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The Open Championship

The Open Championship, often referred to as The Open or the British Open, is the oldest golf tournament in the world, and one of the most prestigious. Founded in 1860, it was originally held annually at Prestwick Golf Club in Scotland. Later the venue rotated between a select group of coastal links golf courses in the United Kingdom. It is organised by The R&A.

The Open is one of the four men's major golf championships, the others being the Masters Tournament, the PGA Championship and the U.S. Open. Since the PGA Championship moved to May in 2019, the Open has been chronologically the fourth and final major tournament of the year. It is held in mid-July.

It is called The Open because it is in theory "open" to all, i.e. professional and amateur golfers. In practice, the current event is a professional tournament in which a small number of the world's leading amateurs also play, by invitation or qualification. The success of the tournament has led to many other open golf tournaments to be introduced around the world.

The winner is named "the Champion Golfer of the Year", a title that dates to the first Open in 1860, and receives the Claret Jug, a trophy first awarded in 1872. The reigning champion is American Brian Harman, who won the 2023 Open at Royal Liverpool Golf Club with a score of 271.

Early tournament years (1860–1870)
The first Open Championship was played on 17 October 1860 at Prestwick Golf Club in Ayrshire, Scotland, over three rounds of the twelve-hole links course. In the mid-19th century golf was played mainly by well-off gentlemen, as hand-crafted clubs and balls were expensive. Professionals made a living from playing for bets, caddying, ball and club making, and instruction. Allan Robertson was the most famous of these pros, and was regarded as the undisputed best golfer between 1843 and his death in 1859. James Ogilvie Fairlie of Prestwick Golf Club decided to form a competition in 1860, "to be played for by professional golfers", and to decide who would succeed Robertson as the "Champion Golfer". Blackheath (England), Perth, Bruntsfield (Edinburgh), Musselburgh and St Andrews golf clubs were invited to send up to three of their best players known as a "respectable caddie" to represent each of the clubs. The winner received the Challenge Belt, made from red leather with a silver buckle and worth £25, which came about thanks to being donated by the Earl of Eglinton, a man with a keen interest in medieval pageantry (belts were the type of trophy that might have been competed for in archery or jousting).

The first rule of the new golf competition was "The party winning the belt shall always leave the belt with the treasurer of the club until he produces a guarantee to the satisfaction of the above committee that the belt shall be safely kept and laid on the table at the next meeting to compete for it until it becomes the property of the winner by being won three times in succession". Eight golfers contested the event, with Willie Park, Sr. winning the championship by 2 shots from Old Tom Morris, and he was declared "The Champion Golfer of the Year".

A year later, it became "open" to amateurs as well as professionals. Ten professionals and eight amateurs contested the event, with Old Tom Morris winning the championship by 4 shots from Willie Park, Sr. A prize fund (£10) was introduced in 1863 split between 2nd, 3rd and 4th (the winner only received the Challenge Belt). From 1864 onwards a cash prize was also paid to the winner. Before this the only financial incentive was scheduling Prestwick's own domestic tournament the same week, this allowed professionals to earn a few days' work caddying for the wealthier gentlemen. Willie Park, Sr. went on to win two more tournaments, and Old Tom Morris three more, before Young Tom Morris won three consecutive titles between 1868 and 1870. The rules stated that he was allowed to keep the belt for achieving this feat. Because no trophy was available, the tournament was not held in 1871.

The introduction of course rotation and the Claret Jug (1872–1889)
On 11 September 1872 agreement was reached between Prestwick, the Honourable Company of Edinburgh Golfers and The Royal and Ancient Golf Club. They decided that each of the three clubs would contribute £10 towards the cost of a new silver trophy, which became known as the Claret Jug, known officially as The Golf Champion Trophy, and hosting of the Open would be rotated between the three clubs. These decisions were taken too late for the trophy to be presented to the 1872 Open champion, who was once again Young Tom Morris. Instead, he was awarded with a medal inscribed 'The Golf Champion Trophy', although he is the first to be engraved on the Claret Jug as the 1872 winner. Medals have been given to, and kept by the winner ever since. Young Tom Morris died in 1875, aged 24.

The tournament continued to be dominated and won by Scottish professionals, to be rotated between the three Scottish golf courses, and played over 36 holes in a single day until 1889.

