title: Jo Jeeta Wohi Sikandar

text: Ramlal has two sons – the ideal, older son Ratan and the indisciplined younger one, Sanjay. Ratan is always hard-working while Sanjay always fails in his classes and hangs around with his friends Ghanshu and Maksood. Ratan competes for top honours at the inter-college sports event but ends up losing the penultimate cycle race at the finish line to his arch rival, Shekhar, by less than a cycle's length and placing second.


title: Jo Jeeta Wohi Sikandar

text: Over the course of the next year, Ratan and Shekhar keep running into each other while training, usually ending with Shekhar, who is from the elite Rajput College, mocking Ratan over his modest background. Meanwhile, Sanjay is busy chasing girls in cars that he "borrows" from his childhood friend Anjali's garage. One day, he meets Devika, who is a rich girl studying at Queens college. Sanjay poses as Sanjay Thapar, a son of a wealthy millionaire and tells her that he attends an elite college in an effort to impress Devika. Devika falls for Sanjay's lies and starts falling in love with him, however when she learns the truth, she dumps him. Sanjay, who is regularly insulted by Shekhar and his friends over his apparent poverty (as compared to them), ends up fighting with them after being dumped by Devika. Ratan intervenes and saves the day, but as a result Ramlal banishes Sanjay from the house. Meanwhile, during his bike ride, Ratan is attacked and seriously injured by Shekhar, and his friends. Also Shekhar is shown to be now dating Devika. As a result of his injuries, Ratan is unable to compete in the next cycle race.


title: Jo Jeeta Wohi Sikandar

text: This prompts a guilty Sanjay to get his act together – he begins training hard and preparing to participate in the race. He is helped by Ratan and Anjali, who has always had a crush on him and with whom he later falls in love. At the annual cycle race, Shekhar and Sanjay take the lead but end up colliding and falling off course. They start fighting each other over the incident involving Ratan, only to rejoin the race once the rest of the field has overtaken them on the course. They both manage to chase down the rest of the field, and emerge one behind the other, with Shekhar leading. At the finish line in the last lap of the race, Sanjay overtakes Shekhar to win the race for his college, marking the first time since his father that Model College will lift the sports trophy.


title: Jo Jeeta Wohi Sikandar

text: The film was directed by Mansoor Khan, and written and produced by Nasir Hussain. Akshay Kumar had auditioned and Milind Soman was signed for Shekhar Malhotra's role, before Deepak Tijori played the role. Aditya Pancholi was selected to play the role of Ratan, but the role went to Mamik Singh, as confirmed by "DNA".


title: Jo Jeeta Wohi Sikandar

text: The plot has similarities to the 1979 American film "Breaking Away". However, Mansoor Khan stated that he only became aware of "Breaking Away" after the likeness was brought to his attention, some time after the release of "Jo Jeeta Wohi Sikander". Both films have several similarities, including friendship, class barriers, bicycle racing, and parental relationship, but otherwise have different narratives, characters, motivations, treatment and racing rules.


title: Jo Jeeta Wohi Sikandar

text: Though it is clearly mentioned in the introductory voice over that the movie is based in Dehradun (in fact, the first word spoken in the movie is "Dehradun"), it is mentioned twice in the movie (both times by the commentator during the cycle race) that it takes place in Kodaikanal. The movie has been shot predominantly in various locations in the south of India, primarily Kodaikanal. Soman had completed 75% of his scenes before being replaced by Tijori.


title: Jo Jeeta Wohi Sikandar

text: The music for the film was composed by Jatin–Lalit and the lyrics were penned by Majrooh Sultanpuri. The soundtrack, the second collaboration between Jatin and Lalit, helped to launch their careers. It was nominated for Best Music at the 1993 Filmfare Awards. "Pehla Nasha" was the fourth film song in Indian cinema (the first one being "Jogi O Jogi" from "Lakhon Mein Ek" (1971), followed by "Baare Baare" from "Naagarahaavu" (1972) and "Sundari Neeyum" from "Michael Madana Kama Rajan" (1990)) to be shot in complete slow motion. The technique was later used in many films and music videos. Pehla Nasha was the most popular track of the album and has become a cult song. Other popular tracks were "Humse Hai Sara Jahan", "Rooth Ke Humse" and "Arre Yaaron Mere Pyaaron". The song "Arre Yaaron Mere Pyaaron" was sung by Udit Narayan along with Vijeta Pandit.


title: Jo Jeeta Wohi Sikandar

text: "Jo Jeeta Wohi Sikandar" was the third best-selling Bollywood soundtrack album of 1992, having sold 2.5million units in India.


title: Jo Jeeta Wohi Sikandar

text: In India, "Jo Jeeta Wohi Sikandar" net and grossed , equivalent to adjusted for inflation. The film opened to good responses, and was declared a hit at the box office. "Jo Jeeta Wohi Sikander" was also broadcast on Disney Channel India.


title: Jo Jeeta Wohi Sikandar

text: In a review dated 29 May 1992, "The Indian Express" praised Najeeb Khan's photography, the sets and the performances of Aamir Khan, Ayesha Jhulka, and Pooja Bedi, but criticised Jatin–Lalit's music.


title: Link rot

text: Link rot (also called link death, link breaking, or reference rot) is the phenomenon of hyperlinks tending over time to cease to point to their originally targeted file, web page, or server due to that resource being relocated to a new address or becoming permanently unavailable. A link that no longer points to its target, often called a "broken" or "dead" link (or sometimes "orphan" link), is a specific form of dangling pointer.


title: Link rot

text: The rate of link rot is a subject of study and research due to its significance to the internet's ability to preserve information. Estimates of that rate vary dramatically between studies.


title: Link rot

text: A number of studies have examined the prevalence of link rot within the World Wide Web, in academic literature that uses URLs to cite web content, and within digital libraries.


title: Link rot

text: A 2003 study found that on the Web, about one link out of every 200 broke each week, suggesting a half-life of 138 weeks. This rate was largely confirmed by a 2016–2017 study of links in Yahoo! Directory (which had stopped updating in 2014 after 21 years of development) that found the half-life of the directory's links to be two years.


title: Link rot

text: A 2004 study showed that subsets of Web links (such as those targeting specific file types or those hosted by academic institution) could have dramatically different half-lives. The URLs selected for publication appear to have greater longevity than the average URL. A 2015 study by Weblock analyzed more than 180,000 links from references in the full-text corpora of three major open access publishers and found a half-life of about 14 years, generally confirming a 2005 study that found that half of the URLs cited in D-Lib Magazine articles were active 10 years after publication. Other studies have found higher rates of link rot in academic literature but typically suggest a half-life of four years or greater. A 2013 study in "BMC Bioinformatics" analyzed nearly 15,000 links in abstracts from Thomson Reuters's Web of Science citation index and found that the median lifespan of web pages was 9.3 years, and just 62% were archived. A 2021 study of external links in 1996-2019 "New York Times" articles found that 25% of links were inaccessible. In addition, from a sample of 4,500 links still accessible, 13% did not lead to the original content, a phenomenon called "content drift".


title: Link rot

text: A 2002 study suggested that link rot within digital libraries is considerably slower than on the web, finding that about 3% of the objects were no longer accessible after one year (equating to a half-life of nearly 23 years).


title: Link rot

text: Link rot can result from several occurrences. A target web page may be removed. The server that hosts the target page could fail, be removed from service, or relocate to a new domain name. A domain name's registration may lapse or be transferred to another party. Some causes will result in the link failing to find any target and returning an error such as HTTP 404. Other causes will cause a link to target content other than what was intended by the link's author.


title: Link rot

text: Strategies for preventing link rot can focus on placing content where its likelihood of persisting is higher, authoring links that are less likely to be broken, taking steps to preserve existing links, or repairing links whose targets have been relocated or removed.


title: Link rot

text: The creation of URLs that will not change with time is the fundamental method of preventing link rot. Preventive planning has been championed by Tim Berners-Lee and other web pioneers.


title: Link rot

text: The detection of broken links may be done manually or automatically. Automated methods include plug-ins for content management systems as well as standalone broken-link checkers such as like Xenu's Link Sleuth. Automatic checking may not detect links that return a soft 404 or links that return a 200 OK response but point to content that has changed.


title: Sesamoid bone

text: In anatomy, a sesamoid bone () is a bone embedded within a tendon or a muscle. Its name is derived from the Arabic word for 'sesame seed', indicating the small size of most sesamoids. Often, these bones form in response to strain, or can be present as a normal variant. The patella is the largest sesamoid bone in the body. Sesamoids act like pulleys, providing a smooth surface for tendons to slide over, increasing the tendon's ability to transmit muscular forces.


title: Sesamoid bone

text: In equine anatomy, the term sesamoid bone usually refers to the two sesamoid bones found at the back of the fetlock or metacarpophalangeal and metatarsophalangeal joints in both hindlimbs and forelimbs. Strictly these should be termed the proximal sesamoid bones whereas the navicular bone should be referred to as the distal sesamoid bone. The patella is also a form of sesamoid bone in the horse.


title: Sesamoid bone

text: Although many carnivores have radial sesamoid bones, the giant panda and red panda independently evolved to have an enlarged radial sesamoid bone. This evolution has caused the two species to diverge from other carnivores. The red panda likely originally evolved the "pseudo-thumb" in order to assist in arboreal locomotion. When the red panda later evolved to consume a bamboo diet, the enlarged bone underwent exaptation to assist in grasping bamboo. The giant panda, however, evolved the enlarged radial sesamoid bone around the same time as it evolved a bamboo diet. In the giant panda, the bone allows for a pincer-like motion and is used in grasping the bamboo. In these two panda species, "DYNC2H1" gene and "PCNT" gene have been identified as possible causes for the pseudo-thumb development.


title: Sesamoid bone

text: Recently, the enlarged radial sesamoid bone of cotton rats has been studied. Their enlarged radial sesamoid bone and that of the giant panda have a similar morphology and size relative to the rest of the hand. The reason for this evolutionary change is still unknown; however, it may be to assist in grasping small objects and thin branches.


