowned by then. Upon first boarding "Storstad", Kendall stormed to the bridge, and levied an accusation at Captain Andersen: "You have sunk my ship!"


title: RMS Empress of Ireland

text: Amongst the dead were the English dramatist and novelist Laurence Irving and his wife Mabel Hackney; the explorer Henry Seton-Karr; Ella Hart-Bennett, the wife of British government official William Hart-Bennett; and Gabriel J. Marks, the first mayor of Suva, Fiji, along with his wife Marion. Lieutenant Charles Lindsay Claude Bowes-Lyon, a first cousin of the future Queen Elizabeth The Queen Mother survived the disaster, but died in combat only five months later on the Western Front near Ypres.


title: RMS Empress of Ireland

text: The passengers included 167 members of the Salvation Army. These travelers, all but eight of whom died, were members of the Canadian Staff Band who were traveling to London for an international conference. One of the four children who survived was 7-year-old Grace Hanagan, who was born in Oshawa, Ontario, on 16 May 1907, and was traveling with her parents, who were among the Salvation Army members who did not survive. Grace was also the last survivor of the sinking and died in St. Catharines, Ontario, on 15 May 1995 at the age of 87.


title: RMS Empress of Ireland

text: "I was travelling second-class with three others in my cabin. I was sure something was wrong when the blow occurred. When I heard the vessel’s siren blowing I jumped up in my bunk, took a lifebelt from the rack over me, and threw the others to the girls. They did not want them at first. I was serious and made them put them on, and as a result they are saved.


title: RMS Empress of Ireland

text: "How I got into the water I do not know. I was getting away from the swarm of people who were around the ship when a big man, wounded in the head, approached and clung to me. I was trying to shake him off, for he was pulling me down, when I saw his head fall forward. I knew he was dead. He drifted away and disappeared. I do not know who it was; it was horrible. I was drifting away myself. When the boat sank the suction took me down. I involuntarily began to paddle with my feet and came to the surface. Then I saw a man swimming. It was then quite light. I watched him, and though I cannot swim a stroke I imitated his arm motions and found I got along a little. I was picked up.


title: RMS Empress of Ireland

text: "When I got to the wharf I found I was the first woman landed. Some one gave me a blanket, and I sat with that on me for about an hour until he came up" – and she indicated Mr. Johnson, who was sitting beside her." -Testimonial from Passenger Alice Bales, 21 years old.


title: RMS Empress of Ireland

text: As for "Storstad"s Chief Officer Alfred Toftenes, little is known of what became of him except that he died in New York City a few years later, in 1918. He is buried in Green-Wood Cemetery in Brooklyn.


title: RMS Empress of Ireland

text: The Commission of Inquiry, held in Quebec, commenced on 16 June 1914 and lasted for eleven days. Presiding over the contentious proceedings was Lord Mersey, who had previously presided over the SOLAS summit the year before, and had headed the official inquiries into a number of significant steamship tragedies, including that of "Titanic". The following year, he would lead the inquiry into the sinking of "Lusitania". Assisting Lord Mersey were two other commissioners: Sir Adolphe-Basile Routhier of Quebec, and Chief Justice Ezekiel McLeod of New Brunswick. All three commissioners were officially appointed by John Douglas Hazen, the Minister of Marine and Fisheries of Canada, under Part X of the Canada Shipping Act.


title: RMS Empress of Ireland

text: At the beginning of the Inquiry twenty questions were formulated by the Canadian government. For example, was "Empress of Ireland" sufficiently and efficiently officered and manned? (Q.4); after the vessels had sighted each other's lights did the atmosphere between them become foggy or misty, so that lights could no longer be seen? If so, did both vessels comply with SOLAS Articles 15 and 16, and did they respectively indicate on their steam whistles or sirens, the course or courses they were taking by the signals set out? (Q.11); was a good and proper lookout kept on board of both vessels? (Q.19); and, was the loss of "Empress of Ireland" or the loss of life, caused by the wrongful act or default of the Master and First Officer of that vessel, and the Master, First, Second and Third Officers of "Storstad", or any of them? (Q.20). All of these questions were addressed by the inquiry and answered in full in its report.


title: RMS Empress of Ireland

text: The inquiry heard testimony from a total of sixty-one witnesses: twenty-four crew and officers of "Empress of Ireland" (including Captain Kendall); twelve crew and officers of "Storstad" (including Captain Andersen); five passengers of "Empress of Ireland"; and twenty other people including two divers, two Marconi wireless operators at Pointe-au-Père, two naval architects, the harbour master at Quebec, and crew and officers of several other ships whose involvement either directly or indirectly was deemed pertinent.