English hosts and winners, and the Great Triumvirate (1890–1914)
In the 1890s, the tournament was won four times by three Englishman (two of whom were amateurs). In 1892 the tournament was played for the first time at the newly built Muirfield, which replaced Musselburgh as the host venue used by the Honourable Company of Edinburgh Golfers. A few years later St George's and Royal Liverpool in England were added to the rotation. From 1892 the tournament was increased in duration to four 18-hole rounds over two days (Prestwick had been extended to an 18-hole course by then ).

Between 1898 and 1925 the tournament either had a cut after 36 holes, or a qualifying event, and the largest field was 226 in 1911. The large field meant sometimes the tournament was spread across up to four days. In 1907 Arnaud Massy from France became the first non-British winner. Royal Cinque Ports in England became the 6th different Open host course in 1909.

The pre-war period is most famous for the Great Triumvirate of Harry Vardon (Jersey), John Henry Taylor (England), and James Braid (Scotland). The trio combined to win The Open Championship 16 times in the 21 tournaments held between 1894 and 1914; Vardon won six times (a record that still stands today) with Braid and Taylor winning five apiece. In the five tournaments in this span the Triumvirate did not win, one or more of them finished runner-up. These rivalries enormously increased the public's interest in golf, but the First World War meant another Open was not held until 1920, and none of the trio won another Open.

American success with Walter Hagen and Bobby Jones, and the last Open at Prestwick (1920–1939)
In 1920 the Open returned, and The Royal and Ancient Golf Club became the sole organiser of the Open Championship. In 1926 they standardised the format of the tournament to spread over three days (18 holes on day 1 and 2, and 36 on day 3), and include both qualifying and a cut.

In 1921 eleven U.S.-based players travelled to Scotland financed by a popular subscription called the "British Open Championship Fund", after a campaign by the American magazine Golf Illustrated. Five of these players were actually British born, and had emigrated to America to take advantage of the high demand for club professionals as the popularity of golf grew. A match was played between the Americans and a team of British professionals, which is seen as a forerunner of the Ryder Cup. When the Open was held two weeks later, one of these visitors, Jock Hutchison, a naturalised American citizen, won in St Andrews, the town of his birth.

In 1922 Walter Hagen won the first of his four Opens, and become the first American-born winner. The period between 1923 and 1933 saw an American-based player win every year (two were British-born), and included three wins by amateur Bobby Jones, and one by Gene Sarazen, who had already won top tournaments in the United States. English players won every year between 1934 and 1939, including two wins by Henry Cotton (he would go on to win a third in 1948).

After overcrowding issues at the 1925 Open at Prestwick, it was decided it was no longer suitable for the growing size of the event, being too short, having too many blind shots, and it could not cope with the volume of spectators. The Open's original venue was replaced on the rota with Carnoustie, which hosted for the first time in 1931. Troon hosted for the first time in 1923, and Royal Lytham & St Annes was also added, hosting for the first time in 1926. Prince's hosted its one and only Open in 1932.

Bobby Locke, Peter Thomson, and Ben Hogan's Triple Crown (1946–1958)
The Open returned after the Second World War to St Andrews, with a victory for American Sam Snead. Bobby Locke became the first South African winner, winning three times in four years between 1949 and 1952, and later winning a fourth title in 1957. Having already won the Masters and the U.S. Open earlier in the year, Ben Hogan won in his one and only Open appearance in 1953 to win the "Triple Crown". His achievement was so well regarded he returned to New York City to a ticker-tape parade. Peter Thomson became the first Australian winner, winning four times in five years between 1954 and 1958, and later winning a fifth title in 1965. After flooding prevented Royal Cinque Ports from hosting, both in 1938 and 1949, it was removed from the rota. The Open was played outside of England and Scotland for the first time in 1951 at Royal Portrush, Northern Ireland.

The period saw fewer American entrants, as the PGA Tour had grown to be quite lucrative, and the PGA Championship was often played at the same or similar time paying triple the prize money. A larger golf ball was also used in America, which meant they had to adjust for the Open.

Player, Palmer, Nicklaus – The Big Three (1959–1974)
In 1959, Gary Player, a young South African, won the first of his three Opens. Only four Americans had entered, but in 1960 Arnold Palmer travelled to Scotland after winning the Masters and U.S. Open, in an attempt to emulate Hogan's 1953 feat of winning all three tournaments in a single year. Although he finished second to Kel Nagle, he returned and won the Open in 1961 and 1962. Palmer was hugely popular in America, and his victories are likely to have been the first time many Americans would have seen the Open on television. This, along with the growth of trans-Atlantic jet travel, inspired many more Americans to travel in the future.