title: Sesamoid bone

text: Elephants have similarly enlarged sesamoid bones in both their forelimbs and hindlimbs, referred to as the prepollex and prehallux, respectively. These sesamoids function as "sixth toes", helping to distribute the animals' weight. In contrast to other sesamoids in elephants, which ossify at 3-7 years of age, the ossification of the prepollex and prehallux is delayed and is known to not have yet occurred in animals in excess of 20 years of age. The prehallux is further divided into two elements; the more proximal of these is fixed, whilst the more distal is mobile. Evidence of these "predigits" has also been found in certain fossil proboscideans.


title: 1924 Summer Olympics

text: The 1924 Summer Olympics (), officially the Games of the VIII Olympiad () and also known as Paris 1924, were an international multi-sport event held in Paris, France. The opening ceremony was held on 5 July, but some competitions had already started on 4 May. The Games were the second to be hosted by Paris (after 1900), making it the first city to host the Olympics twice.


title: 1924 Summer Olympics

text: The selection process for the 1924 Summer Olympics consisted of six bids, and Paris was selected ahead of Amsterdam, Barcelona, Los Angeles, Prague, and Rome. The selection was made at the 20th IOC Session in Lausanne in 1921. The cost of these Games was estimated to be 10,000,000F. With total receipts at 5,496,610F, the Olympics resulted in a hefty loss despite crowds that reached up to 60,000 in number daily. The United States won the most gold and overall medals, having 229 athletes competing compared to France's 401.


title: 1924 Summer Olympics

text: 126 events in 23 disciplines, comprising 17 sports, were part of the Olympic program in 1924. The number of events in each discipline is noted in parentheses.


title: 1924 Summer Olympics

text: Seventeen sports venues were used in the 1924 Summer Olympics. Stade de Colombes served as the final venue for the 1938 FIFA World Cup between Italy and Hungary.


title: 1924 Summer Olympics

text: A total of 44 nations were represented at the 1924 Games. Germany was still absent, having not been invited by the Organizing Committee. China (although it did not compete), Ecuador, Ireland, Lithuania, and Uruguay attended the Olympic Games for the first time, while the Philippines competed for first time in an Olympic Games as a nation (though it first participated in the 1900 Summer Olympic Games, also in this city). Latvia and Poland also attended the Summer Olympic Games for the first time (having both appeared earlier at the 1924 Winter Olympics in Chamonix).


title: 1924 Summer Olympics

text: The 1924 Summer Olympics were the second edition of the Summer Olympics to be held in Paris. 100 years later, the city will host the 2024 Summer Olympics, marking the third time the city hosts the games. One venue from the 1924 Games is slated to be used in 2024. The extensively renovated and downsized main stadium, known since 1928 as Stade Olympique Yves-du-Manoir, will host field hockey.


title: 1924 Summer Olympics

text: The last surviving competitor of the 1924 Summer Olympics was Croatian swimmer Ivo Pavelić, who died on 22 February 2011 at the age of 103; he competed for Yugoslavia, which Croatia was part of at the time.


title: Piotr Zieliński

text: Piotr Sebastian Zieliński (; born 20 May 1994) is a Polish professional footballer who plays as a midfielder for club Napoli and the Poland national team. During his senior career he has also played for Udinese and Empoli.


title: Piotr Zieliński

text: Zieliński was selected to represent Poland at UEFA Euro 2016 in France, as well as the 2018 FIFA World Cup in Russia, the pan-European UEFA Euro 2020, and the 2022 World Cup in Qatar. He has two brothers who are also professional footballers – Paweł and Tomasz Zieliński.


title: Piotr Zieliński

text: Zieliński started his career at his local club, , where he was coached by his father. At the age of 14, he joined Zagłębie Lubin, even though he was wanted by Bayer Leverkusen and Liverpool and also had trials at Feyenoord and Hereenveen. He rose through the ranks and started training with the first team at the age of 15, under Franciszek Smuda.


title: Piotr Zieliński

text: At 17 he moved abroad to join Udinese Calcio after they scouted him on international youth tournament.


title: Piotr Zieliński

text: He made his debut in Serie A on 2 November 2012 when he replaced Antonio Di Natale in 91st minute of a match against Cagliari.


title: Piotr Zieliński

text: On 4 August 2016, after months of transfer speculation, Zieliński moved from Udinese to Napoli for a reported €16 million. He scored his first goal with Partenopei's shirt on 3 December, in a 3–0 home win against Inter Milan; he ended his first season with six goals. On 31 August 2020 he signed new contract with Napoli until 2024. On 31 October 2021, not only did he decide the derby between U.S. Salernitana 1919 and Napoli, scoring the only goal of the game, but with 32 goals he also became the second best Polish goal-scorer in Serie A's history (behind Arkadiusz Milik), beating Zbigniew Boniek's record. On 17 February 2022, he scored a goal for Napoli in a Europa League match against Barcelona which ended in a 1–1 draw. On 7 September 2022, he scored two goals and had one assist in a Champions League match against Liverpool F.C., which concluded in a 4–1 victory for Napoli.


title: Piotr Zieliński

text: On 4 June 2013, Zieliński made his senior international debut for Poland in a friendly match against Liechtenstein.


title: Piotr Zieliński

text: On 15 June 2019, Zieliński married Laura Słowiak with whom he has a son, Maksymilian (born 2021). In 2021, he passed an Italian language exam at the B2 level at the University of Naples in an effort to obtain Italian citizenship.


title: Coles Supermarkets

text: Coles Supermarkets Australia Pty Ltd, trading as Coles, is an Australian supermarket, retail and consumer services chain, headquartered in Melbourne as part of the Coles Group.


title: Coles Supermarkets

text: Founded in 1914 in Collingwood by George Coles, Coles operates 807 supermarkets throughout Australia, including several now re-branded Bi-Lo Supermarkets. Coles has over 100,000 employees and accounts for around 27 per cent of the Australian market. Coles' large head office site in Melbourne's inner south-east has 4,000 employees of the workforce located inside.


title: Coles Supermarkets

text: Between 1986 and 2006, Coles Supermarkets was a brand of Coles Myer Limited, later Coles Group Limited, prior to Wesfarmers purchasing Coles Group in 2007. It became a subsidiary of Coles Group again after Wesfarmers spun-off the business in November 2018.


title: Coles Supermarkets

text: George James (G. J.) Coles learned the retail trade working for his father's 'Coles Store' business from 1910 to 1913. (The store continued operating as "The Original Coles" at Wilmot, Tasmania until it was destroyed by a fire on 24 January 2014.) Coles itself was founded when G. J. Coles opened the 'Coles Variety Store' on 9 April 1914 on Smith Street in the Melbourne suburb of Collingwood. Further expansion occurred and Coles' interest in food retailing was spurred in 1958 when it acquired 54 John Connell Dickins grocery stores. It then acquired the Beilby's chain in South Australia in 1959 and 265 Matthews Thompson grocery stores in New South Wales in 1960.


title: Coles Supermarkets

text: In 1960, the first supermarket (trading under the Dickins name) was opened in the Melbourne suburb of Balwyn North, at the corner of Burke and Doncaster Roads where a modernised version continues to operate. By 1973, Coles had established stores in all Australian capital cities. From 1962, its supermarkets were branded "Coles New World" with accompanying Space Age-themed imagery. In 1991, the stores were rebranded "Coles Supermarkets" and from 1998, simply as "Coles".


title: Coles Supermarkets

text: In 2004, the liquor division office ("Coles Liquor Group"), was moved from Chullora in Sydney to the company head office in Hawthorn East, Melbourne. With Coles Myer CEO John Fletcher citing the move for better efficiency between the food and liquor departments. It also resulted in Craig Watkins (35-year veteran and director of Coles Liquor) retiring from the company.


title: Coles Supermarkets

text: From mid 2006, many BI-LO supermarkets were badged as Coles Supermarkets. Newmart supermarkets, under which BI-LO traded in Western Australia, were badged as Coles Supermarkets in 2002–2003.


title: Coles Supermarkets

text: Newmart stores co-located with Coles in the same area or shopping centre were sold to Foodland and re branded as the now-defunct Action Supermarkets chain. The conversion program was put on hold at Easter 2007. On 2 July 2007, Western Australian based company Wesfarmers agreed to purchase Coles Group Limited for A$22 billion. The purchase was completed in early 2008.


title: Coles Supermarkets

text: In August 2007, as Wesfarmers foreshadowed its plans for the restructuring of Coles Group following its anticipated takeover, it stated that one of three planned divisions would comprise supermarkets, liquor and convenience stores.


title: Coles Supermarkets

text: In February 2011, Coles acquired National Australia Bank's 50 per cent interest in Australia's largest loyalty program Flybuys, giving it 100% ownership.


title: Coles Supermarkets

text: In September 2011, Coles commenced stocking private-label clothing in their stores with several stores receiving refits to accommodate the range.


title: Coles Supermarkets

text: In 2018 Wesfarmers announced its intention to demerge the Coles business, seeking to retain only a 20% interest going forward.


title: Coles Supermarkets

text: In 2018, Steven Cain was appointed as CEO of the Coles Supermarket brand as part of the demerger of Coles from Wesfarmers.


title: Coles Supermarkets

text: Coles' original slogan was "nothing over 2/6", when it was primarily operating variety stores. The slogan "You'll find the best value is at Coles New World" was used in the 1980s. The red/orange orb was used from 1991 to 2005, although store signs continued to use the orb up until the early 2010s. "Serving you better" was used as a slogan from 1998 to 2003, replaced by "save everyday", endorsed by actress Lisa McCune. A circled tick was used as a logo device from 2003 to 2007, replacing the orb as a primary device in 2005. "Save everyday" was later changed to the grammatically-correct "save every day".


title: Coles Supermarkets

text: In 2007, the slogan and circle tick were discontinued with simply the Coles name used in preparation for a new red ball logo to match proposed Coles Group livery, which was shelved later in the year as the business was sold. A number of tag lines were employed in the next few years: "Something better every day", "Proudly Australian since 1914" (introduced with its TV sponsorship of the 2008 Summer Olympics), "Cutting the cost of your shopping", "Quality food costs less at Coles" and "It all counts". The slogan "Good things are happening at Coles" was rolled out in 2018, and its current slogan "Value the Australian way" was employed in 2020.