title: RMS Empress of Ireland

text: Two very different accounts of the collision were given at the Inquiry. "Empress of Ireland"s crew reported that after the pilot had been dropped at Pointe-au-Père, the ship proceeded to sea at full speed in order to obtain an offing from the shore. After a short time the masthead lights of a steamer, which subsequently proved to be "Storstad", were sighted on the starboard bow, approximately six miles away, the weather at that time being fine and clear. After continuing for some time, "Empress of Ireland" altered her course with the object of proceeding down the river. When making this change, the masthead lights of "Storstad" were still visible, about miles away, and according to Captain Kendall it was intended to pass "Storstad" starboard to starboard at no risk of collision. The green light of "Storstad" was then sighted, but a little later a fog bank was seen coming off the land that dimmed "Storstad"s lights. The engines of "Empress of Ireland" were then stopped (and put full speed astern) and her whistle blown three short blasts signifying that this had been done. About a minute later the fog shut out the lights of "Storstad" completely. After exchanging further whistle blasts with "Storstad", her masthead and side lights were seen by Captain Kendall about 100 feet away almost at right angles to "Empress of Ireland" and approaching at high speed. In the hope of possibly avoiding or minimizing the effect of a collision the engines of "Empress of Ireland" were ordered full speed ahead, but it was too late and "Storstad" struck "Empress of Ireland" amidships. Kendall placed the blame firmly on "Storstad" for the collision. Famously, the first words he said to Captain Andersen of "Storstad" after the sinking were, "You have sunk my ship!". He maintained for the rest of his life that it was not his fault the collision occurred.


title: RMS Empress of Ireland

text: "Storstad"s crew reported that the masthead lights of "Empress of Ireland" were first seen on the port bow about 6 or 7 nmi away; the lights were at that time open to starboard. A few minutes later, the green side light of "Empress of Ireland" was seen apparently from 3 to 5 miles away. The green light remained for an interval, and then "Empress of Ireland" was seen to make a change in her course. Her masthead lights came into a (vertical) line, and she showed both the green and the red side lights. She then continued to swing to starboard, shutting out the green and showing only the red light. This light was observed for a few minutes before being obscured by the fog. At this moment, "Empress of Ireland" was about two miles away and "Storstad"s Chief Officer, Mr. Toftenes, assumed that it was "Empress of Ireland"s intention to pass him port to port (red to red), which the ships would do with ample room if their relative positions were maintained. After an exchange of whistle blasts with "Empress of Ireland", "Storstad" was slowed and Captain Andersen (who was asleep in his cabin at the time) was called to the bridge. When he arrived, Andersen saw a masthead light moving quickly across "Storstad"s course from port to starboard whereupon he ordered the engines full speed astern. Immediately after Andersen saw the masthead light, he saw the green light, and a few moments later saw "Empress of Ireland" and the ships then collided.


title: RMS Empress of Ireland

text: After all the evidence that had been heard, the Commissioners stated that the question as to who was to blame resolved itself into a simple issue, namely which of the two ships changed her course during the fog. They could come to "no other conclusion" than that it was "Storstad" that ported her helm and changed her course to starboard, and so brought about the collision. Chief Officer Toftenes of "Storstad" was specifically blamed for wrongly and negligently altering his course in the fog and, in addition, failing to call the captain when he saw the fog coming on.


title: RMS Empress of Ireland

text: After the official inquiry was completed, Captain Andersen was quoted as saying that Lord Mersey was a "fool" for holding him responsible for the collision. He also announced that he intended to file a lawsuit against the CPR.


title: RMS Empress of Ireland

text: An inquiry launched by the Norwegians disagreed with the official report and cleared "Storstad"s crew of all responsibility. Instead, they blamed Kendall, "Empress of Ireland"s captain, for violating the protocol by not passing port to port.


title: RMS Empress of Ireland

text: The CPR won a court case against A. F. Klaveness & Co, the owners of "Storstad", for C$2 million, which is the valuation of silver bullion stored aboard "Empress of Ireland" when she sank. The owners of "Storstad" entered an unsuccessful counterclaim against the CPR for $50,000 damages, contending that "Empress of Ireland" was at fault and alleging negligent navigation on her part. "Storstad" was seized at the request of the CPR and sold for $175,000 to Prudential Trust, an insurance company acting on behalf of AF Klaveness & Co.


title: RMS Empress of Ireland

text: On 5 June 1914, Canadian Pacific announced it had chartered the Allan Line's "Virginian" to fill in the void in service in its fleet left by the loss of "Empress of Ireland", joining "Empress of Britain" and other previously acquired Canadian Pacific ships on the Saint Lawrence run. "Virginian" embarked from her first voyage from Liverpool under Canadian Pacific service on 12 June, which was to have been the next departure date from Liverpool of "Empress of Ireland".


title: RMS Empress of Ireland

text: In 2005 a Canadian television film, "The Last Voyage of the Empress", investigated the sinking with historical reference, model re-enactment, and underwater investigation. The program's opinion was that the cause of the incident appeared to be the fog, exacerbated by the actions of Captain Kendall. Both captains were in their own way telling the truth, but with Kendall omitting the expediency of commanding "Empress of Ireland" in such a way as to keep his company's advertised speed of Atlantic crossing. In order to pass "Storstad" (off "Empress"s starboard bow) to quickly expedite this maintenance of speed, Kendall, in the fog, turned to starboard (towards "Storstad") as part of a manoeuvre to spin back to his previous heading to pass the other ship as originally intended on his starboard side, thereby avoiding what he saw as a time-wasting diversion from his preferred and fast route through the channel. When Captain Anderson of "Storstad" saw "Empress of Ireland" through the fog he thought, by seeing both "Empress of Ireland"s port and starboard lights during its manoeuvre, that "Empress of Ireland" was attempting to pass on the opposite side of "Storstad" than previously apparent and turned his ship to starboard to avoid a collision. However, "Empress of Ireland" turned to port to continue on its original time-saving heading; thus the bow to side collision.


