History.

The first articles in the Romanian Wikipedia were written in July 2003, with the first version of the main page being drafted on 12 July. The user interface, initially in English, started being translated into Romanian by Bogdan Stăncescu (registered with the username Gutza) as soon as he was given sysop rights. The same user subsequently contacted several Romanian universities that were available on the internet, as well as the Romanian Academy, in order to attract new contributors. His efforts were soon remarked by the Romanian media, who invited him on several occasions to introduce the project to the public. By the end of 2003, the Romanian Wikipedia had exceeded 3,000 articles, ranking 16th among all Wikipedias. The 10,000th article was written on 13 December 2004, and the 50,000th on 5 January 2007.  In April 2004, the Romanian Wikipedia supported the launch of the (see Aromanian language).  In June 2004, the Romanian Wikipedia encountered problems concerning its division and the creation of a separate Moldovan Wikipedia (see Moldovan language). A Moldovan-language version of Wikipedia exists as it was created automatically together with a larger number of other Wikipedias, because the language had been assigned a separate ISO 639 code ("mo/mol"—which were deprecated in November 2008 by the ISO authorities). At its beginnings, it worked as a portal redirecting to the Romanian Wikipedia, but in March 2005, it eventually began allowing content (although only intended for Cyrillic Moldovan/Romanian as it was used before 1989 in the Moldavian SSR and remains in use only in Transnistria), starting big editing wars and endless discussion. Between December 2006 up to its deletion in January 2018, it was frozen and editing was no longer permitted. This question was raised from time to time, although users on Wikipedia voted on its closure and its deletion.  The Romanian Wikipedia reached the 100,000 article milestone on 11 January 2008. As of April 2015, it has 300,000 articles and 330,000 registered users, of which 21 are administrators.

Peculiarities.

The logo of the Romanian Wikipedia was slightly different from the logos of other Wikipedias. The letter "И" in the logo was replaced with the Romanian letter "Ă" (A-breve), further adapting this Wikipedia to the local readership.  Articles can contain small spelling variations, mostly regarding the use of the letters "â" and "î", both used for the close central unrounded vowel (cf. Romanian alphabet). According to the 1993 spelling rules promoted by the Romanian Academy, is transcribed as either "î", when used as the first or last letter of words, or "â", when it occurs in the middle of the word (with some exceptions). Still, between 1953 and 1993, the Romanian language only used "î" - after 1964 an exception was made for derivations of the words "România" ("Romania"), "român" ("Romanian") and related words. The Academy rules are mandatory in government organisations and in state schools in Romania. Moldova adopted the Latin alphabet for the Romanian language before the spelling reform in 1993, and it didn't switch to the new spelling up until 2001, using the letter "î" before exclusively (exceptions were made for "România" and the other related words, spelled with "â"). In practice, either usage is acceptable in both countries, and indeed there are publishing houses and printed magazines that use either or both of the two rules. Vojvodina uses the new Romanian spelling. Other spelling differences include "sunt"/"sînt" or "niciun"/"nici un". The Romanian Wikipedia community adopted a language policy stating that both pre-1993 and post-1993 spelling norms are permitted, and editing an article just to switch it from one norm to the other is not acceptable; switching is allowed if the article is significantly expanded or rewritten.  Concerning the addressing policy, Romanian Wikipedia uses the polite forms of the personal pronouns and verbs. A policy on this was discussed in early 2006, and consensus was reached for the use of "dumneavoastră" (polite "you") instead of "tu" (familiar "you") on its pages.

Topics.

In 2019 the Romania Wikipedia has 115 thousand unique categories and 22.75% of them do not have appropriate page in the category. The average article in this language version has 9 categories, while number of unique categories per articles ratio is 0.293. The largest number of articles has People (30%) and Events (25%) category. In Romania Wikipedia articles related to Food and drink and Military has the highest average quality. Content about Government is read more often and has the highest authors' interest on average.

The Romanian Wikipedia (abr. "ro.wiki" or "ro.wp"; ) is the Romanian language edition of Wikipedia, the free encyclopedia. Started on 12 July 2003, as of this edition has about and is the 25th largest Wikipedia edition. In December 2004, users on the Romanian Wikipedia started to talk about founding a local chapter of Wikimedia, "".

Rumunská Wikipedie je jazyková verze Wikipedie v rumunštině. Založena byla v červenci 2003. V lednu 2020 obsahovala přes 403 000 článků a pracovalo pro ni 18 správců. Registrováno bylo přes 504 000 uživatelů, z nichž bylo okolo 920 aktivních. V počtu článků byla 28. největší Wikipedie.


History.

The scale was developed in 1971 by civil engineer Herbert Saffir and meteorologist Robert Simpson, who at the time was director of the U.S. National Hurricane Center (NHC). The scale was introduced to the general public in 1973, and saw widespread use after Neil Frank replaced Simpson at the helm of the NHC in 1974.  The initial scale was developed by Herbert Saffir, a structural engineer, who in 1969 went on commission for the United Nations to study low-cost housing in hurricane-prone areas. While conducting the study, Saffir realized there was no simple scale for describing the likely effects of a hurricane. Mirroring the utility of the Richter magnitude scale for describing earthquakes, he devised a 1–5 scale based on wind speed that showed expected damage to structures. Saffir gave the scale to the NHC, and Simpson added the effects of storm surge and flooding.  In 2009, the NHC made moves to eliminate pressure and storm surge ranges from the categories, transforming it into a pure wind scale, called the Saffir–Simpson Hurricane Wind Scale (Experimental) [SSHWS]. The new scale became operational on May 15, 2010. The scale excludes flood ranges, storm surge estimations, rainfall, and location, which means a Category 2 hurricane that hits a major city will likely do far more cumulative damage than a Category 5 hurricane that hits a rural area. The agency cited various hurricanes as reasons for removing the "scientifically inaccurate" information, including Hurricane Katrina (2005) and Hurricane Ike (2008), which both had stronger than estimated storm surges, and Hurricane Charley (2004), which had weaker than estimated storm surge. Since being removed from the Saffir–Simpson hurricane wind scale, storm surge predicting and modeling is now handled with the use of computer numerical models such as ADCIRC and SLOSH.  In 2012, the NHC expanded the windspeed range for Category 4 by 1 mph in both directions, to 130–156 mph, with corresponding changes in the other units (113–136 kn, 209–251 km/h), instead of 131–155 mph (114–135 kn, 210–249 km/h). The NHC and the Central Pacific Hurricane Center assign tropical cyclone intensities in 5 knot increments, and then convert to mph and km/h with a similar rounding for other reports. So an intensity of 115 kn is rated Category 4, but the conversion to miles per hour (132.3 mph) would round down to 130 mph, making it appear to be a Category 3 storm. Likewise, an intensity of 135 kn (~155 mph, and thus Category 4) is 250.02 km/h, which, according to the definition used before the change would be Category 5. To resolve these issues, the NHC had been obliged to incorrectly report storms with wind speeds of 115 kn as 135 mph, and 135 kn as 245 km/h. The change in definition allows storms of 115 kn to be correctly rounded down to 130 mph, and storms of 135 kn to be correctly reported as 250 km/h, and still qualify as Category 4. Since the NHC had previously rounded incorrectly to keep storms in Category 4 in each unit of measure, the change does not affect the classification of storms from previous years. The new scale became operational on May 15, 2012.

Categories.

The scale separates hurricanes into five different categories based on wind. The U.S. National Hurricane Center classifies hurricanes of Category 3 and above as "major hurricanes", and the Joint Typhoon Warning Center classifies typhoons of 150 mph or greater (strong Category 4 and Category 5) as "super typhoons" (although all tropical cyclones can be very dangerous). Most weather agencies use the definition for sustained winds recommended by the World Meteorological Organization (WMO), which specifies measuring winds at a height of for 10 minutes, and then taking the average. By contrast, the U.S. National Weather Service, Central Pacific Hurricane Center and the Joint Typhoon Warning Center define sustained winds as average winds over a period of one minute, measured at the same height, and that is the definition used for this scale.  The scale is roughly logarithmic in wind speed.  The five categories are described in the following subsections, in order of increasing intensity. Intensity of example hurricanes is from both the time of landfall and the maximum intensity.

Category 1.

Very dangerous winds will produce some damage  Category 1 storms usually cause no significant structural damage to most well-constructed permanent structures; however, they can topple unanchored mobile homes, as well as uproot or snap weak trees. Poorly attached roof shingles or tiles can blow off. Coastal flooding and pier damage are often associated with Category 1 storms. Power outages are typically widespread to extensive, sometimes lasting several days. Even though it is the least intense type of hurricane, they can still produce widespread damage and can be life-threatening storms.  Hurricanes that peaked at Category 1 intensity and made landfall at that intensity include: Beth (1971), Agnes (1972), Juan (1985), Ismael (1995), Danny (1997), Claudette (2003), Gaston (2004), Stan (2005), Humberto (2007), Isaac (2012), Manuel (2013), Earl (2016), Hermine (2016), Newton (2016), Franklin (2017), Nate (2017), Barry (2019), and Lorena (2019).

Category 2.

Extremely dangerous winds will cause extensive damage  Storms of Category 2 intensity often damage roofing material (sometimes exposing the roof) and inflict damage upon poorly constructed doors and windows. Poorly constructed signs and piers can receive considerable damage and many trees are uprooted or snapped. Mobile homes, whether anchored or not, are typically damaged and sometimes destroyed, and many manufactured homes also suffer structural damage. Small craft in unprotected anchorages may break their moorings. Extensive to near-total power outages and scattered loss of potable water are likely, possibly lasting many days.  Hurricanes that peaked at Category 2 intensity and made landfall at that intensity include: Able (1952), Alice (1954), Ella (1958), Fifi (1974), Diana (1990), Calvin (1993), Gert (1993), Rosa (1994), Erin (1995), Alma (1996), Juan (2003), Catarina (2004), Alex (2010), Richard (2010), Tomas (2010), Carlotta (2012), Ernesto (2012), and Arthur (2014).

Category 3.