The period is primarily defined by the competition between Player, Palmer, and Jack Nicklaus. Nicklaus won three times (1966, 1970, 1978) and had a record seven runner-ups. American Lee Trevino also made his mark winning his two Opens back to back in 1971 and 1972, the latter denying Nicklaus a calendar year Grand Slam. The only British champion in this period was Tony Jacklin, and it is also notable for having the first winner from Argentina, Roberto De Vicenzo.

Watson, Ballesteros, Faldo, and Norman (1975–1993)
By 1975, the concept of the modern majors had been firmly established, and the PGA Championship had been moved to August since 1969, so no longer clashed with the Open. This meant the Open had a feel similar to the current tournament, with the leaders after 36 holes going off last (1957 onwards), all players having to use the "bigger ball" (1974 onwards), play spread over four days (1966 onwards, although the days were Wednesday to Saturday until 1980),  and a field containing all the world's best players.

American Tom Watson won in 1975. Turnberry hosted for the first time in 1977, and Watson won the Open for the second time, after one of the most celebrated contests in golf history, when his duel with Jack Nicklaus went to the final shot before Watson emerged as the champion. He would go on to win again in 1980, 1982 and 1983, to win 5 times overall, a record only bettered by Harry Vardon, and he became regarded as one of the greatest links golf players of all time.

In 1976, 19-year-old Spaniard Seve Ballesteros gained attention in the golfing world when he finished second. He would go on to win three Opens (1979, 1984, 1988), and was the first continental European to win since Arnaud Massy in 1907. Other multiple winners in this period were Englishman Nick Faldo with three (1987, 1990, 1992), and Australian Greg Norman with two (1986, 1993).

Tiger Woods and the modern era (1994 onwards)
Every year between 1994 and 2004 had a first-time winner. In 1999, the Open at Carnoustie was famously difficult, and Frenchman Jean van de Velde had a three-shot lead teeing off on the final hole. He ended up triple bogeying after finding the Barry Burn, and Scotman Paul Lawrie, ranked 241st in the world, ended up winning in a playoff. He was 10 strokes behind the leader going into the final round, a record for all majors. He was not the only unheralded champion during this span, as 396th-ranked Ben Curtis and 56th-ranked Todd Hamilton won in 2003 and 2004, respectively.

In 2000, Tiger Woods, having just won the U.S. Open, became champion by a post-war record 8 strokes to become the youngest player to win the career Grand Slam at age 24. After winning the 2002 Masters and U.S. Open, he became the latest American to try to emulate Ben Hogan and win the Open in the same year. His bid came to a halt on Saturday with the worst round of his career up to that time, an 81 (+10) in cold, gusty rain. He went on to win again back-to-back in 2005 and 2006 to bring his total to three wins. Other multiple winners in this era are South African Ernie Els (2002, 2012) and Irishman Pádraig Harrington (2007, 2008).

In 2009, 59-year-old Tom Watson led the tournament through 71 holes and needed just a par on the last hole to become the oldest ever winner of a major championship, and also match Harry Vardon's six Opens. Watson bogeyed, setting up a four-hole playoff, which he lost to Stewart Cink. In 2015, Jordan Spieth became another American to arrive having already won the year's Masters and U.S. Open tournaments. He finished tied for fourth as Zach Johnson became champion. Spieth would go on to win the 2017 Open at Royal Birkdale.

American Phil Mickelson won his first Open, and fifth major, in 2013. In 2016, he was involved in an epic duel with Sweden's Henrik Stenson, which many people compared to the 1977 Duel in the Sun between Jack Nicklaus and Tom Watson. Stenson emerged the winner, and the first Scandinavian winner of a male professional major championship, with a record Open (and major) score of 264 (−20), three shots ahead of Mickelson, and 14 shots ahead of third place. Jack Nicklaus shared his thoughts on the final round, saying: "Phil Mickelson played one of the best rounds I have ever seen played in the Open and Henrik Stenson just played better—he played one of the greatest rounds I have ever seen".

Francesco Molinari won the 2018 Open at Carnoustie by two shots, to become the first Italian major winner. Shane Lowry won the 2019 Open when the tournament returned to Royal Portrush Golf Club, to become the second champion from the Republic of Ireland.