title: RMS Empress of Ireland

text: The conclusion of the programme was that both captains failed to abide by the condition that, on encountering fog, ships should maintain their heading, although the captain of "Storstad" deviated only after seeing the deviation of "Empress of Ireland". In the film, water tank replication of the incident indicated that "Empress of Ireland" could not have been stationary at the point of the collision. It also indicated—through underwater observations of the ship's Engine order telegraph in the engine room—that Kendall's assertion that he gave the order to close watertight doors was probably not true.


title: RMS Empress of Ireland

text: Although the loss of "Empress of Ireland" did not attract the same level of attention as that of "Titanic" two years earlier, the disaster did lead to a change in the design of ships' bows. The sinking of "Empress of Ireland" proved that the reverse slanting, inverted or "tumblehome" prow so common at the time, was deadly in the event of a ship-to-ship collision because it caused massive damage below the waterline, effectively acting as a ram which would smash through an unarmoured hull without difficulty (especially if the ship was steaming at some speed). The bow of "Storstad" struck "Empress of Ireland" like a "chisel into tin". As a result of the disaster, naval designers began to employ the raked bow with the top of the prow forward. This ensured that the energy of any collision would be minimised beneath the surface and only the parts of the bow above the waterline would be affected.


title: RMS Empress of Ireland

text: The rapid sinking of "Empress of Ireland" has also been cited by 20th-century naval architects, John Reid and William Hovgaard, as an example for making the case of discontinuation of longitudinal bulkheads which provide forward and aft separation between the outer coal bunkers and the inner compartments on ships. Though not entirely watertight, these longitudinal bulkheads trapped water between them. When the spaces flooded, this quickly forced a ship to list, pushing the port holes underwater. As flooding continued entering accommodation spaces, this only exacerbated the listing of the ship and dragging of the main deck down into the water. This would lead to the flooding of the upper compartments and finally the capsize and sinking of the ship. Reid and Hovgaard both cited the "Empress of Ireland" disaster as evidence which supported their conclusions that longitudinal subdivision were very hazardous in ship collisions.


title: RMS Empress of Ireland

text: Shortly after the disaster, a salvage operation began on "Empress of Ireland" to recover the purser's safe and the mail. This was deemed a plausible effort due to the wreck's relatively shallow depth at 130 feet(39,62m).


title: RMS Empress of Ireland

text: As they recovered bodies and valuables from the ship, the salvers were faced with limited visibility and strong currents from the Saint Lawrence River. One of the hard-hat divers, Edward Cossaboom, was killed when, it is assumed, he slipped from the hull of the wreck plummeting another to the riverbed below, closing or rupturing his air hose as he fell. He was found lying unconscious on his lifeline and all attempts to revive him after he was brought to the surface failed. It was later reported, implausibly, that the sudden increase in water pressure had so compressed the diver's body that all that remained was a "jellyfish with a copper mantle and dangling canvas tentacles." The salvage crew resumed their operations and recovered 318 bags of mail and 251 bars of silver (silver bullion) worth about $150,000 ($1,099,000 in 2013 when adjusted for inflation).


title: RMS Empress of Ireland

text: In 1964, the wreck was revisited by a group of Canadian divers who recovered a brass bell. In the 1970s, another group of divers recovered a telemotor, pieces of Marconi wireless equipment, a brass porthole and a compass. Robert Ballard, the oceanographer and maritime archaeologist who discovered the wreck of "Titanic" and the German battleship "Bismarck", visited the wreck of "Empress of Ireland" and found that she was being covered by silt. He also discovered that certain artefacts from fixtures to human remains continued to be taken out by "treasure hunters".


title: RMS Empress of Ireland

text: In the province of Quebec, shipwrecks are not afforded explicit protection. However, in 1999 the wreck was declared a site of historical and archaeological importance and thus became protected under the Cultural Property Act and was listed in the register of Historic Sites of Canada. This was the first time that an underwater site had received this status in Quebec.


title: RMS Empress of Ireland

text: This protection was important because, unlike "Titanic", "Empress of Ireland" rests at the relatively shallow depth of . While accessible to skilled recreational divers, the site is dangerous due to the cold water, strong currents and restricted visibility. As of 2009 six people had lost their lives on the dive.


title: RMS Empress of Ireland

text: A number of monuments were erected, particularly by the CPR, to mark the burial places of those passengers and crew whose bodies were recovered in the days that followed the tragic sinking. For example, there are two monuments at Rimouski. One monument is located on the coastal road between Rimouski and Pointe-au-Père and is dedicated to the memory of eighty-eight persons; it is inscribed with twenty names, but the sixty-eight other persons are unidentified. A second monument is located at the cemetery in Rimouski ("Les Jardins commémoratifs Saint-Germain") and is dedicated to the memory of a further seven persons, four of whom are named.


title: RMS Empress of Ireland

text: The CPR also erected several monuments in Quebec, e.g., Mount Hermon Cemetery and St. Patrick's Cemetery, both of which are located on the Sillery Heritage Site, at the formerly independent city of Sillery.