Devastating damage will occur  Tropical cyclones of Category 3 and higher are described as major hurricanes in the Atlantic or Eastern Pacific basins. These storms can cause some structural damage to small residences and utility buildings, particularly those of wood frame or manufactured materials with minor curtain wall failures. Buildings that lack a solid foundation, such as mobile homes, are usually destroyed, and gable-end roofs are peeled off. Manufactured homes usually sustain severe and irreparable damage. Flooding near the coast destroys smaller structures, while larger structures are struck by floating debris. A large number of trees are uprooted or snapped, isolating many areas. Additionally, terrain may be flooded well inland. Near-total to total power loss is likely for up to several weeks and water will likely also be lost or contaminated.  Hurricanes that peaked at Category 3 intensity and made landfall at that intensity include: Easy (1950), Carol (1954), Hilda (1955), Audrey (1957), Isbell (1964), Celia (1970), Ella (1970), Eloise (1975), Olivia (1975), Alicia (1983), Elena (1985), Roxanne (1995), Fran (1996), Isidore (2002), Jeanne (2004), Lane (2006), Karl (2010), and Otto (2016).

Category 4.

Catastrophic damage will occur  Category 4 hurricanes tend to produce more extensive curtainwall failures, with some complete structural failure on small residences. Heavy, irreparable damage and near complete destruction of gas station canopies and other wide span overhang type structures are common. Mobile and manufactured homes are often flattened. Most trees, except for the heartiest, are uprooted or snapped, isolating many areas. These storms cause extensive beach erosion, while terrain may be flooded far inland. Total and long-lived electrical and water losses are to be expected, possibly for many weeks.  The 1900 Galveston hurricane, the deadliest natural disaster to hit the United States, peaked at an intensity that corresponds to a modern-day Category 4 storm. Other examples of storms that peaked at Category 4 intensity and made landfall at that intensity include: Hazel (1954), Gracie (1959), Donna (1960), Flora (1963), Cleo (1964), Betsy (1965), Carmen (1974), Frederic (1979), Joan (1988), Iniki (1992), Luis (1995), Iris (2001), Charley (2004), Dennis (2005), Gustav (2008), Ike (2008), Joaquin (2015), and Harvey (2017).

Category 5.

Catastrophic damage will occur  Category 5 is the highest category of the Saffir–Simpson scale. These storms cause complete roof failure on many residences and industrial buildings, and some complete building failures with small utility buildings blown over or away. Collapse of many wide-span roofs and walls, especially those with no interior supports, is common. Very heavy and irreparable damage to many wood frame structures and total destruction to mobile/manufactured homes is prevalent. Only a few types of structures are capable of surviving intact, and only if located at least inland. They include office, condominium and apartment buildings and hotels that are of solid concrete or steel frame construction, multi-story concrete parking garages, and residences that are made of either reinforced brick or concrete/cement block and have hipped roofs with slopes of no less than 35 degrees from horizontal and no overhangs of any kind, and if the windows are either made of hurricane-resistant safety glass or covered with shutters. Unless all of these requirements are met, the absolute destruction of a structure is certain.  The storm's flooding causes major damage to the lower floors of all structures near the shoreline, and many coastal structures can be completely flattened or washed away by the storm surge. Virtually all trees are uprooted or snapped and some may be debarked, isolating most affected communities. Massive evacuation of residential areas may be required if the hurricane threatens populated areas. Total and extremely long-lived power outages and water losses are to be expected, possibly for up to several months.  Historical examples of storms that made landfall at Category 5 status include: "Cuba" (1924), "Okeechobee" (1928), "Bahamas" (1932), "Cuba–Brownsville" (1933), "Labor Day" (1935), Janet (1955), Camille (1969), Edith (1971), Anita (1977), David (1979), Gilbert (1988), Andrew (1992), Dean (2007), Felix (2007), Irma (2017), Maria (2017), Michael (2018), and Dorian (2019). No Category 5 hurricane is known to have made landfall at that strength in the eastern Pacific basin.

Criticism.

Some scientists, including Kerry Emanuel and Lakshmi Kantha, have criticized the scale as being simplistic, indicating that the scale takes into account neither the physical size of a storm nor the amount of precipitation it produces. Additionally, they and others point out that the Saffir–Simpson scale, unlike the Richter scale used to measure earthquakes, is not continuous, and is quantized into a small number of categories. Proposed replacement classifications include the Hurricane Intensity Index, which is based on the dynamic pressure caused by a storm's winds, and the Hurricane Hazard Index, which is based on surface wind speeds, the radius of maximum winds of the storm, and its translational velocity. Both of these scales are continuous, akin to the Richter scale; however, neither of these scales have been used by officials.

"Categories 6 and 7".

After the series of powerful storm systems of the 2005 Atlantic hurricane season, as well as after Hurricane Patricia, a few newspaper columnists and scientists brought up the suggestion of introducing Category 6, and they have suggested pegging Category 6 to storms with winds greater than. Fresh calls were made for consideration of the issue after Hurricane Irma in 2017, which was the subject of a number of seemingly credible false news reports as a "Category 6" storm, partly in consequence of so many local politicians using the term. Only a few storms of this intensity have been recorded. Of the 36 hurricanes currently considered to have attained Category 5 status in the Atlantic, 18 had wind speeds at or greater and only eight had wind speeds at or greater (the 1935 Labor Day hurricane, Allen, Gilbert, Mitch, Rita, Wilma, Irma, and Dorian). Of the 18 hurricanes currently considered to have attained Category 5 status in the eastern Pacific, only five had wind speeds at or greater (Patsy, John, Linda, Rick, and Patricia), and only three had wind speeds at or greater (Linda, Rick, and Patricia). Most storms which would be eligible for this category were typhoons in the western Pacific, most notably Typhoon Tip in 1979, with sustained winds of, and typhoons Haiyan and Meranti in 2013 and 2016, respectively, each with sustained winds of. Occasionally, suggestions of using even higher wind speeds as the cutoff have been made. In a newspaper article published in November 2018, NOAA research scientist Jim Kossin said that the potential for more intense hurricanes was increasing as the climate warmed, and suggested that Category 6 would begin at, with a further hypothetical Category 7 beginning at.  According to Robert Simpson, there are no reasons for a Category 6 on the Saffir–Simpson Scale because it is designed to measure the potential damage of a hurricane to human-made structures. Simpson stated that "... when you get up into winds in excess of you have enough damage if that extreme wind sustains itself for as much as six seconds on a building it's going to cause rupturing damages that are serious no matter how well it's engineered." Nonetheless, the counties of Broward and Miami-Dade in Florida have building codes that require that critical infrastructure buildings be able to withstand Category 5 winds.

The Saffir–Simpson hurricane wind scale (SSHWS), formerly the Saffir–Simpson hurricane scale (SSHS), classifies hurricanesWestern Hemisphere tropical cyclonesthat exceed the intensities of tropical depressions and tropical stormsinto five categories distinguished by the intensities of their sustained winds. To be classified as a hurricane, a tropical cyclone must have one-minute maximum sustained winds of at least (Category 1). The highest classification in the scale, Category 5, consists of storms with sustained winds over. The classifications can provide some indication of the potential damage and flooding a hurricane will cause upon landfall.

Saffirova–Simpsonova stupnice je stupnice pro klasifikaci tropických cyklón na západní polokouli, které přesáhly intenzitu tropické brázdy nízkého tlaku a tropické bouře, čímž se staly hurikány. Stupnice hurikány rozděluje do pěti kategorií, rozlišovaných podle intenzity jejich trvalých větrů. K tomu, aby byl tropický cyklon označen jako hurikán, musí mít vítr rychlost nejméně 33 m/s (119 km/h). Nejvyšší klasifikace na stupnici (kategorie 5) je vyhrazena pro bouře s větrem přesahujícím 70 m/s (252 km/h).


Early life.

Safin was born in Moscow to Tatar parents, Mubin ("Mikhail") Safin and Rauza Islanova. He speaks Russian, English, and Spanish as well as his native Tatar. His parents are former tennis players and coaches. His younger sister, Dinara, is a former world No. 1 professional tennis player and silver medalist at the 2008 Olympic Games in Beijing. Safin's father managed the local Spartak Tennis Club, where Safin trained in his youth alongside several tennis players, including Anna Kournikova, Elena Dementieva, and Anastasia Myskina.  At the age of 14, Safin moved to Valencia, Spain to gain access to advanced tennis training programs which were not available in Russia. Safin says he grew up "very fast... with no muscles" and that he moved to Spain because clay courts were "better for the knees". He is a supporter of Valencia CF.  In an interview with "USA Today", Safin identified himself as a Muslim, stating, "I'm Russian, but I'm 100% Muslim. All the Muslim people are passionate, stubborn. We have hot blood."

Tennis career.

Early career.

Safin started his professional career in 1997. In 1998, Safin consecutively defeated Andre Agassi and defending champion Gustavo Kuerten at the French Open. He won his first ATP title at the age of 19, in Boston, and later in 1999 he reached the prestigious Paris, Bercy final, losing a closely contested four-set match to No. 1 Andre Agassi.

World No. 1 and Grand Slam history.

Safin held the No. 1 ATP ranking for 9 weeks during 2000 (making him the tallest No. 1 ranked player of all time) when he won his first Grand Slam tournament at the US Open, becoming the only Russian in history to win this tournament in the men's singles draw, by defeating Pete Sampras in straight sets. He barely missed finishing the year as No. 1, the top spot being overtaken by Gustavo Kuerten at the last match of the season, the final of the 2000 Tennis Masters Cup and ATP Tour World Championships (3-0 win over Andre Agassi).  Safin reached three more Grand Slam finals, all at the Australian Open (2002, 2004, and 2005). He has cited nervousness as the reason for his loss in the 2002 event, and physical exhaustion for the 2004 loss. He defeated Lleyton Hewitt in the 2005 final to secure his second Grand Slam in five years. En route to this final, he defeated top-ranked Roger Federer in a five-set semifinal match. Safin described the match as "a brain fight." He also defeated future eight-time Australian Open champion Novak Djokovic, who was making his first appearance in the main draw of a Grand Slam tournament, in the first round losing just three games.  His best result at Wimbledon was reaching the semifinals in 2008, beating No. 3 Novak Djokovic en route. He often lost in the first or second rounds in other years, although he made the quarterfinals in 2001, losing in four sets to eventual champion Goran Ivanišević. Safin dismissed his performance in the 2001 tournament as a result of luck. Safin disliked playing on grass. Safin has said: "It's difficult to [break serve]. It's difficult to play-off the baseline because [of] a lot of bad bounces." With Safin's semifinal performance at Wimbledon in 2008, he became the fourth of five active players at the time to reach the semifinals in all four Grand Slams, joining Roger Federer, David Nalbandian, and Novak Djokovic. Other active players have since then joined the list.