In 2020, the Open Championship was cancelled because of the COVID-19 pandemic. It was the first time the championship had been cancelled since World War II. The R&A also confirmed that Royal St George's, which would have hosted the championship in 2020, would be the host venue in 2021, effectively retaining the Old Course at St Andrews as the venue for the 150th Open.

Links golf course
The Open is always played on a coastal links golf course. Links golf is often described as the "purest" form of golf and keeps a connection with the way the game originated in Scotland in the 15th century. The terrain is open, often without any trees, and will generally be undulating with a sandy base. The golf courses are often primarily shaped by nature, rather than 'built'. Weather, particularly wind, plays an important role, and although there will be a prevailing onshore breeze, changes in the wind direction and strength over the course of the tournament can mean each round of golf has to be played slightly differently. The courses are also famous for deep pot bunkers, and gorse bushes that make up the "rough". A golfer playing on a links course will often adapt his game so the flight of the ball is lower and so is less impacted by the wind, but this will make distance control more difficult. Also due to the windy conditions the speed of the greens are often slower than a golfer might be used to on the PGA Tour, to avoid the ball being moved by a gust.

Old Course at St Andrews
The Old Course at St Andrews is regarded as the oldest golf course in the world, and winning the Open there is widely considered to be one of the pinnacles of achievement in golf. Given the special status of the Old Course, the Open is generally played there once every five years in the modern era, much more frequently than the other courses used for the Open.

Previous champions will often choose St Andrews as their final Open tournament. It has become traditional to come down the 18th fairway to huge applause from the amphitheatre crowds, and to pose for final pictures on the Swilken Bridge with the picturesque clubhouse and town in the background.

Trophy presentation
The Open trophy is the Claret Jug, which has been presented to the champion since 1873 (it was first awarded to Young Tom Morris in 1872, however the trophy was not ready in time—his name is the first to be engraved on it). The original trophy permanently resides on display in the R&A's Clubhouse at St Andrews. Therefore, the trophy that is presented at each Open is a replica which is retained by the winner for a year. It used to be the responsibility of the winner to get his name engraved on the trophy, but 1967 winner Roberto De Vicenzo returned the trophy without having done so. Subsequently, the winner's name is already engraved on it when presented, which often results in television commentators speculating as to when it is safe for the engraver to start.

The winner of the Open is announced as "The Champion Golfer of the Year", a title which has been used since the first Open in 1860. He will nearly always pose for photos with the trophy sitting on one of the distinctive pot bunkers. Three-time winner Jack Nicklaus said holding the Claret Jug was like holding "a newborn baby", and on other players putting champagne or other drinks inside it to celebrate their Open win, he said "I never used the Claret Jug for anything other than what it symbolized – Champion Golfer of the Year."

Name
The first event was held as an invitational tournament, but the next year Prestwick Golf Club declared that "the belt... on all future occasions, shall be open to all the world". In its early years it was often referred to as The Championship but with the advent of the Amateur Championship in 1885, it became more common to refer to it as The Open Championship or simply The Open. The tournament inspired other national bodies to introduce open golf tournaments of their own, such as the U.S. Open, and later many others. To distinguish it from their own national open, it became common in many countries to refer to the tournament as the "British Open". The R&A (the tournament's organiser) continued to refer to it as The Open Championship. During the interwar years, a period with many U.S.-based winners, the term British Open would occasionally be used during the trophy presentation and in British newspapers.

In 2017, a representative of the R&A openly stated that it is a priority to "eradicate the term British Open" and have a single identity and brand of "The Open" in all countries. Tournament partners, such as the PGA Tour, now refer to it without "British" in the title, media rightsholders are contractually required to refer to the event as The Open Championship, and the official website has released a statement titled "Why it's called 'The Open' and not the 'British Open'" stating that "The Open is the correct name for the Championship. It is also the most appropriate". The R&A's stance has attracted criticism from some commentators.

The R&A also run The Senior Open, the over 50s equivalent of the Open, which was officially known as the "Senior British Open" from its inception in 1987 until 2007, when "British" was dropped from the name. The Women's Open, seen by some as the women's equivalent to the Open (although unlike the Open it is not always held on a links course, and was not run by the R&A until 2017) was officially known as the "Women's British Open" from its inception in 1976 until 2020, when the word "British" was dropped from the name as part of a sponsorship deal with AIG.