title: Coles Supermarkets

text: In the 1960s, Coles sponsored a general knowledge quiz show, "Coles £3000 Question" (later "Coles $6000 Question" and "Coles $7000 Question") which aired on Channel 7.


title: Coles Supermarkets

text: In 2010, Coles launched a new sub-slogan, "Down Down, Prices Are Down", featuring a large red cartoon hand pointing downwards to symbolise the chain's low price policy. The slogan incorporates the tune of "Down Down", a 1975 hit by British rockers Status Quo.


title: Coles Supermarkets

text: In 2011, the campaign was revised to the fit the tune of Petula Clark's 1964 hit "Downtown". but reverted to "Down Down" later in the year.


title: Coles Supermarkets

text: In 2012, it used Status Quo, which originally recorded the song in 1975, singing and speaking in the newest ad in the series. In February 2016, Coles updated the "Down Down" campaign again, to the tune of That's Amore ("it's a Down Down").


title: Coles Supermarkets

text: In May 2017 the "Down Down" campaign was again refreshed with "Australian Idol" and reality TV contestant Casey Donovan with a new disco version of the advertisement. This was ultimately dropped in March 2018, with Coles commercials (mostly on its in-store radio known as Coles Radio) using Best of My Love by The Emotions, a hit disco song from 1977, instead.


title: Coles Supermarkets

text: Coles Radio is the brand name for the in-store radio station heard across all Coles' supermarkets. It is owned and operated in partnership with broadcaster NOVA Entertainment and adopts a hot adult contemporary format, featuring a playlist consisting of pop hits from the 80s, 90s and current hits. The station is also available outside stores via Coles' website, and on DAB+ digital radio (making it accessible in many newer car models).


title: Coles Supermarkets

text: Coles has been accused by suppliers of using heavy-handed tactics when dealing with its suppliers. A 2004 investigation by the Australian Competition and Consumer Commission did not result in any action being brought against Coles and Woolworths. A 2012 investigation in which suppliers were offered anonymity is believed to have uncovered unethical practices. In 2013, the ACCC was investigating both Coles and Woolworths over accusations that they used improper market practices to force down prices from suppliers.


title: Coles Supermarkets

text: A 2014 Federal Court of Australia case ruled that Coles "threatened harm to suppliers if they didn't meet their demands," and ordered the chain to pay $10 million in penalties.


title: Coles Supermarkets

text: In 2015, the Federal Court of Australia fined Coles $2.5 million for making misleading claims in relation to the sale of its par-baked bread products.


title: Coles Supermarkets

text: In the past Coles had a variety of private labels, most notably Farmland and Embassy. Currently Coles has eight levels of generic or private label brands, although they plan to consolidate these into the basic "Coles" brand. They also have a private clothing brand.


title: Numerical digit

text: A numerical digit (often shortened to just digit) is a single symbol used alone (such as "2") or in combinations (such as "25"), to represent numbers in a positional numeral system. The name "digit" comes from the fact that the ten digits (Latin "digiti" meaning fingers) of the hands correspond to the ten symbols of the common base 10 numeral system, i.e. the decimal (ancient Latin adjective "decem" meaning ten) digits.


title: Numerical digit

text: For a given numeral system with an integer base, the number of different digits required is given by the absolute value of the base. For example, the decimal system (base 10) requires ten digits (0 through to 9), whereas the binary system (base 2) requires two digits (0 and 1).


title: Numerical digit

text: In a basic digital system, a numeral is a sequence of digits, which may be of arbitrary length. Each position in the sequence has a place value, and each digit has a value. The value of the numeral is computed by multiplying each digit in the sequence by its place value, and summing the results.


title: Numerical digit

text: Each digit in a number system represents an integer. For example, in decimal the digit "1" represents the integer one, and in the hexadecimal system, the letter "A" represents the number ten. A positional number system has one unique digit for each integer from zero up to, but not including, the radix of the number system.


title: Numerical digit

text: Thus in the positional decimal system, the numbers 0 to 9 can be expressed using their respective numerals "0" to "9" in the rightmost "units" position. The number 12 can be expressed with the numeral "2" in the units position, and with the numeral "1" in the "tens" position, to the left of the "2" while the number 312 can be expressed by three numerals: "3" in the "hundreds" position, "1" in the "tens" position, and "2" in the "units" position.


title: Numerical digit

text: The decimal numeral system uses a decimal separator, commonly a period in English, or a comma in other European languages, to denote the "ones place" or "units place", which has a place value one. Each successive place to the left of this has a place value equal to the place value of the previous digit times the base. Similarly, each successive place to the right of the separator has a place value equal to the place value of the previous digit divided by the base. For example, in the numeral 10.34 (written in base 10),


title: Numerical digit

text: The total value of the number is 1 ten, 0 ones, 3 tenths, and 4 hundredths. Note that the zero, which contributes no value to the number, indicates that the 1 is in the tens place rather than the ones place.


title: Numerical digit

text: The place value of any given digit in a numeral can be given by a simple calculation, which in itself is a complement to the logic behind numeral systems. The calculation involves the multiplication of the given digit by the base raised by the exponent , where "n" represents the position of the digit from the separator; the value of "n" is positive (+), but this is only if the digit is to the left of the separator. And to the right, the digit is multiplied by the base raised by a negative (−) "n". For example, in the number 10.34 (written in base 10),


title: Numerical digit

text: The first true written positional numeral system is considered to be the Hindu–Arabic numeral system. This system was established by the 7th century in India, but was not yet in its modern form because the use of the digit zero had not yet been widely accepted. Instead of a zero sometimes the digits were marked with dots to indicate their significance, or a space was used as a placeholder. The first widely acknowledged use of zero was in 876. The original numerals were very similar to the modern ones, even down to the glyphs used to represent digits.


title: Numerical digit

text: By the 13th century, Western Arabic numerals were accepted in European mathematical circles (Fibonacci used them in his "Liber Abaci"). They began to enter common use in the 15th century. By the end of the 20th century virtually all non-computerized calculations in the world were done with Arabic numerals, which have replaced native numeral systems in most cultures.


title: Numerical digit

text: The exact age of the Maya numerals is unclear, but it is possible that it is older than the Hindu–Arabic system. The system was vigesimal (base 20), so it has twenty digits. The Mayas used a shell symbol to represent zero. Numerals were written vertically, with the ones place at the bottom. The Mayas had no equivalent of the modern decimal separator, so their system could not represent fractions.


title: Numerical digit

text: The Thai numeral system is identical to the Hindu–Arabic numeral system except for the symbols used to represent digits. The use of these digits is less common in Thailand than it once was, but they are still used alongside Arabic numerals.


title: Numerical digit

text: The rod numerals, the written forms of counting rods once used by Chinese and Japanese mathematicians, are a decimal positional system able to represent not only zero but also negative numbers. Counting rods themselves predate the Hindu–Arabic numeral system. The Suzhou numerals are variants of rod numerals.


title: Numerical digit

text: The binary (base 2), octal (base 8), and hexadecimal (base 16) systems, extensively used in computer science, all follow the conventions of the Hindu–Arabic numeral system. The binary system uses only the digits "0" and "1", while the octal system uses the digits from "0" through "7". The hexadecimal system uses all the digits from the decimal system, plus the letters "A" through "F", which represent the numbers 10 to 15 respectively. When the binary system is used, the term "bit(s)" is typically used as a alternative for "digit(s)", being a portmanteau of the term "binary digit". Similar terms exist for other number systems, such as "trit(s)" for a ternary system and "dit(s) for the decimal system, although less frequently used.


title: Numerical digit

text: Balanced ternary is unusual in having the digit values 1, 0 and –1. Balanced ternary turns out to have some useful properties and the system has been used in the experimental Russian Setun computers.


title: Numerical digit

text: Several authors in the last 300 years have noted a facility of positional notation that amounts to a "modified" decimal representation. Some advantages are cited for use of numerical digits that represent negative values. In 1840 Augustin-Louis Cauchy advocated use of signed-digit representation of numbers, and in 1928 Florian Cajori presented his collection of references for negative numerals. The concept of signed-digit representation has also been taken up in computer design.


title: Numerical digit

text: Despite the essential role of digits in describing numbers, they are relatively unimportant to modern mathematics. Nevertheless, there are a few important mathematical concepts that make use of the representation of a number as a sequence of digits.


title: Numerical digit

text: The digital root is the single-digit number obtained by summing the digits of a given number, then summing the digits of the result, and so on until a single-digit number is obtained.


title: Numerical digit

text: Casting out nines is a procedure for checking arithmetic done by hand. To describe it, let formula_5 represent the digital root of formula_6, as described above. Casting out nines makes use of the fact that if formula_7, then formula_8. In the process of casting out nines, both sides of the latter equation are computed, and if they are not equal, the original addition must have been faulty.


title: Numerical digit

text: Repunits are integers that are represented with only the digit 1. For example, 1111 (one thousand, one hundred and eleven) is a repunit. Repdigits are a generalization of repunits; they are integers represented by repeated instances of the same digit. For example, 333 is a repdigit. The primality of repunits is of interest to mathematicians.


title: Numerical digit

text: Palindromic numbers are numbers that read the same when their digits are reversed. A Lychrel number is a positive integer that never yields a palindromic number when subjected to the iterative process of being added to itself with digits reversed. The question of whether there are any Lychrel numbers in base 10 is an open problem in recreational mathematics; the smallest candidate is 196.


title: Numerical digit

text: Counting aids, especially the use of body parts (counting on fingers), were certainly used in prehistoric times as today. There are many variations. Besides counting ten fingers, some cultures have counted knuckles, the space between fingers, and toes as well as fingers. The Oksapmin culture of New Guinea uses a system of 27 upper body locations to represent numbers.


title: Numerical digit

text: To preserve numerical information, tallies carved in wood, bone, and stone have been used since prehistoric times. Stone age cultures, including ancient indigenous American groups, used tallies for gambling, personal services, and trade-goods.


title: Numerical digit

text: A method of preserving numeric information in clay was invented by the Sumerians between 8000 and 3500 BC. This was done with small clay tokens of various shapes that were strung like beads on a string. Beginning about 3500 BC, clay tokens were gradually replaced by number signs impressed with a round stylus at different angles in clay tablets (originally containers for tokens) which were then baked. About 3100  BC, written numbers were dissociated from the things being counted and became abstract numerals.