Masters Series.

Safin won five ATP Tennis Masters Series titles during his career. His first was in 2000 when he won the title in Toronto, Canada. He had three wins (2000, 2002, and 2004) in Paris, France, and one in 2004 in Madrid, Spain.

Tennis Masters Cup.

In 2004, Safin reached the semifinal of the Tennis Masters Cup in Houston, Texas, where he was defeated by Federer, 6–3, 7–6. The second-set tiebreak (20–18) was the third-longest tiebreak in the Open Era. Safin also reached the semifinals in 2000.

Davis Cup.

Safin helped Russia achieve its first Davis Cup victory in 2002, with a 3–2 tie-breaking win against France in the final round at the Palais Omnisports Paris Bercy. His Russian team included Yevgeny Kafelnikov, Mikhail Youzhny, Andrei Stoliarov, and captain Shamil Tarpischev. The team made Davis Cup history by being the second to win the event after losing the doubles tie-breaker, and becoming the first team to win a (live-televised) five-set finals match by coming back from a two-set deficit. Safin helped Russia to win the Davis Cup in 2006. After a straight-sets defeat by David Nalbandian in his first match, his doubles victory (partnering Dmitry Tursunov) against Nalbandian and Agustín Calleri and singles victory against José Acasuso drove Russia to victory.  In the 2009 Davis Cup quarterfinal tie, Russia was upset by the Israel Davis Cup team on indoor hard courts at the Nokia Arena in Tel Aviv. Russia was the top-ranked country in Davis Cup standings, and the stage was set by Safin, who prior to the tie told the press: "With all due respect, Israel was lucky to get to the quarterfinals." Safin was held out of the first day of singles, and then went on to lose the clinching doubles match in five sets partnered with doubles specialist Igor Kunitsyn.

Injury history.

A succession of injuries hindered Safin's progress throughout his career.  In 2003, he missed the majority of the season due to a wrist injury.  During the 2005 clay-court season, Safin suffered a knee injury, which he played through all the way up to Wimbledon with the help of pain killers and anti-inflammatories. Safin was subsequently defeated in the early rounds of each of the seven tournaments he played between the Australian Open and the French Open, culminating in an early round defeat at the French Open. Safin made a surprise finals appearance at the Wimbledon tune-up tournament in Halle on grass. He lost the final narrowly to the defending champion, Federer. He only played one tournament in the summer hard-court season, in Cincinnati, where he lost in the quarterfinals to Robby Ginepri. He also missed the Tennis Masters Cup.  Injuries continued to bother Safin in 2006. Although Safin made appearances at the 2006 ATP Masters tournaments at Indian Wells, Miami, Monte Carlo, Rome and Hamburg, his ranking plummeted to as low as No. 104. He began to recover in time for the 2006 US Open, in which Safin defeated No. 4 David Nalbandian in a riveting second-round match. Safin then lost in the fourth round to No. 16 Tommy Haas, also in a fifth-set tiebreaker. Positive performances at the Thailand Open, where he was narrowly edged out by No. 7 seed, James Blake, and the Kremlin Cup in Moscow, the first all-Russian final at that event, losing to compatriot, Ukrainian-born Nikolay Davydenko, marked Safin's recovery. Despite the injury, Safin still posted seven wins against top ten players in 2006, fourth-most on the ATP tour behind just Federer (19), Nadal (10), and Blake (8).

Later career.

2007.

Safin did not play any warm-up tournaments in the run-up to the Australian Open. As Safin was forced to miss the tournament in 2006 because of injury, 2007 was his first Australian Open since he captured the title in 2005. Safin lost against sixth seed Andy Roddick in his third-round match in a grueling 3-hour match. Roddick commented after the match, "With Marat you know you are going to get an emotional roller-coaster. You just have to try and focus on yourself and I was able to do that tonight.  In April, Safin won the deciding quarterfinal Davis Cup rubber against France, beating Paul-Henri Mathieu in straight sets.  Safin reached the third round at Wimbledon, before falling to the defending champion Roger Federer. In July, Safin announced that he and his coach Alexander Volkov were parting ways, and that his new coach would be former pro Hernán Gumy. He won the doubles title at the Kremlin Cup in Moscow in October, his first ATP-level title since the 2005 Australian Open.

2008.

Safin prepared for the Australian Open at the invitational exhibition tournament, the AAMI Kooyong Classic in Melbourne. Other players in the field were Roddick, Fernando González, Nikolay Davydenko, Marcos Baghdatis, Ivan Ljubičić, and Andy Murray. Safin was victorious in his opening match, defeating Andy Murray. before losing in his second match to Andy Roddick, 6–3, 6–3.  In the third-place play-off, Safin rebounded from the Roddick loss and overpowered the prior year's Australian Open runner up Fernando González. Safin won his first-round match at the Australian Open against Ernests Gulbis in straight sets. He was ousted in the second round after a grueling five-set match against Baghdatis.  In February, Safin was granted wildcards into the tournaments at Memphis and Las Vegas. In Memphis, he was edged out by his 2002 Australian Open opponent, Thomas Johansson in the first round. In Las Vegas, he was defeated by Lleyton Hewitt during the semifinals. Safin was defeated by Hewitt once again.  In March, Safin lost in the first round of Indian Wells and Miami, to Jürgen Melzer and qualifier Bobby Reynolds, respectively. In the Davis Cup between Russia and the Czech Republic, Safin defeated No. 9 Tomáš Berdych in a five-set encounter, after being two sets down. This was the first time in his career that he had come back to win a match after being down two sets.  Safin's next tournament was in Valencia. He defeated No. 20-ranked and fourth seed Juan Carlos Ferrero. In spite of the fact that Ferrero is from the Valencia region, Safin was the more popular player, having been based in Valencia for many years and being a well-known Valencia CF fan. – local player Ferrero controversially favouring Real Madrid. He played Dutch teenager Robin Haase in the next round. He won the first set and was up 4–2 in the second set. However, Haase broke back to take it to a tiebreak. Safin had four match points, including one on his serve, but lost the tiebreak, and eventually the match. In the Monte Carlo Masters, Safin defeated Xavier Malisse, but then lost to No. 5 David Ferrer. He then entered the 2008 BMW Open in Munich, Germany, where he beat Carlos Berlocq in the first round. In the second round, he edged out Michael Berrer, but lost to Fernando González in his first quarterfinal of the year, and the first since June 2007 at the Legg Mason Tennis Classic in Washington, D.C. Safin entered the 2008 French Open but was eliminated in the second round by countryman and fourth seed Nikolay Davydenko, in straight sets.  Ranked at No. 75, Safin entered the 2008 Wimbledon Championships, where he defeated Fabio Fognini in the first round. In the second round, he defeated No. 3 player and 2008 Australian Open Champion Novak Djokovic. Safin's victory came as a shock as Djokovic was described as a "serious contender" to win the tournament. In the third round, he played and defeated Italian Andreas Seppi. In the fourth round, he defeated Stanislas Wawrinka. This was the first time he had reached the quarterfinals of a Grand Slam since the 2005 Australian Open. Safin went on to defeat Feliciano López in the quarterfinals to set up a semifinal clash with defending champion Roger Federer. His run to the semifinals was his best record in Wimbledon and made him the first Russian man to ever reach a Wimbledon semifinal. Safin attributed his great run at Wimbledon to the hard work he was putting in with coach Hernán Gumy. Safin then played at the Swedish Open, on clay, in Båstad against Marc López, winning in the first round. He lost his second-round match against Potito Starace.  Safin was awarded a wild card into the Rogers Cup Masters tournament in Toronto. He beat Sam Querrey in the first round. Because of rain delays, he had to play his next match against Stan Wawrinka on the same day. He lost that match. Safin was seeded fifth for his next tournament, the Countrywide Classic in Los Angeles. He defeated Americans John Isner and Wayne Odesnik in the first and second rounds, respectively, to advance to the quarterfinals, where he was defeated by Denis Gremelmayr.  At the US Open, Safin lost in the second round to Tommy Robredo. At the Moscow Kremlin Cup, he defeated Noam Okun, Julien Benneteau, Nikolay Davydenko, and Mischa Zverev, only to lose to another compatriot Igor Kunitsyn in the final. It was Safin's first final appearance since 2006, in the same event. Following the Kremlin Cup, Safin withdrew from the Madrid Masters event with a shoulder injury. His next event was the St. Petersburg Open, at which he lost in the second round. He then lost his first-round match at the final ATP tournament of the calendar: the Paris Masters, to Juan Mónaco. In the post-match conference, he raised the possibility of his retirement from the sport. Via a message posted on his official website, he said he was going to take a holiday and then seriously consider his options regarding his future in tennis. He finished the year 2008 ranked at No. 29.

2009.

Safin started the 2009 season by playing in the Hopman Cup event in Perth with his sister, Dinara Safina. He arrived at the event sporting a bandaged right thumb, two black eyes, a blood-filled left eye, and a cut near his right eye, all suffered in a fight several weeks earlier in Moscow. In the 2009 Hopman Cup, the pair played off in the final representing Russia, but each was defeated in the singles rubbers. Safin said he had decided to play the 2009 season because of a great offer from his manager Ion Ţiriac, he made this decision despite not having a coach.  Safin withdrew from the Kooyong Classic tournament because of a shoulder injury, but recovered to play his first-round Australian Open match, which he won in straight sets over Iván Navarro of Spain. In the second round, Safin defeated another Spanish player, Guillermo García-López. In the third round, he came up against Federer and lost in straight sets. His next tournament was the Barclays Dubai Tennis Championships. He exited in the first round, losing to Richard Gasquet, and exited in the semifinals in doubles with David Ferrer. In March, Safin helped Russia advance to the Davis Cup quarterfinals by beating Victor Crivoi of Romania in the first rubber in straight sets.  Starting the year at No. 29 in the world, he placed in the top 20 during the year for the first time since the end of January 2006. His doubles ranking also improved from 300 to 195. In the first round at Wimbledon, at which he was seeded 14th, he was upset by 21-year-old American Jesse Levine.  Safin played at the Catella Swedish Open at Båstad, where he lost to Nicolás Almagro of Spain. He began his hard-court season by making it to the quarterfinals of the LA Tennis Open (his first quarterfinal of the season), where he lost to Tommy Haas.  He lost in the first round of the U.S. Open, his last Grand Slam, to Austrian Jürgen Melzer. After a second-round loss in the PTT Thailand Open, he found some late form, coming into the China Open tournament held in Beijing; beating José Acasuso in the first round. In the second round, he played Fernando González and produced a win. In the quarterfinals, he lost against top seed Rafael Nadal. As the tour rolled into Moscow for the Kremlin Cup, it marked the beginning of the end for Safin, as he played his last competitive matches in his native Russia. He defeated No. 6 Nikolay Davydenko in the first round, but lost in the second round. He then played at the 2009 St. Petersburg Open, reaching the semifinals.