Status
The Open is recognised as one of the four major championships in golf, and is an official event on the PGA Tour, European Tour, and the Japan Golf Tour.

The Open began in 1860, and for many years it was not the most-followed event in golf, as challenge matches between top golfers were more keenly followed and drew larger crowds. The Great Triumvirate dominated the Open between 1894 and 1914 and were primarily responsible for the formation of the PGA in 1901 which had a big impact in promoting interest in professional golf (and therefore The Open) and increasing playing standards. Between the World Wars, the first wins by Americans were widely celebrated when they broke the dominance previously held by British players. After World War II, although the profile of the tournament remained high in the UK and Commonwealth countries, the low prize money compared to the US events and the cost of travel meant fewer Americans participated. High-profile visits and wins by Ben Hogan and Arnold Palmer, the growth of cheaper and faster transatlantic flights, and the introduction of television coverage recovered its prestige.

When the modern concept of the majors was cemented, the Open was included as one of those four. Thus, the Open is now one of the four majors in golf, along with the U.S. Open, PGA Championship, and Masters Tournament. The term "major" is a universally-acknowledged unofficial term used by players, the media, and golf followers to define the most important tournaments, and performance in them is often used to define the careers of the best golfers. There is often discussion amongst the golfing community as to whether the Open, U.S. Open, or the Masters Tournament is the most prestigious major, but opinion varies (often linked to nationality). The PGA Championship is usually seen as the least prestigious of the four.

In terms of official recognition, the tournament has been an event on the European Tour since its formation in 1972. In 1995, prize money won in the Open was included in the PGA Tour official money list for the first time, a change that caused an increase in the number of American entries. In addition all previous PGA Tour seasons have been retroactively adjusted to include the Open in official money and win statistics. Currently the Open, along with the other three majors and The Players Championship, are the top-tier tournaments in the PGA Tour's FedEx Cup, offering more points than any other non-playoff event. The Open is also an official event on the Japan Golf Tour.

Qualifying
Qualifying was introduced in 1907, and for much of its history, all players had to go through the qualification process. In the modern era, the majority of players get an exemption from qualification which is awarded for previous performance in the Open, performance in high-profile global tournaments (such as other majors), performance in top golf tours, or a high position in the Official World Golf Ranking (OWGR). Five amateurs are also exempt from qualifying by winning various global amateur titles provided they maintain their amateur status prior to The Open.

Another way of qualifying is to finish in a high position in the Open Qualifying Series of global events, which are about twelve tour events across the globe, run by various local golfing organisations.

Any male professional golfer, male amateur golfer whose playing handicap does not exceed 0.4 (i.e. scratch) or has been within World Amateur Golf Ranking listing 1–2,000 during the current calendar year, and any female golfer who finished in the top 5 and ties in the latest edition of any of the five women's majors is eligible to enter local qualifying. If they perform well they will go on to Final Qualifying, which is four simultaneous 36-hole one-day events held across the UK, with 12 players qualifying for the Open. If there are any spots left, then alternates are made up from the highest ranked players in the OWGR who are not already qualified, which brings the total field up to 156 players.

In 2018, the OWGR gave the Open a strength of field rating of 902 (the maximum possible is 1000 if the top 200 players in the world were all in a tournament). This was only bettered by the PGA Championship, a tournament which actively targets a high strength of field rating.

Format
Field: 156 players

Basic Format: 72 hole stroke play. Play 18 holes a day over four days, weather permitting.

Date of Tournament: starts on the day before the third Friday in July.

Tournament Days: Thursday to Sunday.

Tee off times: each player has one morning and one afternoon tee time in first two days in groups of three, which are mostly randomised (with some organiser discretion). Groupings of two on the last two days with last place going off first and leaders going out last.

Cut: after 36 holes, only top 70 and ties play the final 36 holes.

Playoff: if there is a tie for the lead after 72 holes, a three-hole aggregate playoff is held; followed by sudden death if the lead is still tied.

Prizes
Up until 2016, the purse was always stated, and paid, in pounds sterling (£), but was changed in 2017 to US dollars ($) in recognition of the fact that it is the most widely adopted currency for prize money in golf.