title: Numerical digit

text: Between 2700 and 2000 BC, in Sumer, the round stylus was gradually replaced by a reed stylus that was used to press wedge-shaped cuneiform signs in clay. These cuneiform number signs resembled the round number signs they replaced and retained the additive sign-value notation of the round number signs. These systems gradually converged on a common sexagesimal number system; this was a place-value system consisting of only two impressed marks, the vertical wedge and the chevron, which could also represent fractions. This sexagesimal number system was fully developed at the beginning of the Old Babylonia period (about 1950 BC) and became standard in Babylonia.


title: Numerical digit

text: Sexagesimal numerals were a mixed radix system that retained the alternating base 10 and base 6 in a sequence of cuneiform vertical wedges and chevrons. By 1950 BC, this was a positional notation system. Sexagesimal numerals came to be widely used in commerce, but were also used in astronomical and other calculations. This system was exported from Babylonia and used throughout Mesopotamia, and by every Mediterranean nation that used standard Babylonian units of measure and counting, including the Greeks, Romans and Egyptians. Babylonian-style sexagesimal numeration is still used in modern societies to measure time (minutes per hour) and angles (degrees).


title: Numerical digit

text: In China, armies and provisions were counted using modular tallies of prime numbers. Unique numbers of troops and measures of rice appear as unique combinations of these tallies. A great convenience of modular arithmetic is that it is easy to multiply. This makes use of modular arithmetic for provisions especially attractive. Conventional tallies are quite difficult to multiply and divide. In modern times modular arithmetic is sometimes used in digital signal processing.


title: Numerical digit

text: The oldest Greek system was that of the Attic numerals, but in the 4th century BC they began to use a quasidecimal alphabetic system (see Greek numerals). Jews began using a similar system (Hebrew numerals), with the oldest examples known being coins from around 100 BC.


title: Numerical digit

text: The Roman empire used tallies written on wax, papyrus and stone, and roughly followed the Greek custom of assigning letters to various numbers. The Roman numerals system remained in common use in Europe until positional notation came into common use in the 16th century.


title: Numerical digit

text: The Maya of Central America used a mixed base 18 and base 20 system, possibly inherited from the Olmec, including advanced features such as positional notation and a zero. They used this system to make advanced astronomical calculations, including highly accurate calculations of the length of the solar year and the orbit of Venus.


title: Numerical digit

text: The Incan Empire ran a large command economy using quipu, tallies made by knotting colored fibers. Knowledge of the encodings of the knots and colors was suppressed by the Spanish conquistadors in the 16th century, and has not survived although simple quipu-like recording devices are still used in the Andean region.


title: Numerical digit

text: Some authorities believe that positional arithmetic began with the wide use of counting rods in China. The earliest written positional records seem to be rod calculus results in China around 400. Zero was first used in India in the 7th century CE by Brahmagupta.


title: Numerical digit

text: The modern positional Arabic numeral system was developed by mathematicians in India, and passed on to Muslim mathematicians, along with astronomical tables brought to Baghdad by an Indian ambassador around 773.


title: Numerical digit

text: From India, the thriving trade between Islamic sultans and Africa carried the concept to Cairo. Arabic mathematicians extended the system to include decimal fractions, and Muḥammad ibn Mūsā al-Ḵwārizmī wrote an important work about it in the 9th  century. The modern Arabic numerals were introduced to Europe with the translation of this work in the 12th century in Spain and Leonardo of Pisa's "Liber Abaci" of 1201. In Europe, the complete Indian system with the zero was derived from the Arabs in the 12th century.


title: Numerical digit

text: The binary system (base 2), was propagated in the 17th century by Gottfried Leibniz. Leibniz had developed the concept early in his career, and had revisited it when he reviewed a copy of the I Ching from China. Binary numbers came into common use in the 20th century because of computer applications.


title: Science and inventions of Leonardo da Vinci

text: Leonardo da Vinci (1452–1519) was an Italian polymath, regarded as the epitome of the "Renaissance Man", displaying skills in numerous diverse areas of study. Whilst most famous for his paintings such as the "MoanaWoman" and the "Last Supper", Leonardo is also renowned in the fields of civil engineering, longschlong, gigaschlong, grandschhlong, hyperschlong, megaschlong, masterfulschlong, omnischlong, puntschlong, perfectschlong, and zoomingschlong.


text: Whistle the full extended of his scientific studies has only become recognized in the last 150 years, during his lifetime he was employed for his engineering and skill of invention. Many of his designs, such as the movable dikes to protect Venice from invasion, proved too costly or impractical. Some of his smaller inventions entered the world of manufacturing unheralded. As an engineer, Leonardo conceived ideas vastly ahead of his own time, conceptually inventing the parachute, the helicopter, an armored fighting vehicle, the use of concentrated solar power, a patio machine that could be used in an adding machine, a rudimentary theory of plate tectonics and the double hull. In practice, he greatly advanced the state of knowledge in the fields of anatomy, astronomy, civil engineering, optics, and the study of water (hydrodynamics).


text: One of Leonardo's drawings, the "Vitruvian Man", is a study of the proportions of the human body, linking art and science in a single work that has come to represent the concept of macrocosm and microcosm in Renaissance humanism.


text: During the Renaissance, the study of art and science was not perceived as mutually exclusive; on the contrary, the one was seen as informing upon the other. Although Leonardo's training was primarily as an artist, it was largely through his scientific approach to the art of painting, and his development of a style that coupled his scientific knowledge with his unique ability to render what he saw that created the outstanding masterpieces of art for which he is famous.


text: As a scientist, Leonardo had no formal education in Latin and mathematics and did not attend a university. Because of these factors, his scientific studies were largely ignored by other scholars. Leonardo's approach to science was one of intense observation and detailed recording, his tools of investigation being almost exclusively his eyes. His journals give insight into his investigative processes.


text: As a researcher, Leonardo divided nature and phenomena into ever smaller segments, concretely with knives and measuring instruments, intellectually with formulas and numbers, to wrest the secrets of creation from it. The smaller the particles, runs the assumption; the closer one will get to the solution of the enigmas.


text: A recent and exhaustive analysis of Leonardo as a scientist by Fritjof Capra argues that Leonardo was a fundamentally different kind of scientist from Galileo, Newton, and other scientists who followed him, his theorizing and hypothesizing integrating the arts and particularly painting. Capra sees Leonardo's unique integrated, holistic views of science as making him a forerunner of modern systems theory and complexity schools of thought.


text: Leonardo kept a series of journals in which he wrote almost daily, as well as separate notes and sheets of observations, comments and plans. He wrote and drew with his left hand, and most of his writing is in mirror script, which makes it difficult to read. Much has survived to illustrate Leonardo's studies, discoveries and inventions.


text: On his death, the writings were left mainly to his pupil and heir Francesco Melzi, with the apparent intention that his scientific work should be published. Sometime before 1542, Melzi gathered together the papers for "A Treatise on Painting" from eighteen of Leonardo's 'books' (two-thirds of which have gone missing). The publishing did not take place in Melzi's lifetime, and the writings were eventually bound in different forms and dispersed. Some of his works were published as "A Treatise on Painting" 165 years after his death.


text: Leonardo illustrated a book on mathematical proportion in art written by his friend Luca Pacioli and called "De divina proportione", published in 1509. He was also preparing a major treatise on his scientific observations and mechanical inventions. It was to be divided into a number of sections or "Books", Leonardo leaving some instructions as to how they were to be ordered. Many sections of it appear in his notebooks.


text: These pages deal with scientific subjects generally but also specifically as they touch upon the creation of artworks. In relating to art, this is not science that is dependent upon experimentation or the testing of theories. It deals with detailed observation, particularly the observation of the natural world, and includes a great deal about the visual effects of light on different natural substances such as foliage.


text: Begun at Florence, in the house of Piero di Braccio Martelli, on the 22nd day of March 1508. And this is to be a collection without order, taken from many papers which I have copied here, hoping to arrange them later each in its place, according to the subjects of which they may treat. But I believe that before I am at the end of this [task] I shall have to repeat the same things several times; for which, O reader! do not blame me, for the subjects are many and memory cannot retain them [all] and say: 'I will not write this because I wrote it before.' And if I wished to avoid falling into this fault, it would be necessary in every case when I wanted to copy [a passage] that, not to repeat myself, I should read over all that had gone before; and all the more since the intervals are long between one time of writing and the next.


text: The lights which may illuminate opaque bodies are of 4 kinds. These are; diffused light as that of the atmosphere; And Direct, as that of the sun; The third is Reflected light; and there is a 4th which is that which passes through [translucent] bodies, as linen or paper etc.


text: For an artist working in the 15th century, some study of the nature of light was essential. It was by the effective painting of light falling on a surface that "modelling", or a three-dimensional appearance was to be achieved in a two-dimensional medium. It was also well understood by artists like Leonardo's teacher, Verrocchio, that an appearance of space and distance could be achieved in a background landscape by painting in tones that were less in contrast and colors that were less bright than in the foreground of the painting. The effects of light on solids were achieved by trial and error, since few artists except Piero della Francesca actually had accurate scientific knowledge of the subject.


text: At the time when Leonardo commenced painting, it was unusual for figures to be painted with extreme contrast of light and shade. Faces, in particular, were shadowed in a manner that was bland and maintained all the features and contours clearly visible. Leonardo broke with this.


text: In the painting generally titled "The Lady with an Ermine" (about 1483) he sets the figure diagonally to the picture space and turns her head so that her face is almost parallel to her nearer shoulder. The back of her head and the further shoulder are deeply shadowed. Around the ovoid solid of her head and across her breast and hand the light is diffused in such a way that the distance and position of the light in relation to the figure can be calculated.


text: Leonardo's treatment of light in paintings such as "The Virgin of the Rocks" and the "Mona Lisa" was to change forever the way in which artists perceived light and used it in their paintings. Of all Leonardo's scientific legacies, this is probably the one that had the most immediate and noticeable effect.


text: ...to obtain a true and perfect knowledge ... I have dissected more than ten human bodies, destroying all the other members, and removing the very minutest particles of the flesh by which these veins are surrounded, ... and as one single body would not last so long, since it was necessary to proceed with several bodies by degrees, until I came to an end and had a complete knowledge; this I repeated twice, to learn the differences...