Retirement.

Safin's final tournament as a professional tennis player was at the 2009 Paris Masters. In the first round, he saved three match points with three aces against Thierry Ascione, eventually prevailing with a total of 24 aces and 41 winners. On 11 November 2009, Safin's career ended with a second-round defeat by reigning US Open champion Juan Martín del Potro, after which a special presentation ceremony was held on Centre Court at Bercy. Fellow tennis players who joined him in the ceremony included Juan Martín del Potro, Novak Djokovic, Gilles Simon, Tommy Robredo, Frederico Gil, Ivo Karlović, Albert Costa, Marc Rosset, and Younes El Aynaoui.

Playing style.

Safin was often characterized as a powerful offensive baseliner. Boris Becker, in 1999, said that he had not seen anybody hit the ball as hard from both wings for "a long, long time". He has a strong and accurate serve and a great forehand, while also possessing one of the best two-handed backhands of all time. He was also capable of playing at the net, with his volleys also being effective. However, lack of consistency and motivation was described as Safin's ultimate weakness, starting after his victory at the 2005 Australian Open.  Safin generally dominated during the fast indoor hard/carpet season, which is usually during the last few weeks on tour; Safin considered grass to be his least favourite playing surface, despite the similarities between indoor courts and grass courts even though other opponents with similar playing styles generally dominate on it.  He is known as one of the most talented players ever during his time on the tour, however his career was hampered by persistent injuries and lack of determination that prevented the prolongation of his dominance, and is therefore agreed by many pundits and fans as one of the biggest underachievers in tennis.  Safin was also known for his emotional outbursts during matches, and smashed numerous rackets. Safin is estimated to have smashed 48 racquets in 1999. In 2011, Safin stated that during his career he broke 1055 racquets.

Equipment.

Safin has used the Head Prestige Classic 600 since 1997 however throughout the years sported numerous paintjobs of the latest Head Prestige rackets (i.e. intelligence, Liquidmetal, Flexpoint and Microgel). His racquets used to be strung using Babolat VS Natural Team Gut 17L gauge, but he then switched to Luxilon Big Banger Original at 62 to 67 pounds. His apparel was manufactured by Adidas.

Career statistics.

Grand Slam tournament performance timeline.

"At the 2003 Australian Open, Safin withdrew prior to the third round."

Post-retirement career.

Since retirement Safin has been an official for the Russian Tennis Federation and a member of the Russian Olympic Committee. In 2011, he began playing at the ATP Champions Tour.  In December 2011, Safin was elected to the Russian Parliament as a member of Vladimir Putin's United Russia Party, representing Nizhny Novgorod.  In 2018 a book was published about "Facing Marat Safin: Symposium of a Champion' by author Scoop Malinowski in English.

Marat Mubinovich Safin (, ; born 27 January 1980) is a Russian politician and retired professional tennis player. He achieved the Association of Tennis Professionals (ATP) world No. 1 singles ranking on 20 November 2000. Nobody taller than Safin has ever reached the No. 1 ranking. Safin is the older brother of former world No. 1 WTA player Dinara Safina. They are the only brother–sister tandem in tennis history who have both achieved No. 1 rankings. On court, Safin was famous for his emotional outbursts and sometimes fiery temper.

Marat Safin (* 27. ledna 1980) je bývalý profesionální ruský tenista tatarské národnosti. Nejlepších výsledků dosáhl v roce 2000, kdy mu díky sedmi turnajovým vítězstvím patřilo v listopadu a prosinci 1. místo na žebříčku ATP. Jeho mladší sestra Dinara Safina byla světovou jedničkou na žebříčku WTA.


History.

The curvature of a differentiable curve was originally defined through osculating circles. In this setting, Augustin-Louis Cauchy showed that the center of curvature is the intersection point of two infinitely close normal lines to the curve.

Plane curves.

Intuitively, the curvature is a measure of the instantaneous rate of change of direction of a point that moves on the curve: the larger the curvature, the larger this rate of change. In other words, the curvature measures how fast the unit tangent vector to the curve rotates. In fact, it can be proved that this instantaneous rate of change is exactly the curvature. More precisely, suppose that the point is moving on the curve at a constant speed of one unit, that is, the position of the point is a function of the parameter, which may be thought as the time or as the arc length from a given origin. Let be a unit tangent vector of the curve at, which is also the derivative of with respect to. Then, the derivative of with respect to is a vector that is normal to the curve and whose length is the curvature.  For being meaningful, the definition of the curvature and its different characterizations require that the curve is continuously differentiable near, for having a tangent that varies continuously; it requires also that the curve is twice differentiable at, for insuring the existence of the involved limits, and of the derivative of.  The characterization of the curvature in terms of the derivative of the unit tangent vector is probably less intuitive than the definition in terms of the osculating circle, but formulas for computing the curvature are easier to deduce. Therefore, and also because of its use in kinematics, this characterization is often given as a definition of the curvature.

Osculating circle.

Historically, the curvature of a differentiable curve was defined through the osculating circle, which is the circle that best approximates the curve at a point. More precisely, given a point on a curve, every other point of the curve defines a circle (or sometimes a line) passing through and tangent to the curve at. The osculating circle is the limit, if it exists, of this circle when tends to. Then the "center" and the "radius of curvature" of the curve at are the center and the radius of the osculating circle. The curvature is the reciprocal of radius of curvature. That is, the curvature is where is the radius of curvature.  This definition is difficult to manipulate and to express in formulas. Therefore, other equivalent definitions have been introduced.

In terms of arc-length parametrization.

Every differentiable curve can be parametrized with respect to arc length. In the case of a plane curve, this means the existence of a parametrization, where and are real-valued differentiable functions whose derivatives satisfy This means that the tangent vector has a norm equal to one and is thus a unit tangent vector.  If the curve is twice differentiable, that is, if the second derivatives of and exist, then the derivative of exists. This vector is normal to the curve, its norm is the curvature, and it is oriented toward the center of curvature. That is,  Moreover, as the radius of curvature is and the center of curvature is on the normal to the curve, the center of curvature is the point If is the unit normal vector obtained from by a counterclockwise rotation of, then with. The real number is called the oriented or signed curvature. It depends on both the orientation of the plane (definition of counterclockwise), and the orientation of the curve provided by the parametrization. In fact, the change of variable provides another arc-length parametrization, and changes the sign of.

In terms of a general parametrization.

Let be a proper parametric representation of a twice differentiable plane curve. Here "proper" means that on the domain of definition of the parametrization, the derivative is defined, differentiable and nowhere equal to the zero vector.  With such a parametrization, the signed curvature is where primes refer to derivatives with respect to. The curvature is thus  These can be expressed in a coordinate-free way as  These formulas can be derived from the special case of arc-length parametrization in the following way. The above condition on the parametrisation imply that the arc length is a differentiable monotonic function of the parameter, and conversely that is a monotonic function of. Moreover, by changing, if needed, to, one may suppose that these functions are increasing and have a positive derivative. Using notation of the preceding section and the chain rule, one has and thus, by taking the norm of both sides where the prime denotes the derivation with respect to.  The curvature is the norm of the derivative of with respect to. By using the above formula and the chain rule this derivative and its norm can be expressed in terms of and only, with the arc-length parameter completely eliminated, giving the above formulas for the curvature.

Graph of a function.

The graph of a function, is a special case of a parametrized curve, of the form As the first and second derivatives of are 1 and 0, previous formulas simplify to for the curvature, and to for the signed curvature.  In the general case of a curve, the sign of the signed curvature is somehow arbitrary, as depending on an orientation of the curve. In the case of the graph of a function, there is a natural orientation by increasing values of. This makes significant the sign of the signed curvature.  The sign of the signed curvature is the same as the sign of the second derivative of. If it is positive then the graph has an upward concavity, and, if it is negative the graph has a downward concavity. It is zero, then one has an inflection point or an undulation point.  When the slope of the graph (that is the derivative of the function) is small, the signed curvature is well approximated by the second derivative. More precisely, using big O notation, one has  It is common in physics and engineering to approximate the curvature with the second derivative, for example, in beam theory or for deriving wave equation of a tense string, and other applications where small slopes are involved. This allows often considering as linear systems that are nonlinear otherwise.

Polar coordinates.

If a curve is defined in polar coordinates by the radius expressed as a function of the polar angle, that is is a function of, then its curvature is where the prime refers to differentiation with respect to.  This results from the formula for general parametrizations, by considering the parametrization

Implicit curve.

For a curve defined by an implicit equation with partial derivatives denoted,,,,, the curvature is given by  The signed curvature is not defined, as it depends on an orientation of the curve that is not provided by the implicit equation. Also, changing into does not change the curve, but changes the sign of the numerator if the absolute value is omitted in the preceding formula.  A point of the curve where is a singular point, which means that the curve in not differentiable at this point, and thus that the curvature is not defined (most often, the point is either a crossing point or a cusp).  Above formula for the curvature can be derived from the expression of the curvature of the graph of a function by using the implicit function theorem and the fact that, on such a curve, one has

Examples.

It can be useful to verify on simple examples that the different formulas given in the preceding sections give the same result.

Circle.

A common parametrization of a circle of radius is. The formula for the curvature gives  It follows, as expected, that the radius of curvature is the radius of the circle, and that the center of curvature is the center of the circle.  The circle is a rare case where the arc-length parametrization is easy to compute, as it is It is an arc-length parametrization, since the norm of is equal to one. This parametrization gives the same value for the curvature, as it amounts to division by in both the numerator and the denominator in the preceding formula.  The same circle can also be defined by the implicit equation with. Then, the formula for the curvature in this case gives

Parabola.