title: RMS Empress of Ireland

text: The Salvation Army erected its own monument at the Mount Pleasant Cemetery in Toronto. The inscription reads, "In Sacred Memory of 167 Officers and Soldiers of the Salvation Army Promoted to Glory From the Empress of Ireland at Daybreak, Friday May 29, 1914". A memorial service is held there every year on the anniversary of the accident.


title: RMS Empress of Ireland

text: The hundredth anniversary of the sinking of "Empress of Ireland" was commemorated in May 2014, by numerous events, including an exhibition at the Canadian Museum of History entitled "Empress of Ireland: Canada's Titanic" which moved to the Canadian Museum of Immigration at Pier 21 in 2015.


title: RMS Empress of Ireland

text: Canada Post issued two stamps to commemorate the event. The Empress of Ireland domestic Permanent stamp was designed by Isabelle Toussaint, and is lithographed in seven colours. The Official First Day Cover was cancelled in Rimouski where survivors and victims were initially brought following the tragedy. The international denomination stamp was designed by Susan Scott using the oil on canvas illustration she commissioned from marine artist Aristides Balanos, and printed using lithography in six colours. The Official First Day Cover was cancelled at Pointe-au-Père, Quebec, the town closest to the site of the sinking.


title: Hyperbolic geometry

text: In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate of Euclidean geometry is replaced with:


title: Hyperbolic geometry

text: Hyperbolic plane geometry is also the geometry of pseudospherical surfaces, surfaces with a constant negative Gaussian curvature. Saddle surfaces have negative Gaussian curvature in at least some regions, where they locally resemble the hyperbolic plane.


title: Hyperbolic geometry

text: A modern use of hyperbolic geometry is in the theory of special relativity, particularly the Minkowski model.


title: Hyperbolic geometry

text: When geometers first realised they were working with something other than the standard Euclidean geometry, they described their geometry under many different names; Felix Klein finally gave the subject the name hyperbolic geometry to include it in the now rarely used sequence elliptic geometry (spherical geometry), parabolic geometry (Euclidean geometry), and hyperbolic geometry.


title: Hyperbolic geometry

text: In the former Soviet Union, it is commonly called Lobachevskian geometry, named after one of its discoverers, the Russian geometer Nikolai Lobachevsky.


title: Hyperbolic geometry

text: This page is mainly about the 2-dimensional (planar) hyperbolic geometry and the differences and similarities between Euclidean and hyperbolic geometry. See hyperbolic space for more information on hyperbolic geometry extended to three and more dimensions.


title: Hyperbolic geometry

text: Hyperbolic geometry is more closely related to Euclidean geometry than it seems: the only axiomatic difference is the parallel postulate.


title: Hyperbolic geometry

text: When the parallel postulate is removed from Euclidean geometry the resulting geometry is absolute geometry.


title: Hyperbolic geometry

text: All theorems of absolute geometry, including the first 28 propositions of book one of Euclid's "Elements", are valid in Euclidean and hyperbolic geometry.


title: Hyperbolic geometry

text: Propositions 27 and 28 of Book One of Euclid's "Elements" prove the existence of parallel/non-intersecting lines.


title: Hyperbolic geometry

text: This difference also has many consequences: concepts that are equivalent in Euclidean geometry are not equivalent in hyperbolic geometry; new concepts need to be introduced.


title: Hyperbolic geometry

text: Further, because of the angle of parallelism, hyperbolic geometry has an absolute scale, a relation between distance and angle measurements.


title: Hyperbolic geometry

text: Single lines in hyperbolic geometry have exactly the same properties as single straight lines in Euclidean geometry. For example, two points uniquely define a line, and line segments can be infinitely extended.


title: Hyperbolic geometry

text: Two intersecting lines have the same properties as two intersecting lines in Euclidean geometry. For example, two distinct lines can intersect in no more than one point, intersecting lines form equal opposite angles, and adjacent angles of intersecting lines are supplementary.


title: Hyperbolic geometry

text: When a third line is introduced, then there can be properties of intersecting lines that differ from intersecting lines in Euclidean geometry. For example, given two intersecting lines there are infinitely many lines that do not intersect either of the given lines.


title: Hyperbolic geometry

text: These properties are all independent of the model used, even if the lines may look radically different.


title: Hyperbolic geometry

text: Non-intersecting lines in hyperbolic geometry also have properties that differ from non-intersecting lines in Euclidean geometry:


title: Hyperbolic geometry

text: This implies that there are through "P" an infinite number of coplanar lines that do not intersect "R".


title: Hyperbolic geometry

text: Some geometers simply use the phrase ""parallel" lines" to mean ""limiting parallel" lines", with "ultraparallel" lines meaning just "non-intersecting".


title: Hyperbolic geometry

text: These limiting parallels make an angle "θ" with "PB"; this angle depends only on the Gaussian curvature of the plane and the distance "PB" and is called the angle of parallelism.


title: Hyperbolic geometry

text: For ultraparallel lines, the ultraparallel theorem states that there is a unique line in the hyperbolic plane that is perpendicular to each pair of ultraparallel lines.


title: Hyperbolic geometry

text: Let formula_2, where formula_3 is the Gaussian curvature of the plane. In hyperbolic geometry, formula_4 is negative, so the square root is of a positive number.


title: Hyperbolic geometry

text: Therefore, in hyperbolic geometry the ratio of a circle's circumference to its radius is always strictly greater than formula_7, though it can be made arbitrarily close by selecting a small enough circle.