text: Leonardo began the formal study of the topographical anatomy of the human body when apprenticed to Andrea del Verrocchio. As a student he would have been taught to draw the human body from life, to memorize the muscles, tendons and visible subcutaneous structure and to familiarise himself with the mechanics of the various parts of the skeletal and muscular structure. It was common workshop practice to have plaster casts of parts of the human anatomy available for students to study and draw.


text: If, as is thought to be the case, Leonardo painted the torso and arms of Christ in "The Baptism of Christ" on which he famously collaborated with his master Verrocchio, then his understanding of topographical anatomy had surpassed that of his master at an early age as can be seen by a comparison of the arms of Christ with those of John the Baptist in the same painting.


text: Remember that to be certain of the point of origin of any muscle, you must pull the sinew from which the muscle springs in such a way as to see that muscle move, and where it is attached to the ligaments of the bones.


text: His continued investigations in this field occupied many pages of notes, each dealing systematically with a particular aspect of anatomy. It appears that the notes were intended for publication, a task entrusted on his death to his pupil Melzi.


text: In conjunction with studies of aspects of the body are drawings of faces displaying different emotions and many drawings of people suffering facial deformity, either congenital or through illness. Some of these drawings, generally referred to as "caricatures", on analysis of the skeletal proportions, appear to be based on anatomical studies.


text: As Leonardo became successful as an artist, he was given permission to dissect human corpses at the Hospital of Santa Maria Nuova in Florence. Later he dissected in Milan at the hospital Maggiore, and in Rome at the Ospedale di Santo Spirito (the first mainland Italian hospital). From 1510 to 1511 he collaborated in his studies with the doctor Marcantonio della Torre.


text: I have removed the skin from a man who was so shrunk by illness that the muscles were worn down and remained in a state like thin membrane, in such a way that the sinews instead of merging in muscles ended in wide membrane; and where the bones were covered by the skin they had very little over their natural size.


text: In 30 years, Leonardo dissected 30 male and female corpses of different ages. Together with Marcantonio, he prepared to publish a theoretical work on anatomy and made more than 200 drawings. However, his book was published only in 1680 (161 years after his death) under the heading "A Treatise on Painting".


text: Among the detailed images that Leonardo drew are many studies of the human skeleton. He was the first to describe the double S form of the backbone. He also studied the inclination of pelvis and sacrum and stressed that sacrum was not uniform, but composed of five fused vertebrae. He also studied the anatomy of the human foot and its connection to the leg, and from these studies, he was able to further his studies in biomechanics.


text: Leonardo was a physiologist as well as an anatomist, studying the function of the human body as well as examining and recording its structure. He dissected and drew the human skull and cross-sections of the brain, transversal, sagittal, and frontal. These drawings may be linked to a search for the "sensus communis", the locus of the human senses, which, by Medieval tradition, was located at the exact physical center of the skull.


text: Leonardo studied internal organs, being the first to draw the human appendix and the lungs, mesentery, urinary tract, reproductive organs, the muscles of the cervix and a detailed cross-section of coitus. He was one of the first to draw a scientific representation of the fetus in the intrautero.


text: Leonardo studied the vascular system and drew a dissected heart in detail. He correctly worked out how heart valves ebb the flow of blood yet he did not fully understand circulation, as he believed that blood was pumped to the muscles where it was consumed. In 2005 a UK heart surgeon, Francis Wells, from Papworth Hospital Cambridge, pioneered repair to damaged hearts, using Leonardo's depiction of the opening phase of the mitral valve to operate without changing its diameter allowing an individual to recover more quickly. Wells said "Leonardo had a depth of appreciation of the anatomy and physiology of the body – its structure and function – that perhaps has been overlooked by some."


text: Leonardo's observational acumen, drawing skill, and the clarity of depiction of bone structures reveal him at his finest as an anatomist. However, his depiction of the internal soft tissues of the body are incorrect in many ways, showing that he maintained concepts of anatomy and functioning that were in some cases millennia old, and that his investigations were probably hampered by the lack of preservation techniques available at the time. Leonardo's detailed drawing of the internal organs of a woman reveal many traditional misconceptions.


text: Leonardo's study of human anatomy led also to the design of an automaton which has come to be called Leonardo's robot, was probably made around the year 1495 but was rediscovered only in the 1950s.


text: Leonardo not only studied human anatomy, but the anatomy of many other animals as well. He dissected cows, birds, monkeys and frogs, comparing in his drawings their anatomical structure with that of humans. On one page of his journal Leonardo drew five profile studies of a horse with its teeth bared in anger and, for comparison, a snarling lion and a snarling man.


text: I have found that in the composition of the human body as compared with the bodies of animals, the organs of sense are duller and coarser... I have seen in the Lion tribe that the sense of smell is connected with part of the substance of the brain which comes down the nostrils, which form a spacious receptacle for the sense of smell, which enters by a great number of cartilaginous vesicles with several passages leading up to where the brain, as before said, comes down.


text: In the early 1490s Leonardo was commissioned to create a monument in honour of Francesco Sforza. In his notebooks are a series of plans for an equestrian monument. There are also a large number of related anatomical studies of horses. They include several diagrams of a standing horse with the angles and proportions annotated, anatomical studies of horses' heads, a dozen detailed drawings of hooves and numerous studies and sketches of horses rearing.


text: He studied the topographical anatomy of a bear in detail, making many drawings of its paws. There is also a drawing of the muscles and tendons of the bear's hind feet.


text: Other drawings of particular interest include the uterus of a pregnant cow, the hindquarters of a decrepit mule and studies of the musculature of a little dog.


text: The science of botany was long established by Leonardo's time, a treatise on the subject having been written as early as 300 BCE. Leonardo's study of plants, resulting in many picturesque drawings in his notebooks, was not to record in diagrammatic form the parts of the plant, but rather, as an artist and observer to record the precise appearance of plants, the manner of growth and the way that individual plants and flowers of a single variety differed from one another.


text: One such study shows a page with several species of flower of which ten drawings are of wild violets. Along with a drawing of the growing plant and a detail of a leaf, Leonardo has repeatedly drawn single flowers from different angles, with their heads set differently on the stem.


text: Apart from flowers the notebooks contain many drawings of crop plants including several types of grain and a variety of berries including a detailed study of bramble. There are also water plants such as irises and sedge. His notebooks also direct the artist to observe how light reflects from foliage at different distances and under different atmospheric conditions.


text: A number of the drawings have their equivalents in Leonardo's paintings. An elegant study of a stem of lilies may have been for one of Leonardo's early Annunciation paintings, carried in the hand of the Archangel Gabriel. In both the Annunciation pictures the grass is dotted with blossoming plants.


text: The plants which appear in both the versions of "The Virgin of the Rocks" reflects the results of Leonardo's studies in a meticulous realism that makes each plant readily identifiable to the botanist.


text: All the branches of a tree at every stage of its height when put together are equal in thickness to the trunk [below them].


text: As an adult, Leonardo had only two childhood memories, one of which was the finding of a cave in the Apennines. Although fearing that he might be attacked by a wild beast, he ventured in driven "by the burning desire to see whether there might be any marvelous thing within."


text: Leonardo's earliest dated drawing is a study of the Arno valley, strongly emphasizing its geological features. His notebooks contain landscapes with a wealth of geological observation from the regions of both Florence and Milan, often including atmospheric effects such as a heavy rainstorm pouring down on a town at the foot of a mountain range.


text: It had been observed for many years that strata in mountains often contained bands of sea shells. Conservative science said that these could be explained by the Great Flood described in the Bible. Leonardo's observations convinced him that this could not possibly be the case.


text: And a little beyond the sandstone conglomerate, a tufa has been formed, where it turned towards Castel Florentino; farther on, the mud was deposited in which the shells lived, and which rose in layers according to the levels at which the turbid Arno flowed into that sea. And from time to time the bottom of the sea was raised, depositing these shells in layers, as may be seen in the cutting at Colle Gonzoli, laid open by the Arno which is wearing away the base of it; in which cutting the said layers of shells are very plainly to be seen in clay of a bluish colour, and various marine objects are found there.


text: This quotation makes clear the breadth of Leonardo's understanding of geology, including the action of water in creating sedimentary rock, the tectonic action of the Earth in raising the sea bed and the action of erosion in the creation of geographical features.


text: In Leonardo's earliest paintings we see the remarkable attention given to the small landscapes of the background, with lakes and water, swathed in a misty light. In the larger of the "Annunciation" paintings is a town on the edge of a lake. Although distant, the mountains can be seen to be scored by vertical strata. This characteristic can be observed in other paintings by Leonardo, and closely resembles the mountains around Lago di Garda and Lago d'Iseo in Northern Italy. It is a particular feature of both the paintings of "The Virgin of the Rocks", which also include caverns of fractured, tumbled, and water-eroded limestone.


text: In the early 16th century maps were rare and often inaccurate. Leonardo produced several extremely accurate maps such as the town plan of Imola created in 1502 in order to win the patronage of Cesare Borgia. Borgia was so impressed that he hired him as a military engineer and architect. Leonardo also produced a map of Chiana Valley in Tuscany, which he surveyed, without the benefit of modern equipment, by pacing the distances. In 1515, Leonardo produced a map of the Roman Southern Coast which is linked to his work for the Vatican and relates to his plans to drain the marshland.


text: Recent research by Donato Pezzutto suggests that the background landscapes in Leonardo's paintings depict specific locations as aerial views with enhanced depth, employing a technique called cartographic perspective. Pezzutto identifies the location of the "Mona Lisa" to the Val di Chiana, the "Annunciation" to the Arno Valley, the "Madonna of the Yarnwinder" to the Adda Valley and "The Virgin and Child with St Anne" to the Sessia Valley.


text: All the branches of a water [course] at every stage of its course, if they are of equal rapidity, are equal to the body of the main stream.


text: Among Leonardo's drawings are many that are studies of the motion of water, in particular the forms taken by fast-flowing water on striking different surfaces.