Champion's prizes and benefits
The champion receives trophies, the winner's prize money, and several exemptions from world golf tours and tournaments. He is also likely to receive a winner's bonus from his sponsors. The prizes and privileges on offer for the champion included:

 * The Golf Champion Trophy (commonly known as the Claret Jug). The winner keeps the trophy until the next Open, at which point it must be returned, and a replica is provided as a replacement.
 * The winner's gold medal (originally awarded in 1872 when the Claret Jug was not yet ready, and since awarded to all champions).
 * If the winner is a professional, then the winner's share (18%) of the purse.
 * Guaranteed entry to all future Open Championships until the age of 60, and entry to the next ten Opens, even if over the age of 60.
 * Entry to the next five editions of the Masters Tournament, PGA Championship, and U.S. Open.
 * Five year membership to the PGA Tour and the European Tour.
 * Entry to the next edition of the WGC-HSBC Champions.
 * Entry to the next five editions of The Players Championship, and the five invitational tournaments (Genesis Invitational, Fort Worth Invitational, the Arnold Palmer Invitational, the RBC Heritage, and the Memorial Tournament) on the PGA Tour.
 * Automatic invitations to three of the five senior majors once they turn 50; they receive a one-year invitation to the U.S. Senior Open and a lifetime invitation to the Senior PGA Championship and Senior Open Championship.
 * FedEx Cup, Race to Dubai, Ryder Cup/Presidents Cup, and Official World Golf Ranking points.

From 1860 to 1870, the winner received the challenge belt. When this was awarded to Young Tom Morris permanently for winning three consecutive tournaments, it was replaced by the gold medal (1872 onwards), and the Claret Jug (1873 onwards).

Other prizes and benefits, based upon finishing position
There are several benefits from being placed highly in the Open. These are:

 * The runners up each receive a silver salver.
 * If the player is a professional, then a share of the purse. There is a distribution curve for those who make the cut, with 1st place getting 18%, 2nd 10.4%, 3rd 6.7%, 4th 5.2%, and 5th 4.2%. The percentage continues to fall by placing with 21st getting 1% and 37th 0.5%. Professionals who miss the cut received between US$7,375 and US$4,950.
 * The top 10 players, including ties, get entry to the next edition of The Open Championship.
 * The top 4 players, including ties, get entry to the next edition of the Masters Tournament.
 * FedEx Cup, Race to Dubai, Ryder Cup/Presidents Cup, and Official World Golf Ranking points.

Amateur medals
Since 1949 the leading amateur completing the final round receives a silver medal. Since 1972, any other amateur who competes in the final round receives a bronze medal. Amateurs do not receive prize money.

Professional Golfers' Association (of Great Britain and Ireland) awards
The Professional Golfers' Association (of Great Britain and Ireland) also mark the achievements of their own members in The Open.

 * Ryle Memorial Medal – awarded since 1901 to the winner if he is a PGA member.
 * Braid Taylor Memorial Medal – awarded since 1966 to the highest finishing PGA member.
 * Tooting Bec Cup – awarded since 1924 to the PGA member who records the lowest single round during the championship.

The Braid Taylor Memorial Medal and the Tooting Bec Cup are restricted to members born in, or with a parent or parents born in, the United Kingdom or Republic of Ireland.

Courses
The Open Championship has always been held on a coastal links golf course in Scotland, England or Northern Ireland. The hosting pattern has been:
 * 1860–1870: Prestwick Golf Club is the sole host.
 * 1872–1892: three-year rotation among Prestwick, St Andrews, and Musselburgh (replaced by Muirfield in 1892) golf clubs.
 * 1893–1907: five-year rotation among Prestwick, Royal St George's, St Andrews, Muirfield, and Royal Liverpool Golf Clubs.
 * 1908–1939: six-year rotation, initially among Prestwick, Royal Cinque Ports, St Andrews, Royal St George's, Muirfield, and Royal Liverpool Golf Clubs, thus alternating between Scotland and England. A few changes were made to the rota of 6 courses after World War I.
 * 1946–1972: alternating between Scottish and English golf clubs continues, but without a fixed rota. Exceptions were St Andrews hosting pre- and post-World War II, and Northern Ireland hosting in 1951.
 * Since 1973: usually three Scottish and two English courses hosting in a five-year period, mostly alternating between the two countries, with St Andrews hosting about every five years. Northern Ireland returned in 2019.

Overview
A total of 14 courses have hosted the Open, with ten currently active as part of the rotation, and four have been retired from the rotation (shown in italics). The year the golf course was originally built is shown in parentheses.