Consider the parabola.  It is the graph of a function, with derivative, and second derivative. So, the signed curvature is It has the sign of for all values of. This means that, if, the concavity is upward directed everywhere; if, the concavity is downward directed; for, the curvature is zero everywhere, confirming that the parabola degenerates into a line in this case.  The (unsigned) curvature is maximal for, that is at the stationary point (zero derivative) of the function, which is the vertex of the parabola.  Consider the parametrization. The first derivative of is, and the second derivative is zero. Substituting into the formula for general parametrizations gives exactly the same result as above, with replaced by. If we use primes for derivatives with respect to the parameter.  The same parabola can also be defined by the implicit equation with. As, and, one obtains exactly the same value for the (unsigned) curvature. However, the signed curvature is meaningless here, as is a valid implicit equation for the same parabola, which gives the opposite sign for the curvature.

Frenet–Serret formulas for plane curves.

The expression of the curvature In terms of arc-length parametrization is essentially the first Frenet–Serret formula where the primes refer to the derivatives with respect to the arc length, and is the normal unit vector in the direction of.  As planar curves have zero torsion, the second Frenet–Serret formula provides the relation  For a general parametrization by a parameter, one needs expressions involving derivatives with respect to. As these are obtained by multiplying by the derivatives with respect to, one has, for any proper parametrization

Space curves.

As in the case of curves in two dimensions, the curvature of a regular space curve in three dimensions (and higher) is the magnitude of the acceleration of a particle moving with unit speed along a curve. Thus if is the arc-length parametrization of then the unit tangent vector is given by and the curvature is the magnitude of the acceleration: The direction of the acceleration is the unit normal vector, which is defined by  The plane containing the two vectors and is the osculating plane to the curve at. The curvature has the following geometrical interpretation. There exists a circle in the osculating plane tangent to whose Taylor series to second order at the point of contact agrees with that of. This is the osculating circle to the curve. The radius of the circle is called the radius of curvature, and the curvature is the reciprocal of the radius of curvature:  The tangent, curvature, and normal vector together describe the second-order behavior of a curve near a point. In three-dimensions, the third order behavior of a curve is described by a related notion of torsion, which measures the extent to which a curve tends to move in a helical path in space. The torsion and curvature are related by the Frenet–Serret formulas (in three dimensions) and their generalization (in higher dimensions).

General expressions.

For a parametrically-defined space curve in three dimensions given in Cartesian coordinates by, the curvature is  where the prime denotes differentiation with respect to the parameter. This can be expressed independently of the coordinate system by means of the formula  where × denotes the vector cross product. Equivalently,  Here the T denotes the matrix transpose. This last formula (without cross product) is also valid for the curvature of curves in a Euclidean space of any dimension.

Curvature from arc and chord length.

Given two points and on, let be the arc length of the portion of the curve between and and let denote the length of the line segment from to. The curvature of at is given by the limit  where the limit is taken as the point approaches on. The denominator can equally well be taken to be. The formula is valid in any dimension. Furthermore, by considering the limit independently on either side of, this definition of the curvature can sometimes accommodate a singularity at. The formula follows by verifying it for the osculating circle.

Surfaces.

The curvature of curves drawn on a surface is the main tool for the defining and studying the curvature of the surface.

Curves on surfaces.

For a curve drawn on a surface (embedded in three-dimensional Euclidean space), several curvatures are defined, which relates the direction of curvature to the surface's unit normal vector, including the: Any non-singular curve on a smooth surface has its tangent vector contained in the tangent plane of the surface. The normal curvature,, is the curvature of the curve projected onto the plane containing the curve's tangent and the surface normal ; the geodesic curvature,, is the curvature of the curve projected onto the surface's tangent plane; and the geodesic torsion (or relative torsion),, measures the rate of change of the surface normal around the curve's tangent.  Let the curve be arc-length parametrized, and let so that form an orthonormal basis, called the Darboux frame. The above quantities are related by:

Principal curvature.

All curves with the same tangent vector will have the same normal curvature, which is the same as the curvature of the curve obtained by intersecting the surface with the plane containing and. Taking all possible tangent vectors, the maximum and minimum values of the normal curvature at a point are called the principal curvatures, and, and the directions of the corresponding tangent vectors are called principal normal directions.

Normal sections.

Curvature can be evaluated along surface normal sections, similar to above (see for example the Earth radius of curvature).

Gaussian curvature.

In contrast to curves, which do not have intrinsic curvature, but do have extrinsic curvature (they only have a curvature given an embedding), surfaces can have intrinsic curvature, independent of an embedding. The Gaussian curvature, named after Carl Friedrich Gauss, is equal to the product of the principal curvatures,. It has a dimension of length and is positive for spheres, negative for one-sheet hyperboloids and zero for planes. It determines whether a surface is locally convex (when it is positive) or locally saddle-shaped (when it is negative).  Gaussian curvature is an "intrinsic" property of the surface, meaning it does not depend on the particular embedding of the surface; intuitively, this means that ants living on the surface could determine the Gaussian curvature. For example, an ant living on a sphere could measure the sum of the interior angles of a triangle and determine that it was greater than 180 degrees, implying that the space it inhabited had positive curvature. On the other hand, an ant living on a cylinder would not detect any such departure from Euclidean geometry; in particular the ant could not detect that the two surfaces have different mean curvatures (see below), which is a purely extrinsic type of curvature.  Formally, Gaussian curvature only depends on the Riemannian metric of the surface. This is Gauss's celebrated Theorema Egregium, which he found while concerned with geographic surveys and mapmaking.  An intrinsic definition of the Gaussian curvature at a point is the following: imagine an ant which is tied to with a short thread of length. It runs around while the thread is completely stretched and measures the length of one complete trip around. If the surface were flat, the ant would find. On curved surfaces, the formula for will be different, and the Gaussian curvature at the point can be computed by the Bertrand–Diguet–Puiseux theorem as  The integral of the Gaussian curvature over the whole surface is closely related to the surface's Euler characteristic; see the Gauss–Bonnet theorem.  The discrete analog of curvature, corresponding to curvature being concentrated at a point and particularly useful for polyhedra, is the (angular) defect; the analog for the Gauss–Bonnet theorem is Descartes' theorem on total angular defect.  Because (Gaussian) curvature can be defined without reference to an embedding space, it is not necessary that a surface be embedded in a higher-dimensional space in order to be curved. Such an intrinsically curved two-dimensional surface is a simple example of a Riemannian manifold.

Mean curvature.

The mean curvature is an "extrinsic" measure of curvature equal to half the sum of the principal curvatures,. It has a dimension of length. Mean curvature is closely related to the first variation of surface area. In particular, a minimal surface such as a soap film has mean curvature zero and a soap bubble has constant mean curvature. Unlike Gauss curvature, the mean curvature is extrinsic and depends on the embedding, for instance, a cylinder and a plane are locally isometric but the mean curvature of a plane is zero while that of a cylinder is nonzero.

Second fundamental form.

The intrinsic and extrinsic curvature of a surface can be combined in the second fundamental form. This is a quadratic form in the tangent plane to the surface at a point whose value at a particular tangent vector to the surface is the normal component of the acceleration of a curve along the surface tangent to ; that is, it is the normal curvature to a curve tangent to (see above). Symbolically, where is the unit normal to the surface. For unit tangent vectors, the second fundamental form assumes the maximum value and minimum value, which occur in the principal directions and, respectively. Thus, by the principal axis theorem, the second fundamental form is Thus the second fundamental form encodes both the intrinsic and extrinsic curvatures.

Shape operator.

An encapsulation of surface curvature can be found in the shape operator,, which is a self-adjoint linear operator from the tangent plane to itself (specifically, the differential of the Gauss map).  For a surface with tangent vectors and normal, the shape operator can be expressed compactly in index summation notation as  The Weingarten equations give the value of in terms of the coefficients of the first and second fundamental forms as The principal curvatures are the eigenvalues of the shape operator, the principal curvature directions are its eigenvectors, the Gauss curvature is its determinant, and the mean curvature is half its trace.

Curvature of space.

By extension of the former argument, a space of three or more dimensions can be intrinsically curved. The curvature is "intrinsic" in the sense that it is a property defined at every point in the space, rather than a property defined with respect to a larger space that contains it. In general, a curved space may or may not be conceived as being embedded in a higher-dimensional ambient space; if not then its curvature can only be defined intrinsically.  After the discovery of the intrinsic definition of curvature, which is closely connected with non-Euclidean geometry, many mathematicians and scientists questioned whether ordinary physical space might be curved, although the success of Euclidean geometry up to that time meant that the radius of curvature must be astronomically large. In the theory of general relativity, which describes gravity and cosmology, the idea is slightly generalised to the "curvature of spacetime"; in relativity theory spacetime is a pseudo-Riemannian manifold. Once a time coordinate is defined, the three-dimensional space corresponding to a particular time is generally a curved Riemannian manifold; but since the time coordinate choice is largely arbitrary, it is the underlying spacetime curvature that is physically significant.  Although an arbitrarily curved space is very complex to describe, the curvature of a space which is locally isotropic and homogeneous is described by a single Gaussian curvature, as for a surface; mathematically these are strong conditions, but they correspond to reasonable physical assumptions (all points and all directions are indistinguishable). A positive curvature corresponds to the inverse square radius of curvature; an example is a sphere or hypersphere. An example of negatively curved space is hyperbolic geometry. A space or space-time with zero curvature is called flat. For example, Euclidean space is an example of a flat space, and Minkowski space is an example of a flat spacetime. There are other examples of flat geometries in both settings, though. A torus or a cylinder can both be given flat metrics, but differ in their topology. Other topologies are also possible for curved space. See also shape of the universe.

Generalizations.