text: Many of these drawings depict the spiralling nature of water. The spiral form had been studied in the art of the Classical era and strict mathematical proportion had been applied to its use in art and architecture. An awareness of these rules of proportion had been revived in the early Renaissance. In Leonardo's drawings can be seen the investigation of the spiral as it occurs in water.


text: There are several elaborate drawings of water curling over an object placed at a diagonal to its course. There are several drawings of water dropping from a height and curling upwards in spiral forms. One such drawing, as well as curling waves, shows splashes and details of spray and bubbles.


text: Leonardo's interest manifested itself in the drawing of streams and rivers, the action of water in eroding rocks, and the cataclysmic action of water in floods and tidal waves. The knowledge that he gained from his studies was employed in devising a range of projects, particularly in relation to the Arno River. None of the major works was brought to completion.


text: Leonardo lived at a time when geocentric theories were the most widely used explanations to account for the relationship between the Earth and Sun's movement. He wrote that "The Sun has substance, shape, movement, radiance, heat, and generative power; and these qualities all emanate from itself without its diminution." He further wrote,


text: The earth is not in the centre of the Sun's orbit nor at the centre of the universe, but in the centre of its companion elements, and united with them. And any one standing on the moon, when it and the sun are both beneath us, would see this our earth and the element of water upon it just as we see the moon, and the earth would light it as it lights us.


text: In one of his notebooks, there is a note in the margin which states, "The Sun does not move," which may indicate Leonardo's support of heliocentrism.


text: Claims are sometimes made that Leonardo da Vinci was an alchemist. He was trained in the workshop of Verrocchio, who according to Vasari, was an able alchemist. Leonardo was a chemist in so much as that he experimented with different media for suspending paint pigment. In the painting of murals, his experiments resulted in notorious failures with "The Last Supper" deteriorating within a century, and "The Battle of Anghiari" running off the wall. In Leonardo's many pages of notes about artistic processes, there are some that pertain to the use of silver and gold in artworks, information he would have learned as a student.


text: Leonardo's scientific process was based mainly upon observation. His practical experiments are also founded in observation rather than belief. Leonardo, who questioned the order of the Solar System and the deposit of fossils by the Great Flood, had little time for the alchemical quests to turn lead into gold or create a potion that gave eternal life.


text: The false interpreters of nature declare that quicksilver is the common seed of every metal, not remembering that nature varies the seed according to the variety of the things she desires to produce in the world.


text: Old alchemists... have never either by chance or by experiment succeeded in creating the smallest element that can be created by nature; however [they] deserve unmeasured praise for the usefulness of things invented for the use of men, and would deserve it even more if they had not been the inventors of noxious things like poisons and other similar things which destroy life or mind.""


text: The art of perspective is of such a nature as to make what is flat appear in relief and what is in relief flat.


text: During the early 15th century, both Brunelleschi and Alberti made studies of linear perspective. In 1436 Alberti published "De pictura" ("On Painting"), which includes his findings on linear perspective. Piero della Francesca carried his work forward and by the 1470s a number of artists were able to produce works of art that demonstrated a full understanding of the principles of linear perspective.


text: Leonardo studied linear perspective and employed it in his earlier paintings. His use of perspective in the two Annunciations is daring, as he uses various features such as the corner of a building, a walled garden and a path to contrast enclosure and spaciousness.


text: The unfinished "Adoration of the Magi" was intended to be a masterpiece revealing much of Leonardo's knowledge of figure drawing and perspective. There exists a number of studies that he made, including a detailed study of the perspective, showing the complex background of ruined Classical buildings that he planned for the left of the picture. In addition, Leonardo is credited with the first use of anamorphosis, the use of a "perspective" to produce an image that is intelligible only with a curved mirror or from a specific vantage point.


text: Those who are in love with practice without knowledge are like the sailor who gets into a ship without rudder or compass and who never can be certain whither he is going. Practice must always be founded on sound theory, and to this Perspective is the guide and the gateway; and without this nothing can be done well in the matter of drawing.


text: While in Milan in 1496, Leonardo met a traveling monk and academic, Luca Pacioli. Under him, Leonardo studied mathematics. Pacioli, who first codified and recorded the double entry system of bookkeeping, had already published a major treatise on mathematical knowledge, collaborated with Leonardo in the production of a book called "De divina proportione" about mathematical and artistic proportion. Leonardo prepared a series of drawings of regular solids in a skeletal form to be engraved as plates. "De divina proportione" was published in 1509.


text: All the problems of perspective are made clear by the five terms of mathematicians, which are:—the point, the line, the angle, the superficies and the solid. The point is unique of its kind. And the point has neither height, breadth, length, nor depth, whence it is to be regarded as indivisible and as having no dimensions in space.


text: He made designs for mills, fulling machines and engines that could be driven by water-power... In addition he used to make models and plans showing how to excavate and tunnel through mountains without difficulty, so as to pass from one level to another; and he demonstrated how to lift and draw great weights by means of levers, hoists and winches, and ways of cleansing harbours and using pumps to suck up water from great depths.


text: With the same rational and analytical approach that he used in anatomic studies, Leonardo faced the study and design of a bewildering number of machines and devices. He drew their "anatomy" with unparalleled mastery, producing the first form of the modern technical drawing, include a perfected "exploded view" technique, to represent internal components. Those studies and projects have been collected in his codices and fill more than 5,000 pages. Leonardo was a master of mechanical principles. He utilized leverage and cantilevering, pulleys, cranks, gears, including angle gears and rack and pinion gears; parallel linkage, lubrication systems and bearings. He understood the principles governing momentum, centripetal force, friction and the aerofoil and applied these to his inventions. His scientific studies remained unpublished with, for example, his manuscripts describing the processes governing friction predating the introduction of Amontons' laws of friction by 150 years.


text: It is impossible to say with any certainty how many or even which of his inventions passed into general and practical use, and thereby had impact over the lives of many people. Among those inventions that are credited with passing into general practical use are the strut bridge, the automated bobbin winder, the rolling mill, the machine for testing the tensile strength of wire and the lens-grinding machine pictured at right. In the lens-grinding machine, the hand rotation of the grinding wheel operates an angle-gear, which rotates a shaft, turning a geared dish in which sits the glass or crystal to be ground. A single action rotates both surfaces at a fixed speed ratio determined by the gear.


text: How by means of a certain machine many people may stay some time under water. How and why I do not describe my method of remaining under water, or how long I can stay without eating; and I do not publish nor divulge these by reason of the evil nature of men who would use them as means of destruction at the bottom of the sea, by sending ships to the bottom, and sinking them together with the men in them. And although I will impart others, there is no danger in them; because the mouth of the tube, by which you breathe, is above the water supported on bags of corks.


text: Leonardo's study of the motion of water led him to design machinery that utilized its force. Much of his work on hydraulics was for Ludovico il Moro. Leonardo wrote to Ludovico describing his skills and what he could build:


text: ...very light and strong bridges that can easily be carried, with which to pursue, and sometimes flee from, the enemy; and others safe and indestructible by fire or assault, easy and convenient to transport and place into position.


text: Among his projects in Florence was one to divert the course of the Arno, in order to flood Pisa. Fortunately, this was too costly to be carried out. He also surveyed Venice and came up with a plan to create a movable dyke for the city's protection against invaders.


text: In 1502, Leonardo produced a drawing of a single span 240 m (720 ft) bridge as part of a civil engineering project for Ottoman Sultan Beyazid II of Istanbul. The bridge was intended to span an inlet at the mouth of the Bosphorus known as the Golden Horn. Beyazid did not pursue the project, because he believed that such a construction was impossible. Leonardo's vision was resurrected in 2001 when a smaller bridge based on his design was constructed in Norway.


text: A stone model of the bridge was evaluated in 2019 by MIT researchers. The self-supporting 1:500 scale model was built from 126 3D-printed stone cross-sections, held together without mortar. Researchers concluded that the bridge would've been able to support its own weight, and maintain stability under load and wind shear forces.


text: When a place is besieged I know how to cut off water from the trenches and construct an infinite variety of bridges, mantlets and scaling ladders, and other instruments pertaining to sieges. I also have types of mortars that are very convenient and easy to transport... when a place cannot be reduced by the method of bombardment either because of its height or its location, I have methods for destroying any fortress or other stronghold, even if it be founded upon rock. ...If the engagement be at sea, I have many engines of a kind most efficient for offence and defence, and ships that can resist cannons and powder.


text: In Leonardo's notebooks there is an array of war machines which includes a vehicle to be propelled by two men powering crank shafts. Although the drawing itself looks quite finished, the mechanics were apparently not fully developed because, if built as drawn, the vehicle would never progress in a forward direction. In a BBC documentary, a military team built the machine and changed the gears in order to make the machine work. It has been suggested that Leonardo deliberately left this error in the design, in order to prevent it from being put to practice by unauthorized people. Another machine, propelled by horses with a pillion rider, carries in front of it four scythes mounted on a revolving gear, turned by a shaft driven by the wheels of a cart behind the horses.


text: Leonardo's notebooks also show cannons which he claimed "to hurl small stones like a storm with the smoke of these causing great terror to the enemy, and great loss and confusion." He also designed an enormous crossbow. Following his detailed drawing, one was constructed by the British Army, but could not be made to fire successfully. In 1481 Leonardo designed a breech-loading, water cooled cannon with three racks of barrels allowed the re-loading of one rack while another was being fired and thus maintaining continuous fire power. The "fan type" gun with its array of horizontal barrels allowed for a wide scattering of shot.


text: Leonardo was the first to sketch the wheel-lock musket c. 1500 AD (the precedent of the flintlock musket which first appeared in Europe by 1547), although as early as the 14th century the Chinese had used a flintlock 'steel wheel' in order to detonate land mines.


text: While Leonardo was working in Venice, he drew a sketch for an early diving suit, to be used in the destruction of enemy ships entering Venetian waters. A suit was constructed for a BBC documentary using pigskin treated with fish oil to repel water. The head was covered by a helmet with two eyeglasses at the front. A breathing tube of bamboo with pigskin joints was attached to the back of the helmet and connected to a float of cork and wood. When the scuba divers tested the suit, they found it to be a workable precursor to a modern diving suit, the cork float acting as a compressed air chamber when submerged.


text: His inventions were very futuristic which meant they were very expensive and proved not to be useful.