title: Hyperbolic geometry

text: If the Gaussian curvature of the plane is −1 then the geodesic curvature of a circle of radius "r" is: formula_8


title: Hyperbolic geometry

text: In hyperbolic geometry, there is no line all of whose points are equidistant from another line. Instead, the points that all have the same orthogonal distance from a given line lie on a curve called a hypercycle.


title: Hyperbolic geometry

text: Another special curve is the horocycle, a curve whose normal radii (perpendicular lines) are all limiting parallel to each other (all converge asymptotically in one direction to the same ideal point, the centre of the horocycle).


title: Hyperbolic geometry

text: Through every pair of points there are two horocycles. The centres of the horocycles are the ideal points of the perpendicular bisector of the line-segment between them.


title: Hyperbolic geometry

text: The length of the line-segment is the shortest length between two points. The arc-length of a hypercycle connecting two points is longer than that of the line segment and shorter than that of a horocycle, connecting the same two points. The arclength of both horocycles connecting two points are equal. The arc-length of a circle between two points is larger than the arc-length of a horocycle connecting two points.


title: Hyperbolic geometry

text: If the Gaussian curvature of the plane is −1 then the geodesic curvature of a horocycle is 1 and of a hypercycle is between 0 and 1.


title: Hyperbolic geometry

text: Unlike Euclidean triangles, where the angles always add up to π radians (180°, a straight angle), in hyperbolic geometry the sum of the angles of a hyperbolic triangle is always strictly less than π radians (180°, a straight angle). The difference is referred to as the defect.


title: Hyperbolic geometry

text: The area of a hyperbolic triangle is given by its defect in radians multiplied by "R". As a consequence, all hyperbolic triangles have an area that is less than or equal to "R"π. The area of a hyperbolic ideal triangle in which all three angles are 0° is equal to this maximum.


title: Hyperbolic geometry

text: As in Euclidean geometry, each hyperbolic triangle has an incircle. In hyperbolic geometry, if all three of its vertices lie on a horocycle or hypercycle, then the triangle has no circumscribed circle.


title: Hyperbolic geometry

text: As in spherical and elliptical geometry, in hyperbolic geometry if two triangles are similar, they must be congruent.


title: Hyperbolic geometry

text: A special polygon in hyperbolic geometry is the regular apeirogon, a uniform polygon with an infinite number of sides.


title: Hyperbolic geometry

text: In Euclidean geometry, the only way to construct such a polygon is to make the side lengths tend to zero and the apeirogon is indistinguishable from a circle, or make the interior angles tend to 180 degrees and the apeirogon approaches a straight line.


title: Hyperbolic geometry

text: However, in hyperbolic geometry, a regular apeirogon has sides of any length (i.e., it remains a polygon).


title: Hyperbolic geometry

text: The side and angle bisectors will, depending on the side length and the angle between the sides, be limiting or diverging parallel (see lines above).


title: Hyperbolic geometry

text: If the bisectors are limiting parallel the apeirogon can be inscribed and circumscribed by concentric horocycles.


title: Hyperbolic geometry

text: If the bisectors are diverging parallel then a pseudogon (distinctly different from an apeirogon) can be inscribed in hypercycles (all vertices are the same distance of a line, the axis, also the midpoint of the side segments are all equidistant to the same axis.)


title: Hyperbolic geometry

text: Like the Euclidean plane it is also possible to tessellate the hyperbolic plane with regular polygons as faces.


title: Hyperbolic geometry

text: There are an infinite number of uniform tilings based on the Schwarz triangles ("p" "q" "r") where 1/"p" + 1/"q" + 1/"r" < 1, where "p", "q", "r" are each orders of reflection symmetry at three points of the fundamental domain triangle, the symmetry group is a hyperbolic triangle group. There are also infinitely many uniform tilings that cannot be generated from Schwarz triangles, some for example requiring quadrilaterals as fundamental domains.


title: Hyperbolic geometry

text: Though hyperbolic geometry applies for any surface with a constant negative Gaussian curvature, it is usual to assume a scale in which the curvature "K" is −1.


title: Hyperbolic geometry

text: In hyperbolic geometry, the sum of the angles of a quadrilateral is always less than 360 degrees, and hyperbolic rectangles differ greatly from Euclidean rectangles since there are no equidistant lines, so a proper Euclidean rectangle would need to be enclosed by two lines and two hypercycles. These all complicate coordinate systems.


title: Hyperbolic geometry

text: There are however different coordinate systems for hyperbolic plane geometry. All are based around choosing a point (the origin) on a chosen directed line (the "x"-axis) and after that many choices exist.


title: Hyperbolic geometry

text: The Lobachevski coordinates "x" and "y" are found by dropping a perpendicular onto the "x"-axis. "x" will be the label of the foot of the perpendicular. "y" will be the distance along the perpendicular of the given point from its foot (positive on one side and negative on the other).


title: Hyperbolic geometry

text: Another coordinate system measures the distance from the point to the horocycle through the origin centered around formula_9 and the length along this horocycle.


title: Hyperbolic geometry

text: Other coordinate systems use the Klein model or the Poincare disk model described below, and take the Euclidean coordinates as hyperbolic.