The mathematical notion of "curvature" is also defined in much more general contexts. Many of these generalizations emphasize different aspects of the curvature as it is understood in lower dimensions.  One such generalization is kinematic. The curvature of a curve can naturally be considered as a kinematic quantity, representing the force felt by a certain observer moving along the curve; analogously, curvature in higher dimensions can be regarded as a kind of tidal force (this is one way of thinking of the sectional curvature). This generalization of curvature depends on how nearby test particles diverge or converge when they are allowed to move freely in the space; see Jacobi field.  Another broad generalization of curvature comes from the study of parallel transport on a surface. For instance, if a vector is moved around a loop on the surface of a sphere keeping parallel throughout the motion, then the final position of the vector may not be the same as the initial position of the vector. This phenomenon is known as holonomy. Various generalizations capture in an abstract form this idea of curvature as a measure of holonomy; see curvature form. A closely related notion of curvature comes from gauge theory in physics, where the curvature represents a field and a vector potential for the field is a quantity that is in general path-dependent: it may change if an observer moves around a loop.  Two more generalizations of curvature are the scalar curvature and Ricci curvature. In a curved surface such as the sphere, the area of a disc on the surface differs from the area of a disc of the same radius in flat space. This difference (in a suitable limit) is measured by the scalar curvature. The difference in area of a sector of the disc is measured by the Ricci curvature. Each of the scalar curvature and Ricci curvature are defined in analogous ways in three and higher dimensions. They are particularly important in relativity theory, where they both appear on the side of Einstein's field equations that represents the geometry of spacetime (the other side of which represents the presence of matter and energy). These generalizations of curvature underlie, for instance, the notion that curvature can be a property of a measure; see curvature of a measure.  Another generalization of curvature relies on the ability to compare a curved space with another space that has "constant" curvature. Often this is done with triangles in the spaces. The notion of a triangle makes senses in metric spaces, and this gives rise to spaces.

In mathematics, curvature is any of several strongly related concepts in geometry. Intuitively, the curvature is the amount by which a curve deviates from being a straight line, or a surface deviates from being a plane.

Pojem křivost se používá především v matematice k vyjádření odchylky od přímého směru. Je vyjádřena jako převrácená hodnota poloměru formula_1.


Biography.

McBrain was born in Hackney, London, and first wanted to learn the drums at a young age after watching Joe Morello performing with The Dave Brubeck Quartet on television. At the age of ten, he started to play drums with pots, pans and other kitchen utensils, before, to his parents' dismay, he began drumming on the gas cooker with a pair of knives and chipped off the paintwork. McBrain recalls that he was eleven or twelve before his father bought him his first drum kit, "which was basically one snare, one tom-tom, one cymbal, two drumsticks and a pair of brushes." He soon started playing Rolling Stones and Beatles covers with school bands, before he began regularly playing "pubs and weddings" by the age of 14.  Although he obtained a degree in engineering at Southgate Technical College at his parents' request, upon finishing his education, McBrain paid his rent by undertaking session work, before deciding to join his first "proper" band, "The 18th Fairfield Walk", later known as "Peyton Bond". A small pub band, which he decided was "never gonna go anywhere" as they only performed Otis Redding, The Beatles and The Who covers, McBrain soon left to join "The Wells Street Blues Band", which renamed themselves "The Axe" in 1969. Although this group would play their own material, the band split up after an argument between the singer and the guitarist, and McBrain began playing with Billy Day, a singer and keyboardist, and Michael "Mickey" Lesley, a guitarist, in 1971. At that point, he was known as "Nicky", a nickname given to him by his parents after his teddy bear, Nicholas, until an intoxicated Billy Day introduced him to Dick Asher, head of CBS Records, as "Neeko", while they were recording at CBS Studios, Whitfield Street. McBrain liked the name, changing it to "Nicko" "so that it sounded more English", and decided to keep it even after leaving the group. In 1973, McBrain performed on a single by Cockerel Chorus, "Nice One Cyril", on the label Young Blood.  Also in 1973, McBrain played on a self-titled album by guitarist Gordon Giltrap. This is notable not only as McBrain's album debut, but also because Giltrap in 1978 released an album called "Fear of the Dark" and used a font for his logo that is quite similar to the one used by Iron Maiden.  In 1975, he began playing with Streetwalkers, before joining Pat Travers, singer Jenny Darren, McKitty and then the French band, Trust, with whom he met Iron Maiden for the first time, while touring together in 1981. In 1982, the band asked McBrain to replace their previous drummer, Clive Burr, and, as news of Burr's departure had not yet been announced, McBrain made his first appearance with Iron Maiden on German TV disguised as Eddie. He formed a close partnership with bassist, Steve Harris, and completed what many critics consider the band's "definitive" line-up, releasing a series of gold and platinum selling albums throughout the 1980s.  Although the band's line-up changed during the 1990s, McBrain remained in Iron Maiden and, since the return of Adrian Smith and Bruce Dickinson in 1999, the group has undergone a resurgence in popularity, and are now considered by some as "bigger than ever". When he's not recording and touring with Iron Maiden, McBrain often plays with side projects including a band called McBrain Damage which played Iron Maiden covers. In March 2017, he was a guest drummer with the 8G Band on Late Night with Seth Meyers.  Although he writes the drum parts for all the band's songs, McBrain registered his first and only album songwriting credit for "New Frontier", from 2003's "Dance of Death", which expresses his opposition to human cloning, arising from his religious beliefs. However, McBrain had received two previous songwriting credits for non-album tracks: 1984's "Mission From 'Arry", which was actually a recording of a backstage argument with Steve Harris, and 1992's "Nodding Donkey Blues", which were B-sides of the singles "2 Minutes to Midnight" and "Be Quick or Be Dead", respectively.

Drumming style.

McBrain's drumming has been an important element of Iron Maiden's sound from 1983's "Piece of Mind" onwards, with guitarist Adrian Smith remarking that, "he always had the chops and the technique, but in Maiden he really exploded, to the point where a lot of stuff we did after he joined was then founded on his playing, all those busy patterns he does, displaying tremendous technique." As described in detail on the band's 2004, "Piece of Mind"'s opening track, "Where Eagles Dare", famously displays McBrain's ability to use the single drum pedal very quickly, plus his rapid tom fills.  He is often considered among the best and most influential heavy metal/hard rock drummers of all time. In the 2008 "Live After Death" DVD, Steve Gadd, McBrain's then drum technician, comments that, on the World Slavery Tour, some drummers would refer to McBrain as an 'octopus' after witnessing the way in which his stamina gives him the ability to use all of his large signature drum kit in concert.  McBrain often employs the back end of his left hand drum stick to allow for more powerful "snare hits". He is known for not using a double bass pedal, with Bruce Dickinson commenting that he refused to use one on "Where Eagles Dare", considering them 'undrummerish'. He claims to have only ever used a double pedal once on "Face in the Sand", from "Dance of Death", preferring to use a DW 5000 Accelerator single pedal. Since switching to the DW pedal in 2000, McBrain plays barefoot, stating that it gives him "more freedom."  Steve Harris remarks that "...he can play all kinds of music. Drummers from other bands sit round the back of him to see what he's doing, but he's got his kit set so he doesn't even look at what he's hitting half the time". After McBrain joined the band in 1982, Harris also noted how much easier playing with McBrain was for a songwriter, with Adrian Smith claiming that, "Steve loves playing with him. [They] used to work for hours going over these bass and drum patterns."  In 1988, McBrain collaborated with Andrew Chapman on a book entitled "Iron Maiden & Nicko McBrain's Rhythms of the Beast", which was published by Warner Bros. Music in 1990. The book featured complete transcriptions of McBrain's drum work on twelve classic Iron Maiden songs, including six live versions as recorded on the band's 1985 album "Live After Death". After selling internationally for several years, the book was taken out of print. Used copies are occasionally found for sale online.  In 1991, McBrain released an instructional drum video, entitled "Rhythms of the Beast" (not related to the above book of the same name), which was re-released on DVD in 2010. The video features McBrain demonstrating his technique, and covers tuning, soloing and parts of the drum kit.

Equipment.

McBrain is a long-time user of Paiste cymbals and currently plays British Drum Company drums, moving from Sonor Drums and having previously endorsed Premier. For "A Matter of Life and Death" he used his Ludwig metal shell LM 402 snare drum which was purchased in 1975, making it the oldest drum in his kit. He endorses Vic Firth signature drum sticks, also using them for his own drumming. As of 2016, McBrain also uses Remo drumheads, Sonor hardware, an LP cowbell and a DW 9000 single pedal (painted gold).

Tour Kit.

Sonor SQ2 Custom Drum Kit  Sticks Cymbals by Paiste:  McBrain's cymbals do not bear the standard Paiste logos. They are labelled with the brand name using the Iron Maiden logo font.

Previous kits.

Premier Elite Drums with custom finish (2010):  Sonor Phonic Plus High Tech Drums (1986–87):

Personal life.

McBrain is married to Rebecca McBrain (née Dempsy) and has two sons: Nicholas (born 1983) and Justin (born 1992). He lives in Boca Raton, Florida.  McBrain converted to Christianity in 1999 after an experience in the Spanish River Church, near his Boca Raton home. His wife, Rebecca, had been asking him to attend with her, and upon entering the church, McBrain soon found himself crying as he experienced a "calling". Recounting the tale, he said "I just sat there thinking, 'I didn't drink last night... why can't I stand?' I had this love affair with Jesus going on in my heart."  In 1988, McBrain appeared as a guest on "The Sooty Show", in which he played drums with Sooty and Sweep. In reference to his appearance on the show, McBrain's drum kit has since been decorated with a Sooty puppet, which is often dressed accordingly with the band's corresponding tours.  McBrain has a pilot's licence, for which he has a twin engine rating.  In 2009, he opened a restaurant called Rock 'N' Roll Ribs in Coral Springs, Florida. The restaurant received positive reviews on an episode of "Check, Please! South Florida" and was awarded "Best Ribs of 2012" by "New Times Broward-Palm Beach".  McBrain is a fan of snooker and has attended the World Snooker Championships at the Crucible Theatre, Sheffield. He also enjoys playing golf in his spare time, along with his bandmate Dave Murray, and is a friend of Swedish golfer and Florida resident Jesper Parnevik, whom he met at Ullna Golf Club in Sweden.  Since he is a lifelong enthusiast of Jaguar Cars, the manufacturer built a custom XKR-S model to McBrain's specifications in 2012. In March 2018, "Jaguar Land Rover Classic Works" revealed a customized Jaguar XJ Series III for McBrain.  In 2015, McBrain stopped drinking alcohol after seeing an interview in which he had had too much wine and has remained sober to this day.  In 2018, he also launched a musical instrument store named Drum One in Manchester, England. The retailer specialises in drum kits and related merchandise. To promote the launch of the store, McBrain conducted an interview with Deep Purple drummer Ian Paice

Michael Henry "Nicko" McBrain (born 5 June 1952) is an English musician and drummer of the British heavy metal band Iron Maiden, which he joined in 1982. Having played in small pub bands from the age of 14, after graduating school McBrain paid his bills with session work before he joined a variety of artists, such as Streetwalkers, Pat Travers, and the French political band, Trust. He joined Iron Maiden in time to debut on their fourth album (replacing Clive Burr), "Piece of Mind" (1983), and has remained with them since, contributing to a total of thirteen studio releases.