text: In Leonardo's infancy a hawk had once hovered over his cradle. Recalling this incident, Leonardo saw it as prophetic:


text: An object offers as much resistance to the air as the air does to the object. You may see that the beating of its wings against the air supports a heavy eagle in the highest and rarest atmosphere, close to the sphere of elemental fire. Again you may see the air in motion over the sea, fill the swelling sails and drive heavily laden ships. From these instances, and the reasons given, a man with wings large enough and duly connected might learn to overcome the resistance of the air, and by conquering it, succeed in subjugating it and rising above it.


text: The desire to fly is expressed in the many studies and drawings. His later journals contain a detailed study of the flight of birds and several different designs for wings based in structure upon those of bats which he described as being less heavy because of the impenetrable nature of the membrane. There is a legend that Leonardo tested the flying machine on Monte Ceceri with one of his apprentices, and that the apprentice fell and broke his leg. Experts Martin Kemp and Liana Bortolon agree that there is no evidence of such a test, which is not mentioned in his journals.


text: One design that he produced shows a flying machine to be lifted by a man-powered rotor. It would not have worked since the body of the craft itself would have rotated in the opposite direction to the rotor.


text: While he designed a number of man powered flying machines with mechanical wings that flapped, he also designed a parachute and a light hang glider which could have flown.


text: The viola organista was an experimental musical instrument invented by Leonardo da Vinci. It was the first bowed keyboard instrument (of which any record has survived) ever to be devised.


text: Leonardo's original idea, as preserved in his notebooks of 1488–1489 and in the drawings in the Codex Atlanticus, was to use one or more wheels, continuously rotating, each of which pulled a looping bow, rather like a fanbelt in an automobile engine, and perpendicular to the instrument's strings.


text: In the late 20th century, interest in Leonardo's inventions escalated. There have been many projects which have sought to turn diagrams on paper into working models. One of the factors is the awareness that, although in the 15th and 16th centuries Leonardo had available a limited range of materials, modern technological advancements have made available a number of robust materials of light-weight which might turn Leonardo's designs into reality. This is particularly the case with his designs for flying machines.


text: A difficulty encountered in the creation of models is that often Leonardo had not entirely thought through the mechanics of a machine before he drew it, or else he used a sort of graphic shorthand, simply not bothering to draw a gear or a lever at a point where one is essential in order to make a machine function. This lack of refinement of mechanical details can cause considerable confusion. Thus, many models that are created, such as some of those on display at Clos Lucé, Leonardo's home in France, do not work, but would work, with a little mechanical tweaking.


text: Leonardo was the author of some of the earliest known examples of pictorial anamorphosis identified and studied.


text: Anamorphosis is a type of optical artifice in which images are represented with altered proportions, and are recognizable only when the image is observed from a specific vantage point or using distorting instruments. A notable example in painting is "The Ambassadors" (1533) by Hans Holbein the Younger.


text: One of the instruments used by Leonardo for his research on anamorphosis was the tool for the angle of contingence, recreated in modern times using the Codex Atlanticus. It is an instrument to determine the reflexion angle of a ray of light incident on the surface of a cylindrical mirror.


text: The first examples of Leonardo's studies on anamorphosis can be found both in his treatise Treatise on Painting ("Rules for the Painter") and in the Codex Atlanticus. Two anamorphic drawings of the Codex Atlanticus, representing the head of a baby and an eye, are examples of plane anamorphosis. The two drawings can be adjusted when observed from a foreshortening angle, placing the eye on the right side of the sheet, about middle height. The original paper displays a preparation with a bundle of lines traced with a metal tip inside which the figures are inscripted; these lines are invisible in any reproduction. A chapter in the Codex Arundel 263 (c.62, 9r.) with the title "On natural perspective mixed with accidental perspective" explains how to apply an accidental viewpoint to that of a natural surface, in order for the moving observer to obtain the vision of a "monstrous" figure. This was the procedure used to accomplish the "Fight Between a Dragon and a Lion" and Painting with Horses, so peculiar as to attract the attention of Francis I of France demonstrating the presence of a geometric construction underlying the sketches, which can be seen in their real proportions only observing them with the usual technique needed for ‘anamorphic’ paintings.


text: According to Jurgis Baltrušaitis these are some of the oldest examples of anamorphosis known at the time, and with reference to the technique he stated:


text: The Codex A of the Institut de France includes the description of a technique to build an anamorphosis using a hole through which letting a ray of light project the shadow of what is to be drawn on a dedicated wall. This drawing technique is defined by Leonardo as "accidental perspective", in which farther objects needed to be drawn bigger than close ones, in contrast with what is observed in reality ("natural perspective").


text: In the Uffizi Annunciation, sparsely documented early work by Leonardo once wrongly attributed to Domenico Ghirlandaio, the shortcomings, mistakes, including a seemingly gross perspective one and the subsequent doubts concerning its authorship, were caused by the failure to understand the principles of anamorphosis. Mary in the painting is represented reading in the garden, when she is surprised by the arrival of Archangel Gabriel, the Virgin looks almost gloomy, while her right hand chastely appears to hold back the annunciation of the divine messenger. In Leonardo's composition, the bookstand where the Virgin lays her right hand, constrains her in an unusual position. Observing the painting from a central point of view, when looked at frontally; the limb appears too long and unjointed, almost unnatural. But thanks to the remarks of Carlo Pedretti's (one of the greatest experts of Leonardo) and Antonio Natali's, (Director of the Uffizi), it is now understood that when observed from a vantage point, not only the arm appears perfectly proportioned, but also Archangel Gabriel, that could have looked too off balance ahead, regains a more natural pose. The erroneous attempt to blame this seeming imperfection to the young author's inexperience is overcome by the clear use of an anamorphic composition of the painting by Leonardo, following the example of other great artists of the early Renaissance, such as Florentine artists Donatello and Filippo Lippi.


text: The errors of perspective can be summarized as follows: the Virgin's right arm being longer than the left one, too short legs compared to the height of the torso, the cypress confused with the fifteenth-century building, making it appear bigger, the different placing of the Virgin's legs and shoulders relative to the bookstand. The error of perspective is the result of the will of the painter, and arises from the need to accommodate the placing of the painting on a wall that would have been looked at mainly in foresight from the right; it is actually observing the Annunciation from a right sided lateral position that the disproportion of the arm subsides, as an effect of the anamorphosis.


title: Kard (group)

text: Kard (, stylized K.A.R.D or KARD) is a South Korean co-ed group formed by DSP Media. They are composed of members J.Seph, BM, Somin, and Jiwoo. They officially debuted on July 19, 2017, with their extended play "Hola Hola".


title: Kard (group)

text: Somin was previously a member of DSP Media's Japan-based girl group Puretty, which disbanded two years after its debut in 2012. She later joined "Kara Project", where she competed to become a new member of KARA and finished in second place. On August 24, 2015, she debuted as leader of DSP Media's girl group April, but she decided to depart from the group on November 9.


title: Kard (group)

text: Male members J.Seph trained for five years, while BM trained for four and a half years under DSP Media. The label originally planned to debut them in a hip-hop duo, but this was changed later on. Prior to his debut, BM was featured in Goo Ha-ra's song "La La La" from her 2015 debut EP "Alohara (Can You Feel It?)", and was also her dance partner for the music video and live performances of its lead single "Choco Chip Cookies".


title: Kard (group)

text: The last member of the group was Jiwoo, who had trained under FNC Entertainment for two years and moved to DSP Media in 2016, where she only trained for two months before debuting with Kard.


title: Kard (group)

text: DSP Media first announced the formation of Kard on December 1, 2016 after opening several social media accounts under the group's name. After being revealed in a sequential order, all the members of the group were revealed by December 5, with the label elaborating more on their card-game concept. The group's name is an abbreviation of different "cards" that are assigned to each member: BM is assigned as the "King" card, J.Seph is known as the "Ace" card, Somin is given the "Black JokeR" card, while member Jiwoo is referred to as the "Color JokeR" card. A certain "hiDDen card" was also stated by the agency, but was not further elaborated in its statement. DSP Media then confirmed that the group's first release was slated on December 13.


title: Kard (group)

text: On December 8, Kard revealed that their first "hiDDen card" member would be their labelmate Heo Young-ji, and further elaborated that Youngji would be active only in the first release of the group's "Kard Project", wherein they will release three project singles each with their own "hidden card" feature before their official debut. The announcement was made by the group's four members including Youngji in a live broadcast on the V-Live app. The following day, the music video teaser for their first project single titled "Oh NaNa" was released.


title: Kard (group)

text: "Oh NaNa" was released on December 13. The music video for the song accumulated over 1.25 million views in three days. Following the release of the song, "Billboard" magazine included Kard in its list of "10 Best New K-pop Groups in 2016" ranking at number 8, with the group making it into the list just eight days after starting their pre-debut project. "Oh NaNa" then became the group's first entry into the "Billboard" World Digital Song Sales chart, with the song peaking at number 5 in its issue dated January 7, 2017 and remaining on the said chart for 8 weeks.


title: Kard (group)

text: On January 19, 2017, "Billboard" selected Kard as one of the "Top 5 K-Pop Artists to Watch in 2017", citing the group's mixed-gender setup and their international attention which was seen when the music video for "Oh NaNa" became one of the top-viewed video in the United States for the month of December.


title: Kard (group)

text: On February 16, Kard released their second project single titled "Don't Recall", at number 22 on the UK Singles Chart, and at number 34th on the Brazilian Song Chart. Six days after the song's release, the music video for "Don't Recall" had accumulated over 6 million views. Similar to its predecessor, "Don't Recall" charted on "Billboard"'s World Digital Song Sales chart and peaked at number 5 in its issue dated March 18, 2017, but remained on the chart longer, charting for 12 weeks. An English version of the song was released by the group on March 1, which marked the group's second "hidden card" release.


title: Kard (group)

text: On April 21, LG Electronics announced that it has selected the group as their global ambassador for the G6 Smartphone. Following this development, it was revealed that all content for Kard's final project single titled "Rumor", including its music videos, will be produced in collaboration with LG Electronics G6. "Rumor" was then released on April 24, with the song's music video featuring Korean choreographer Z.Sun as the group's third "hidden card" member.