title: Hyperbolic geometry

text: A Cartesian-like coordinate system ("x, y") on the oriented hyperbolic plane is constructed as follows. Choose a line in the hyperbolic plane together with an orientation and an origin "o" on this line. Then:


title: Hyperbolic geometry

text: In this coordinate system, straight lines take one of these forms (("x", "y") is a point on the line; "x", "y", "A", and "α" are parameters):


title: Hyperbolic geometry

text: Generally, these equations will only hold in a bounded domain (of "x" values). At the edge of that domain, the value of "y" blows up to ±infinity. See also Coordinate systems for the hyperbolic plane#Polar coordinate system.


title: Hyperbolic geometry

text: Since the publication of Euclid's Elements circa 300 BCE, many geometers made attempts to prove the parallel postulate. Some tried to prove it by assuming its negation and trying to derive a contradiction. Foremost among these were Proclus, Ibn al-Haytham (Alhacen), Omar Khayyám, Nasīr al-Dīn al-Tūsī, Witelo, Gersonides, Alfonso, and later Giovanni Gerolamo Saccheri, John Wallis, Johann Heinrich Lambert, and Legendre.


title: Hyperbolic geometry

text: Their attempts were doomed to failure (as we now know, the parallel postulate is not provable from the other postulates), but their efforts led to the discovery of hyperbolic geometry.


title: Hyperbolic geometry

text: The theorems of Alhacen, Khayyam and al-Tūsī on quadrilaterals, including the Ibn al-Haytham–Lambert quadrilateral and Khayyam–Saccheri quadrilateral, were the first theorems on hyperbolic geometry. Their works on hyperbolic geometry had a considerable influence on its development among later European geometers, including Witelo, Gersonides, Alfonso, John Wallis and Saccheri.


title: Hyperbolic geometry

text: In the 18th century, Johann Heinrich Lambert introduced the hyperbolic functions and computed the area of a hyperbolic triangle.


title: Hyperbolic geometry

text: In the 19th century, hyperbolic geometry was explored extensively by Nikolai Ivanovich Lobachevsky, János Bolyai, Carl Friedrich Gauss and Franz Taurinus. Unlike their predecessors, who just wanted to eliminate the parallel postulate from the axioms of Euclidean geometry, these authors realized they had discovered a new geometry.


title: Hyperbolic geometry

text: Gauss wrote in an 1824 letter to Franz Taurinus that he had constructed it, but Gauss did not publish his work. Gauss called it "non-Euclidean geometry" causing several modern authors to continue to consider "non-Euclidean geometry" and "hyperbolic geometry" to be synonyms. Taurinus published results on hyperbolic trigonometry in 1826, argued that hyperbolic geometry is self consistent, but still believed in the special role of Euclidean geometry. The complete system of hyperbolic geometry was published by Lobachevsky in 1829/1830, while Bolyai discovered it independently and published in 1832.


title: Hyperbolic geometry

text: In 1868, Eugenio Beltrami provided models (see below) of hyperbolic geometry, and used this to prove that hyperbolic geometry was consistent if and only if Euclidean geometry was.


title: Hyperbolic geometry

text: The term "hyperbolic geometry" was introduced by Felix Klein in 1871. Klein followed an initiative of Arthur Cayley to use the transformations of projective geometry to produce isometries. The idea used a conic section or quadric to define a region, and used cross ratio to define a metric. The projective transformations that leave the conic section or quadric stable are the isometries. "Klein showed that if the Cayley absolute is a real curve then the part of the projective plane in its interior is isometric to the hyperbolic plane..."


title: Hyperbolic geometry

text: The discovery of hyperbolic geometry had important philosophical consequences. Before its discovery many philosophers (for example Hobbes and Spinoza) viewed philosophical rigour in terms of the "geometrical method", referring to the method of reasoning used in "Euclid's Elements".


title: Hyperbolic geometry

text: Kant in the "Critique of Pure Reason" came to the conclusion that space (in Euclidean geometry) and time are not discovered by humans as objective features of the world, but are part of an unavoidable systematic framework for organizing our experiences.


title: Hyperbolic geometry

text: It is said that Gauss did not publish anything about hyperbolic geometry out of fear of the "uproar of the Boeotians", which would ruin his status as "princeps mathematicorum" (Latin, "the Prince of Mathematicians").


title: Hyperbolic geometry

text: The "uproar of the Boeotians" came and went, and gave an impetus to great improvements in mathematical rigour, analytical philosophy and logic. Hyperbolic geometry was finally proved consistent and is therefore another valid geometry.


title: Hyperbolic geometry

text: Because Euclidean, hyperbolic and elliptic geometry are all consistent, the question arises: which is the real geometry of space, and if it is hyperbolic or elliptic, what is its curvature?


title: Hyperbolic geometry

text: Lobachevsky had already tried to measure the curvature of the universe by measuring the parallax of Sirius and treating Sirius as the ideal point of an angle of parallelism. He realised that his measurements were not precise enough to give a definite answer, but he did reach the conclusion that if the geometry of the universe is hyperbolic, then the absolute length is at least one million times the diameter of the earth's orbit (, 10 parsec).


title: Hyperbolic geometry

text: Henri Poincaré, with his sphere-world thought experiment, came to the conclusion that everyday experience does not necessarily rule out other geometries.