Michael Henry McBrain (* 5. června 1952 Hackney, Londýn) je britský bubeník a skladatel heavymetalové skupiny Iron Maiden. V 70. letech se objevil na několika albech Pata Traverse a mezi lety 1975 a 1976 také hrál se skupinou Streetwalkers. Na začátku 80. let hrál v kapele McKitty. Během vystoupení skupiny McKitty v Belgii se poprvé setkal s baskytaristou Stevem Harrisem z Iron Maiden, Harrisovi se líbilo jeho bubenické sólo, které vystřihl při poruše McKittyho kytary. K Iron Maiden se připojil roku 1983 (album Piece of Mind), kde nahradil Cliva Burra. Nicko McBrain se také často objevuje v horních tabulkách různých žebříčků o bubenících, díky jeho schopnostem ve studiu i na pódiu. V žebříčku časopisu "Rhythm" 50 největších bubeníků všech dob dosáhl 18. pozice.


History.

Prehistory.

The phenomenon of the shadow has always aroused human curiosity and inspired artistic representation, as recorded by Pliny the Elder, and various forms of shadow play since the 1st millennium BCE. The photogram in essence is a means by which the fall of light and shade on a surface may be automatically captured and preserved. To do so required a substance that would react to light, and from the 17th century photochemical reactions were progressively observed or discovered in salts of silver, iron, uranium and chromium. In 1725 Johann Heinrich Schulze was the first to demonstrate a temporary photographic effect in silver salts, confirmed by Carl Wilhhelm Scheele in 1777, who found that violet light caused the greatest reaction in silver chloride. Humphry Davy and Thomas Wedgewood reported that they had produced pictures from stencils on leather and paper, but had no means of fixing them and some organic substances respond to light, as evidenced in sunburn (an effect used by Dennis Oppenheim in his 1970 "Reading Position for Second Degree Burn") and photosynthesis (with which Lloyd Godman forms images).

Nineteenth century.

The first photographic negatives made were photograms (though the first permanent photograph was made with a camera by Niécephore Niépce). William Henry Fox Talbot called these "photogenic drawings", which he made by placing leaves or pieces of lace onto sensitized paper, then left them outdoors on a sunny day to expose. This produced a dark background with a white silhouette of the placed object.  As an advance on the ancient art of nature prints, in which specimens were inked to make an impression on paper, from 1843, Anna Atkins produced a book titled "British Algae: Cyanotype Impressions" in instalments; the first to be illustrated with photographs. The images were all photograms of botanical specimens, mostly seaweeds, which she made using Sir John Herschel's cyanotype process, which yields blue images. This very rare book can be seen in the National Media Museum in Bradford, England.

Modernism.

In Modernism, and especially in Dada and Constructivism and in the formalist dissections of the Bauhaus, the photogram enabled experiments in abstraction by Christian Schad as early as 1918, Man Ray in 1921, and Moholy-Nagy in 1922, through dematerialisation and distortion, merging and interpenetration of forms, and flattening of perspective.

Christian Schad's'schadographs'.

In 1918 Christian Schad's experiments with the photogram were inspired by Dada, creating photograms from random arrangements of discarded objects he had collected such as torn tickets, receipts and rags. Some argue that he was the first to make this an art form, preceding Man Ray and László Moholy-Nagy by at least a year or two, and one was published in March 1920 in the magazine "Dadaphone" by Tristan Tzara, who dubbed them 'Schadographs'.

Man Ray's 'rayographs'.

Photograms were used in the 20th century by a number of photographers, particularly Man Ray, whose "rayographs" were also given the name by Dada leader Tzara. Ray described his (re-)discovery of the process in his 1963 autobiography;  In his photograms, Man Ray made combinations of objects—a comb, a spiral of cut paper, an architect’s French curve—some recognisable, others transformed, typifying Dada's rejection of'style', emphasising chance and abstraction. He published a selection of these rayographs as "Champs délicieux" in December 1922, with an introduction by Tzara. His 1923 film "Le Retour à la Raison" ('Return to Reason') adapts rayograph technique to moving images.

Other 20th century artists.

In the 1930s artists including Theodore Roszak, and Piet Zwart made photograms while Luigi Veronesi combined the photographic image with oil on canvas in large-scale colour images by preparing a light-sensitive canvas on which he placed objects in the dark for exposure and then fixing. The shapes became the matrix for an abstract painting to which he applied colour and added drawn geometric lines to enhance the dynamics, exhibiting them at the Galerie L’Equipe in Paris in 1938-1939. Bronislaw Schlabs, Julien Coulommier, Andrzej Pawlowski, Beksinki and Kurt Wendlandt were photogram artists in the 1940s and 1950s; Lina Kolarova, Rene Mächler, and Andreas Mulas in the 1970s; and Tony Ceballos, Kare Magnole, Andreas Müller-Pohle, and Floris M. Neusüss in the 1980s.

Contemporary.

Established contemporary artists who are widely known for using photograms are Adam Fuss, Susan Derges and Christian Marclay, and younger artists worldwide continue to value the materiality of the technique in the digital age.

Procedure.

The customary approach to making a photogram is to use a darkroom and enlarger and to proceed as one would in making a conventional print, but instead of using a negative, to arrange objects on top of a piece of photographic paper for exposure under the enlarger lamp which can conveniently be controlled with the timer switch and aperture controls. That will give a result similar to the image at left; since the enlarger emits light through a lens aperture, the shadows of even tall objects like the beaker standing upright on the paper will stay sharp; the more so at smaller apertures.  The print is then processed, washed, and dried.  At this stage the image will look similar to a negative, in which shadows are white. A contact-print onto a fresh sheet of photographic paper will reverse the tones if a more naturalistic result is desired, which may be facilitated by making the initial print on film.  However, there are other arrangements for making photograms, and devising them is part of the creative process. Alice Lex-Nerlinger used the conventional darkroom approach in making photograms as a variation on her airbrushed stencil paintings, since lighting penetrating the translucent paper from which she cut her pictures would print a variegated texture she could not otherwise obtain.  One variable is the light source, or sources, used. A broad source of light will cast nuances of shadow; umbra, penumbra and antumbra, as shown in the accompanying diagram.  Photograms may be made outdoors providing the photographic emulsion is sufficiently slow to permit it. Direct sunlight is a point-source of light (like that of an enlarger), while cloudy conditions give soft-edged shadows around three-dimensional objects placed on the photosensitive surface. The cyanotype process ('blueprints') such as that used by Anna Atkins (see above), is slow and insensitive enough that coating it on paper, fabric, timber or other supports can be done in subdued light indoors. Exposure outdoors may take many minutes depending on conditions, and its progress may be gauged by inspection as the coating darkens. 'Printing-out paper' or other daylight-printing material such as gum bichromate may also enable outdoor exposure. Christian Schad simply placed tram tickets and other ephemera under glass on printing-out paper on his window-sill for exposure.  Conventional monochrome or colour, or direct-positive photographic material may be exposed in the dark using a flash unit, as does Adam Fuss for his photograms that capture the movement of a crawling baby, or an eel in shallow water. Susan Derges captures water currents in the same way, while Harry Nankin has immersed large sheets of monochrome photographic paper at the edge of the sea and mounted a flash on a specially-constructed oversize tripod above it to capture the action of waves and seaweeds washing over the paper surface.  Other variations include using the light of a television screen or computer display, pressing the photosensitive paper to the surface. Multiple light sources or exposing with multiple flashes of light, or moving the light source during exposure, projecting shadows from a low-angle light, and using successive exposures while moving, removing or adding shadows, will produce multiple shadows of varying quality.

A photogram [from the combining form φωτω- (phōtō-) of Ancient Greek φῶς (phôs, “light”), and Ancient Greek suffix -γραμμα (-gramma), from γράμμα (grámma, “written character, letter, that which is drawn”), from γράφω (gráphō, “to scratch, to scrape, to graze”)] is a photographic image made without a camera by placing objects directly onto the surface of a light-sensitive material such as photographic paper and then exposing it to light.

Fotogram je umělecká fotografická technika bez fotografického optického přístroje – fotoaparátu. Jde o stínový obraz vytvořený tak, že autor v temné komoře umístí pod zvětšovací přístroj nebo jiný zdroj světla neexponovaný fotopapír (resp. jakýkoliv světlocitlivý materiál), na kterém vytvoří kompozici z různě průsvitných předmětů. Po osvícení papíru, jeho vyvolání a ustálení vznikne obraz, kde na černém pozadí vystupují bílé, případně šedé předměty – podle délky expozice a průhlednosti předmětů.


Etymology.

The name is thought to derive from an Old Slavic word "sopot" meaning "stream" or "spring". The same root occurs in a number of other Old Slavic toponyms; it is probably onomatopeic, imitating the sound of running water - murmur ("Šepot").  The name is first recorded as "Sopoth" in 1283 and "Sopot" in 1291. The German "Zoppot" is directly derived from the original name. In the 19th century and in the interwar years the German name was re-Polonized as "Sopoty" (a plural form, closer to the German pronunciation). "Sopot" was made the official Polish name when the town came again under Polish rule in 1945.

History.

Early history.

The area of today's Sopot contains the site of a 7th-century Slavonic (Pomeranian) stronghold. Initially it was a commercial trade outpost for commerce extending both up the Vistula river and to cities north across the Baltic Sea. With time the significance of the stronghold diminished and by the 10th century it was reduced to a fishing village, eventually abandoned. However, a century later the area was settled again and two villages were founded within the borders of today's' city: Stawowie and Gręzowo. They were first mentioned in 1186 as being granted to the Cistercian abbey in Oliwa. Another of the villages that constitute today's Sopot, Świemirowo, was first mentioned in 1212 in a document by Mestwin I, who granted it to the Premonstratensian (Norbertine) monastery in nearby Żukowo.  The village of Sopot, which later became the namesake for the whole city, was first mentioned in 1283 when it was granted to the Cistercians. At that time it was part of Poland until the 14th-century Teutonic invasion.By 1316, the abbey had bought all villages in the area and became the owners of all the area of the city. After the Second Peace of Thorn (1466) the area was reincorporated into the Kingdom of Poland.