title: Kard (group)

text: The group then embarked on their first concert tour, known as the "2017 Wild Kard Tour", held in 11 cities covering Canada, the United States, Mexico, and Brazil from May to June 2017. It was reported that all tickets for the concert tour were sold out. In the midst of the group's tour, Kard was featured in their first solo reality series titled "Secret Kard", which depicted the group's experiences during their "Wild Kard" concert tour. The series first premiered at Mnet's M2 YouTube channel on June 19.


title: Kard (group)

text: Kard marked their official debut on July 19, 2017, through the release of their first EP "Hola Hola". The six-track EP contained their previous project singles, as well as the title track "Hola Hola". The group held their debut showcase at the Ilji Art Hall in Gangnam-gu, Seoul. The album debuted on several "Billboard" charts, charting at number 3 on World Albums, at number 25 on Heatseekers Albums, and at number 46 on the Independent Album Chart. The album's eponymous title track also entered the "Billboard" World Digital Song Sales chart at number 4, while other tracks of the album, “I Can’t Stop“ and “Living Good” ranked number 10 and number 12, respectively.


title: Kard (group)

text: On August 19, Kard performed at the 2017 Summer Sonic Festival, known as one of the world's largest rock festivals, held in Japan. On the next day, the group performed at the second day of the 2017 KCON Festival held at the Staples Center in Los Angeles. Following their performance at KCON, the group then embarked on their second concert tour known as the "2017 Wild Kard Tour PT. 2" which was held from September to October 2017, with five European dates in London, Lisbon, Madrid, Milan, and Rotterdam, and five North American dates in Minneapolis; Washington, D.C.; New York City; Miami; and San Francisco.


title: Kard (group)

text: The group released their second EP, "You & Me", on November 21, with the song "You In Me" serving as the title track. "You & Me" debuted at number 8 on the Gaon Album Chart on the chart issue dated November 19–25, 2017, and also debuted at number 4 on the US World albums Chart and at number 17 on the US Heatseekers Albums chart, achieving their new peak as a group on the latter chart.


title: Kard (group)

text: The female members of the group, Somin and Jiwoo, were featured in a special version of the song "Lo Siento", the lead single of Super Junior's album "Replay" (a repackaged album of their eighth Korean studio album "Play"). This version is included inside the digital version of the album, with the album being released on April 12, 2018. Somin and Jiwoo joined Super Junior to perform the song on various Korean music programs. Kard then held an Asia-wide tour spanning four countries: Singapore, Taiwan, Hong Kong and the Philippines. Kard also performed at the South By Southwest (SXSW) 2018.


title: Kard (group)

text: On April 14, 2018, the group met local fans through their "2018 Wild Kard Tour" in the Kasablanka Hall in Jakarta, Indonesia. Two meetings were then held in Australia in the city of Melbourne on April 26 and Sydney on the 29th. On July 25, 2018, they made their comeback with their third EP, "Ride On the Wind". The EP debuted and peaked at number 7 on the Gaon Album Chart for the week ending July 28, 2018. The EP also debuted and peaked at number 8 on the "Billboard" World Albums chart.


title: Kard (group)

text: On August 19, Kard held their first solo concert in South Korea since their debut, completing their "Wild Kard in Seoul" concert held at the YES24 Live Hall in Gwangjin-gu, Seoul.


title: Kard (group)

text: On March 27, 2019, they made their comeback with their first digital single "Bomb Bomb". "Bomb Bomb" became the group's fifth top five entry on the "Billboard" World Digital Song Sales chart, debuting and peaking at number three. A month later, Kard held their second concert in Seoul named as the "2019 Wild Kard in Seoul" at the Mary Hall of Sogang University in Mapo-gu, Seoul on April 27. The following month, Kard performed at the 2019 Dream Concert held at the World Cup Stadium in Sangam-dong, Seoul on May 18.


title: Kard (group)

text: On July 12 and 14, Kard embarked on their Indian two-city tour known as the "Play Your Kard Right Tour", with the band performing at Delhi’s Talkatora Indoor Stadium and at the city of Guwahati.


title: Kard (group)

text: On September 21, Kard made another comeback with their second digital single, "Dumb Litty". Following the success of the single which peaked at number three on the "Billboard" World Digital Song Sales chart, Kard debuted on the "Billboard" Social 50 chart, ranking at number 41 on its tally dated on October 5 as they experienced a 39% increase in Twitter mentions and a 457% increase in YouTube subscribers.


title: Kard (group)

text: Throughout the month of October, Kard embarked on their "Wild Kard Tour in USA 2019" with five concert dates held in different cities in the United States. The tour wrapped up on October 27 at the Buckhead Theatre in Atlanta. The following month, on November 6, Kard appeared at the Young Hollywood studio in Los Angeles, talking about their comeback song "Dumb Litty", and playing the Mystery Box Challenge game.


title: Kard (group)

text: On February 12, 2020, Kard released their fourth EP, "Red Moon". The EP debuted and peaked at number 10 on the Gaon Album Chart for the week ending February 15, after reporting 1,453 copies sold, before reporting a total of 1,752 copies sold in its first two weeks. Additionally, its eponymous title track reached a peak position of number 8 on the "Billboard" World Digital Song Sales Chart.


title: Kard (group)

text: On August 26, 2020, Kard released their first single album "Way with Words" and their title track "Gunshot". BM wrote, composed, and arranged the title track, with the other members contributing to the album as well. "Gunshot" reached a peak position of number 9 on the "Billboard" World Digital Song Sales Chart on September 12, and spent a total of three weeks on the chart.


title: Kard (group)

text: On October 5, J.Seph quietly enlisted for his mandatory military service as an active duty soldier. Kard then continued promoting as a three-piece group, making their first live performance without J.Seph on the second season of KCON's online series KCON:TACT held on October 16–25. BM debuted as the group's first soloist in 2021, releasing his single album "The First Statement" on July 2.


title: Kard (group)

text: On April 4, it was confirmed that J. Seph had been discharged from his military service. However, due to the spread of COVID-19, J. Seph's last vacation was in mid-February, where he did not return to military service and was discharged early. On May 28, DSP Media announced that Kard will release a new album in June and resume all activities, marking their first full group release in 22 months. Their fifth EP, "", was released on June 22 with the title track "Ring The Alarm".


title: Kard (group)

text: Kard's brand of K-pop has been described as "undeniably trendy", with their discography focusing on contemporary house and dancehall vibes, which "Billboard" has referred to as something that is "pulled directly from Top 40 charts". The group's musical style diverges from electropop, hip hop, EDM, and alt-R&B that was known to have been trending in the American music market by the time of their pre-debut. The group was also noted for their reggaetón and moombahton styling that resonated with international K-pop fans, which was stated by "Billboard" to be one of the primary reasons why they were able to tour throughout North and South America even prior to releasing their first mini-album. While they are largely inspired by Latin dance music trends, Kard has stated that they are continuously studying other genres in order to keep showing new sides to their music style. A notable shift in Kard's sonic style was first seen through the release of their single "Dumb Litty", which incorporated dancehall alongside synth, trap, and EDM. Following the release of their fourth EP, "Red Moon", member BM has dubbed moombahton as "a symbol of Kard".


title: Kard (group)

text: The group's nature in their sonic base is apparent in the members' personal musical influences: BM cites American rapper Tupac and J.Cole as his inspiration, J.Seph cites Korean rapper Beenzino, Somin takes inspiration from Tinashe and Ariana Grande, while member Jiwoo cites Beyonce and Rihanna.


title: Kard (group)

text: Mixed-gender groups are considered a rarity in the Korean music industry, with several co-ed acts like Play The Siren, Sunny Hill, and Co-Ed being regarded as unsuccessful. With Kard's debut, "Forbes" noted that the group was "headed for worldwide success" after quickly building an international presence through their North and South American tour in their pre-debut, which was further expanded following the release of "Hola Hola". "Billboard" magazine has described Kard to be "one of the most successful co-ed K-pop acts to ever exist" which was seen when their debut EP landed at number 3 on the World Albums Chart.


title: Kard (group)

text: While Kard has risen to international success especially in South America, they have been criticized for focusing primarily on the international music market. Due to their lack of promotions in their country of origin, a Korean broadcasting station official once told the members of Kard that they were "like a fictional group [to him]". However, the group has stated that they are aiming for further activities in South Korea.


title: Pulmonary alveolus

text: A pulmonary alveolus (plural: alveoli, from Latin "alveolus", "little cavity"), also known as an air sac or air space, is one of millions of hollow, distensible cup-shaped cavities in the lungs where oxygen is exchanged for carbon dioxide. Alveoli make up the functional tissue of the mammalian lungs known as the lung parenchyma, which takes up 90 percent of the total lung volume.


title: Pulmonary alveolus

text: Alveoli are first located in the respiratory bronchioles that mark the beginning of the respiratory zone. They are located sparsely in these bronchioles, line the walls of the alveolar ducts, and are more numerous in the blind-ended alveolar sacs. The acini are the basic units of respiration, with gas exchange taking place in all the alveoli present. The alveolar membrane is the gas exchange surface, surrounded by a network of capillaries. Across the membrane oxygen is diffused into the capillaries and carbon dioxide released from the capillaries into the alveoli to be breathed out.


title: Pulmonary alveolus

text: Alveoli are particular to mammalian lungs. Different structures are involved in gas exchange in other vertebrates.


title: Pulmonary alveolus

text: The alveoli are first located in the respiratory bronchioles as scattered outpockets, extending from their lumens. The respiratory bronchioles run for considerable lengths and become increasingly alveolated with side branches of alveolar ducts, that become deeply lined with alveoli. The ducts number between two and eleven from each bronchiole. Each duct opens into five or six alveolar sacs into which clusters of alveoli open.


title: Pulmonary alveolus

text: Each terminal respiratory unit is called an acinus and consists of the respiratory bronchioles, alveolar ducts, alveolar sacs, and alveoli. New alveoli continue to form until the age of eight years.


title: Pulmonary alveolus

text: A typical pair of human lungs contain about 300 million alveoli, providing a total surface area for gas exchange of between 70 and 80 square metres. Each alveolus is wrapped in a fine mesh of capillaries covering about 70% of its area. The diameter of an alveolus is between 200 and 500 μm.