title: Hyperbolic geometry

text: The geometrization conjecture gives a complete list of eight possibilities for the fundamental geometry of our space. The problem in determining which one applies is that, to reach a definitive answer, we need to be able to look at extremely large shapes – much larger than anything on Earth or perhaps even in our galaxy.


title: Hyperbolic geometry

text: Special relativity places space and time on equal footing, so that one considers the geometry of a unified spacetime instead of considering space and time separately. Minkowski geometry replaces Galilean geometry (which is the three-dimensional Euclidean space with time of Galilean relativity).


title: Hyperbolic geometry

text: In relativity, rather than considering Euclidean, elliptic and hyperbolic geometries, the appropriate geometries to consider are Minkowski space, de Sitter space and anti-de Sitter space, corresponding to zero, positive and negative curvature respectively.


title: Hyperbolic geometry

text: Hyperbolic geometry enters special relativity through rapidity, which stands in for velocity, and is expressed by a hyperbolic angle. The study of this velocity geometry has been called kinematic geometry. The space of relativistic velocities has a three-dimensional hyperbolic geometry, where the distance function is determined from the relative velocities of "nearby" points (velocities).


title: Hyperbolic geometry

text: The hyperbolic plane is a plane where every point is a saddle point. There exist various pseudospheres in Euclidean space that have a finite area of constant negative Gaussian curvature.


title: Hyperbolic geometry

text: By Hilbert's theorem, it is not possible to isometrically immerse a complete hyperbolic plane (a complete regular surface of constant negative Gaussian curvature) in a three-dimensional Euclidean space.


title: Hyperbolic geometry

text: Other useful models of hyperbolic geometry exist in Euclidean space, in which the metric is not preserved. A particularly well-known paper model based on the pseudosphere is due to William Thurston.


title: Hyperbolic geometry

text: The art of crochet has been used (see ) to demonstrate hyperbolic planes, the first such demonstration having been made by Daina Taimiņa.


title: Hyperbolic geometry

text: In 2000, Keith Henderson demonstrated a quick-to-make paper model dubbed the "hyperbolic soccerball" (more precisely, a truncated order-7 triangular tiling).


title: Hyperbolic geometry

text: Instructions on how to make a hyperbolic quilt, designed by Helaman Ferguson, have been made available by Jeff Weeks.


title: Hyperbolic geometry

text: Various pseudospheres – surfaces with constant negative Gaussian curvature – can be embedded in 3-dimensional space under the standard Euclidean metric, and so can be made into tangible physical models. Of these, the tractoid (often called the pseudosphere) is the best known; using the tractoid as a model of the hyperbolic plane is analogous to using a cone or cylinder as a model of the Euclidean plane. However, the entire hyperbolic plane cannot be embedded into Euclidean space in this way, and various other models are more convenient for abstractly exploring hyperbolic geometry.


title: Hyperbolic geometry

text: There are four models commonly used for hyperbolic geometry: the Klein model, the Poincaré disk model, the Poincaré half-plane model, and the Lorentz or hyperboloid model. These models define a hyperbolic plane which satisfies the axioms of a hyperbolic geometry.


title: Hyperbolic geometry

text: Despite their names, the first three mentioned above were introduced as models of hyperbolic space by Beltrami, not by Poincaré or Klein. All these models are extendable to more dimensions.


title: Hyperbolic geometry

text: The Beltrami–Klein model, also known as the projective disk model, Klein disk model and Klein model, is named after Eugenio Beltrami and Felix Klein.


title: Hyperbolic geometry

text: For the two dimensions this model uses the interior of the unit circle for the complete hyperbolic plane, and the chords of this circle are the hyperbolic lines.


title: Hyperbolic geometry

text: For higher dimensions this model uses the interior of the unit ball, and the chords of this "n"-ball are the hyperbolic lines.


title: Hyperbolic geometry

text: The Poincaré disk model, also known as the conformal disk model, also employs the interior of the unit circle, but lines are represented by arcs of circles that are orthogonal to the boundary circle, plus diameters of the boundary circle.


title: Hyperbolic geometry

text: The Poincaré half-plane model takes one-half of the Euclidean plane, bounded by a line "B" of the plane, to be a model of the hyperbolic plane. The line "B" is not included in the model.


title: Hyperbolic geometry

text: The Euclidean plane may be taken to be a plane with the Cartesian coordinate system and the x-axis is taken as line "B" and the half plane is the upper half ("y" > 0 ) of this plane.


title: Hyperbolic geometry

text: The hyperboloid model or Lorentz model employs a 2-dimensional hyperboloid of revolution (of two sheets, but using one) embedded in 3-dimensional Minkowski space. This model is generally credited to Poincaré, but Reynolds says that Wilhelm Killing used this model in 1885


title: Hyperbolic geometry

text: The hemisphere model is not often used as model by itself, but it functions as a useful tool for visualising transformations between the other models.


title: Hyperbolic geometry

text: The hemisphere model is part of a Riemann sphere, and different projections give different models of the hyperbolic plane:


title: Hyperbolic geometry

text: In 1966 David Gans proposed a flattened hyperboloid model in the journal "American Mathematical Monthly". It is an orthographic projection of the hyperboloid model onto the xy-plane.