Polish-Lithuanian Commonwealth.

The spa for the citizens of Gdańsk has been active since the 16th century. Until the end of that century most noble and magnate families from Gdańsk built their manor houses in Sopot. During the negotiations of the Treaty of Oliva King John II Casimir of Poland and his wife Queen Marie Louise Gonzaga lived in one of them, while Swedish negotiator Magnus de la Gardie resided in another — it has been known as the "Swedish Manor" ("Dwór Szwedzki") ever since. The Swedish Manor was later the place of stay of Polish Kings Augustus II the Strong (in 1710) and Stanisław Leszczyński (in 1733).  During the 1733 War of the Polish Succession, Stanisław Leszczyński stayed in Sopot a few days before going to the nearby city of Gdańsk. Afterwards Imperial Russian troops besieged Gdańsk and a year later looted and burned the village of Sopot to the ground. Much of Sopot would remain abandoned during and in the following years after the conflict, as the patricians of Gdańsk, exhausted by the war, could not afford to rebuild the Sopot residences.  In the 1750s, Polish nobility of Pomerania began to rebuild the village. In 1757 and 1758 most of the ruined manors were bought by the magnate family of Przebendowski. General Józef Przebendowski bought nine of these palaces and in 1786 his widow, Bernardyna Przebendowska (née von Kleist), bought the remaining two. Also the Sierakowski family acquired some properties, including the destroyed Swedish Manor. After the Partitions of Poland, in the 1790s, Count built the Sierakowski Mansion at the site of the Swedish Manor, a typical Polish manor house, which remains one of the most distinctive buildings of pre-spa Sopot.

Kingdom of Prussia.

Sopot was annexed by the Kingdom of Prussia in 1772 in the First Partition of Poland. Following the new laws imposed by King Frederick the Great, church property was confiscated by the state. The village was still being reconstructed and in 1806 the area was sold to the Danzig/Gdańsk merchant Carl Christoph Wegner. However, until 1819 it did not develop significantly, its population in 1819 was 350, compared to 301 in the year of Prussian annexation. In 1819, Wegner opened the first public bath in Zoppot and tried to promote the newly established spa among the inhabitants of Danzig (Gdańsk), but the undertaking was a financial failure. However, in 1823 Dr. Jean Georg Haffner, a former medic of the French army, financed a new bath complex that gained significant popularity. In the following years, Haffner erected more facilities. By 1824, a sanatorium was opened to the public, as well as a 63-metre pier, cloakrooms, and a park. Haffner died in 1830, but his enterprise was continued by his stepson, Ernst Adolf Böttcher. The latter continued to develop the area and in 1842 opened a new theatre and sanatorium. By then the number of tourists coming to Zoppot every year had risen to almost 1,200.  In 1870 Zoppot saw the opening of its first rail line: the new Danzig-Kołobrzeg (then "Kolberg") rail road that was later extended to Berlin. Good rail connections added to the popularity of the area and by 1900 the number of tourists had reached almost 12,500 a year.  In 1873, the village of Zoppot became an administrative centre of the Gemeinde. Soon other villages were incorporated into it and in 1874 the number of inhabitants of the village rose to over 2,800. In 1877, the self-government of the Gemeinde bought the village from the descendants of Dr. Haffner and started its further development. A second sanatorium was constructed in 1881 and the pier was extended to 85 metres. In 1885, the gas works were built. Two years later, tennis courts were built and the following year a horse-racing track was opened to the public. There were also several facilities built for the permanent inhabitants of Zoppot, not only for the tourists. Among those were two new churches: Protestant (September 17, 1901) and Catholic (December 21, 1901). From the late 19th century, there was a significant influx of German settlers with the slow growth of the Polish population, resulting in a change in ethnic proportions in favor of the former. Since the late 19th century the city became a holiday resort for the inhabitants of nearby Danzig, as well as wealthy aristocrats from Berlin, Warsaw, and Königsberg. Poles visited the city in large numbers and the spa was very popular among the Polish intellectual elite, to the extent that the early 20th-century Polish writer named it "the extension of Warsaw to the Baltic Sea". Germans and Russians also visited the city. At the beginning of the 20th century it was a favourite spa of Emperor Wilhelm II of Germany. On October 8, 1901, Wilhelm II granted Zoppot city rights, spurring further rapid growth. In 1904 a new balneological sanatorium was opened, followed in 1903 by a lighthouse. In 1907, new baths south of the old ones were built in Viking style. In 1909 a new theatre was opened in the nearby forest within the city limits, in the place where today the Sopot Festival is held every year. By 1912, a third complex of baths, sanatoria, hotels, and restaurants was opened, attracting even more tourists. Shortly before World War I the city had 17,400 permanent inhabitants and over 20,000 tourists every year.

Free City of Danzig.

Following the signing of the Treaty of Versailles in 1919, Zoppot became a part of the Free City of Danzig in customs union with the re-established Polish Republic. Due to the proximity of the Polish and German borders, the economy of the town soon recovered. The new casino became one of the main sources of income of the free-city state. In 1927, the city authorities rebuilt the Kasino-Hotel, one of the most notable landmarks in Sopot today. After World War II, it was renamed as the Grand Hotel and continues to be one of the most luxurious hotels in Poland.  A Richard Wagner festival was held in the nearby Forest Opera in 1922. The festival's success caused Zoppot to be sometimes referred to as the "Bayreuth of the North". As a result of the influx of Germans in the previous decades, who took over the most important functions in the city, some Poles became Germanized, however a significant indigenous Polish community was still present in the city, and there was also a Jewish community. In 1928, the pier was extended to its present length of 512 metres. Since then it has remained the longest wooden pier in Europe and one of the longest in the world. In 1928, the city was visited 29,192 visitors, mostly Poles and in the early 1930s it reached the peak of its popularity among foreign tourists — more than 30,000 annually (this number does not include tourists from Danzig itself). However, by the 1930s, tensions on the nearby Polish-German border and the rising popularity of Nazism in Germany and also among local Germans saw a decline in foreign tourism. The Nazi Party, supported by many local Germans, took power in the city. Local Poles and Jews were discriminated against and in 1938 local German Nazis burned down Zoppot's synagogue.

World War II (1939-1945).

World War II broke out on September 1, 1939 after the German invasion of Poland. The following day the Free City of Danzig was annexed by Nazi Germany and most of the local Poles, Kashubians, and Jews were arrested and murdered during the "Intelligenzaktion", imprisoned or expelled. Due to the war, the city's tourist industry collapsed. The last Wagner Festival was held in 1942. The city remained under German rule until early 1945. In March the Nazis began evacuating the German population along with forced laborers. On March 23, 1945, the Soviet Army took over the city after several days of fighting, in which Zoppot lost approximately 10% of its buildings.  As per the Potsdam Conference, Zoppot was incorporated into the post-war Polish state and renamed Sopot. The authorities of Gdańsk Voivodeship were located in Sopot until the end of 1946. Most of the German inhabitants who had remained in the city, by 1 November 1945 6.000 Germans still lived in the town, after the evacuation before the advancing Red Army were soon to be expelled, to make room for Polish settlers from former eastern Polish territories annexed by the Soviet Union.

Polish People's Republic (1945-1989).

Sopot recovered rapidly after the war. A tramway line to Gdańsk was opened, as well as the School of Music, the School of Maritime Trade, a library, and an art gallery. During the city presidency of Jan Kapusta the town opened an annual Arts Festival in 1948. In 1952, the tramways were replaced by a heavy-rail commuter line connecting Gdańsk, Sopot, and Gdynia. Although in 1954 the School of Arts was moved to Gdańsk, Sopot remained an important centre of culture, and in 1956 the first Polish jazz festival was held there (until then jazz had been banned by the Communist authorities). This was the forerunner of the continuing annual Jazz Jamboree in Warsaw.  In 1961, the Sopot International Song Festival was inaugurated, although it was held in Gdańsk for its first three years – it moved to its permanent venue at Sopot's Forest Opera in 1964. In 1963, the main street of Sopot ("Bohaterów Monte Cassino", "the Heroes of Monte Cassino") was turned into a pedestrian-only promenade.  New complexes of baths, sanatoria, and hotels were opened in 1972 and 1975. By 1977, Sopot had approximately 54,500 inhabitants, the highest ever in its history. In 1979, the historical town centre was declared a national heritage centre by the government of Poland.

Third Polish Republic (1989 onwards).

In 1995, the southern bath and sanatoria complex were extended significantly and the Saint Adalbert spring opened two years later, as a result in 1999 Sopot regained its official spa town status. In 1999, Pope John Paul II visited Sopot, about 800,000 pilgrims attended his mass.  In 2001, Sopot celebrated the 100th anniversary of its city charter.  Sopot is currently undergoing a period of intense development, including the building of a number of five star hotels and spa resorts on the waterfront. The main pedestrianized street, Monte Cassino, has also been extended by diverting traffic underneath it, meaning the whole street is now pedestrianized. Sopot, aside from Warsaw boasts the highest property prices in Poland.

Sights and attractions.

Among the historic sights are:  Other landmarks include:

Politics and local government.

Districts.

Sopot is divided into 16 administrative divisions:

Transport.

The city is covered by both the Gdynia and Gdańsk municipal bus lines, the regional commuter rail line (with three stops in the city: Sopot Wyścigi, Sopot, and Sopot Kamienny Potok), and the Polish national railway, PKP. Sopot is one of four Polish towns to have trolleybuses. The others are Lublin, Tychy and Gdynia.

Sports.

There are many popular professional sports teams in Sopot and the tri-city area. The most popular in Sopot today is probably basketball thanks to the award-winning Prokom Trefl Sopot. Amateur sports are played by thousands of Sopot citizens, as well as in schools of all levels (elementary, secondary, and university). Sopot held the IAAF World Indoor Championships in 2014.

International relations.

Sopot is twinned with:

Sopot (Kashubian: "Sopòt"; German: "Zoppot", ) is a seaside resort city in Eastern Pomerania on the southern coast of the Baltic Sea in northern Poland, with a population of approximately 40,000.

Sopoty, ( nebo také "Sopòt nebo" "Copòt", což znamená „bláto“; ) je město v severním Polsku v Pomořském vojvodství u Gdaňského zálivu Baltského moře mezi městy Gdaňsk a Gdyně, se kterými tvoří tzv. Trojměstí.