title: Hyperbolic geometry

text: This model is not as widely used as other models but nevertheless is quite useful in the understanding of hyperbolic geometry.


title: Hyperbolic geometry

text: The band model employs a portion of the Euclidean plane between two parallel lines. Distance is preserved along one line through the middle of the band. Assuming the band is given by formula_27, the metric is given by formula_28.


title: Hyperbolic geometry

text: All models essentially describe the same structure. The difference between them is that they represent different coordinate charts laid down on the same metric space, namely the hyperbolic plane.


title: Hyperbolic geometry

text: The characteristic feature of the hyperbolic plane itself is that it has a constant negative Gaussian curvature, which is indifferent to the coordinate chart used. The geodesics are similarly invariant: that is, geodesics map to geodesics under coordinate transformation.


title: Hyperbolic geometry

text: Hyperbolic geometry generally is introduced in terms of the geodesics and their intersections on the hyperbolic plane.


title: Hyperbolic geometry

text: Once we choose a coordinate chart (one of the "models"), we can always embed it in a Euclidean space of same dimension, but the embedding is clearly not isometric (since the curvature of Euclidean space is 0). The hyperbolic space can be represented by infinitely many different charts; but the embeddings in Euclidean space due to these four specific charts show some interesting characteristics.


title: Hyperbolic geometry

text: Every isometry (transformation or motion) of the hyperbolic plane to itself can be realized as the composition of at most three reflections. In "n"-dimensional hyperbolic space, up to "n"+1 reflections might be required. (These are also true for Euclidean and spherical geometries, but the classification below is different.)


title: Hyperbolic geometry

text: illustrate the conformal disc model (Poincaré disk model) quite well. The white lines in "III" are not quite geodesics (they are hypercycles), but are close to them. It is also possible to see quite plainly the negative curvature of the hyperbolic plane, through its effect on the sum of angles in triangles and squares.


title: Hyperbolic geometry

text: For example, in "Circle Limit III" every vertex belongs to three triangles and three squares. In the Euclidean plane, their angles would sum to 450°; i.e., a circle and a quarter. From this, we see that the sum of angles of a triangle in the hyperbolic plane must be smaller than 180°. Another visible property is exponential growth. In "Circle Limit III", for example, one can see that the number of fishes within a distance of "n" from the center rises exponentially. The fishes have an equal hyperbolic area, so the area of a ball of radius "n" must rise exponentially in "n".


title: Hyperbolic geometry

text: The art of crochet has been used to demonstrate hyperbolic planes (pictured above) with the first being made by Daina Taimiņa, whose book "Crocheting Adventures with Hyperbolic Planes" won the 2009 Bookseller/Diagram Prize for Oddest Title of the Year.


title: Hyperbolic geometry

text: Hyperbolic geometry is not limited to 2 dimensions; a hyperbolic geometry exists for every higher number of dimensions.


title: Hyperbolic geometry

text: Hyperbolic space of dimension "n" is a special case of a Riemannian symmetric space of noncompact type, as it is isomorphic to the quotient


title: Hyperbolic geometry

text: The orthogonal group acts by norm-preserving transformations on Minkowski space R, and it acts transitively on the two-sheet hyperboloid of norm 1 vectors. Timelike lines (i.e., those with positive-norm tangents) through the origin pass through antipodal points in the hyperboloid, so the space of such lines yields a model of hyperbolic "n"-space. The stabilizer of any particular line is isomorphic to the product of the orthogonal groups O("n") and O(1), where O("n") acts on the tangent space of a point in the hyperboloid, and O(1) reflects the line through the origin. Many of the elementary concepts in hyperbolic geometry can be described in linear algebraic terms: geodesic paths are described by intersections with planes through the origin, dihedral angles between hyperplanes can be described by inner products of normal vectors, and hyperbolic reflection groups can be given explicit matrix realizations.


title: Hyperbolic geometry

text: In small dimensions, there are exceptional isomorphisms of Lie groups that yield additional ways to consider symmetries of hyperbolic spaces. For example, in dimension 2, the isomorphisms allow one to interpret the upper half plane model as the quotient and the Poincaré disc model as the quotient . In both cases, the symmetry groups act by fractional linear transformations, since both groups are the orientation-preserving stabilizers in of the respective subspaces of the Riemann sphere. The Cayley transformation not only takes one model of the hyperbolic plane to the other, but realizes the isomorphism of symmetry groups as conjugation in a larger group. In dimension 3, the fractional linear action of on the Riemann sphere is identified with the action on the conformal boundary of hyperbolic 3-space induced by the isomorphism . This allows one to study isometries of hyperbolic 3-space by considering spectral properties of representative complex matrices. For example, parabolic transformations are conjugate to rigid translations in the upper half-space model, and they are exactly those transformations that can be represented by unipotent upper triangular matrices.


title: K. Subrahmanyam

text: Krishnaswamy Subrahmanyam (19 January 1929 – 2 February 2011) was a prominent international strategic affairs analyst, journalist and former Indian civil servant. Considered a proponent of "Realpolitik", Subrahmanyam was an influential voice in Indian security affairs for a long time. He was most often referred to as the doyen of India's strategic affairs community, and as the premier ideological champion of India's nuclear deterrent. His son S Jaishankar was appointed India's External Affairs Minister in 2019.