Prestwick Golf Club (1851): Prestwick is The Open's original venue, and hosted 24 Opens in all, including the first 12. Old Tom Morris designed the original 12 hole course, but it was subsequently redesigned and expanded to be an 18-hole course in 1882. Serious overcrowding problems at Prestwick in 1925 meant that the course was never again used for the Open, and was replaced by Carnoustie Golf Links as the third Scottish course.

Old Course at St Andrews (1552): considered the oldest golf course in the world, and referred to as "the home of golf". In 1764, the Society of St Andrews Golfers reduced the course from 22 to 18 holes and created what became the standard round of golf throughout the world. Famous features include the "Hell Bunker" (14th) and the Road Hole (17th). Due to its special status St Andrews usually hosts the Open every five years in the modern era. It is designed to be played in wind, so can result in low scores in benign conditions.

Musselburgh Links (c. 1672): a 9-hole course that hosted six Opens as it was used by the Honourable Company of Edinburgh Golfers, one of the organisers of The Open between 1872 and 1920. When the Honourable Company built their own course in 1891 (Muirfield), it took over hosting duties. Musselburgh was unhappy with this and organised another rival 'Open' competition prior to the Muirfield event, one with greater prize money.

Muirfield (1891): built by the Honourable Company of Edinburgh Golfers to replace Musselburgh on the rota. Known for the circular arrangement the course has, which means the wind direction on each hole changes, and can make it tricky to navigate. Briefly removed from the rota in 2016–17 due to not having any female members.

Royal St George's Golf Club (1887): often simply referred to as Sandwich. The first venue to host in England, and the only venue on the current rota in Southern England. It went 32 years without hosting between 1949 and 1981, but returned following the rebuilding of three holes, tee changes to another two holes, and improved road links. Known for having the deepest bunker on the rota (4th hole).

Royal Liverpool Golf Club (1869): often simply referred to as Hoylake. Royal Liverpool went 39 years without hosting between 1967 and 2006, but returned following changes to tees, bunkers, and greens. In 2006, Tiger Woods won by using his driver just once.

Royal Cinque Ports Golf Club (1892): hosted the 1909 and 1920 Opens, and was scheduled to host in 1938 and 1949 but both had to be moved to Royal St George's Golf Club due to abnormally high tides flooding the course. It was removed from the rota but is still used for qualifying.

Royal Troon Golf Club (1878): first used in 1923 instead of Muirfield when "some doubts exists as to the Honourable Company of Edinburgh Golfers being desirous of their course being used for the event". Redesigned, lengthened, and strengthened by James Braid shortly before it held its first Open. Famous features include the "Postage Stamp" 8th hole, and the 601 yards 6th.

Royal Lytham & St Annes Golf Club (1886): a relatively short course, but has 167 bunkers which demand accuracy. Slightly inland as some coastal homes have been built since the course first opened.

Carnoustie Golf Links (1835):  replaced Prestwick after it was no longer suitable for the Open. It went through modifications prior to the 1999 Open. Thought of as being the toughest of the Open venues, especially the last three holes, and is well remembered for Jean van de Velde triple bogeying on the 18th when he only needed a double bogey to win. Prince's Golf Club (1906): only hosted once in 1932. Has been redesigned in 1950 due to war damage.

Royal Portrush Golf Club (1888): the only venue to host the Open outside England and Scotland when it hosted in 1951. With the Troubles in Northern Ireland significantly diminished since the 1998 Good Friday Agreement, and after the successful hosting of the Irish Open it returned as host in 2019. The course underwent significant changes before the 2019 Open, including replacing the 17th and 18th holes, which also provided the space for spectators and corporate hospitality that a modern major requires.

Royal Birkdale Golf Club (1894): extensively redesigned by Fred Hawtree and JH Taylor to create the current layout in 1922, it is known for its sand dunes towering the fairways. Often ranked as England's best Open venue.

Turnberry (1906): made its Open debut in 1977, when Tom Watson and Jack Nicklaus famously played the Duel in the Sun. Known to be one of the most picturesque Open venues, it was bought by Donald Trump in 2014, who has spent substantial amounts renovating the course. On 11 January 2021, in the aftermath of the 2021 United States Capitol attack the week prior, the R&A announced that it will not stage a championship at Turnberry "in the foreseeable future".

Hosting record of each course
References:

Records

 * Oldest winner: Old Tom Morris (46 years, 113 days), 1867.
 * Youngest winner: Young Tom Morris (17 years, 161 days), 1868.
 * Most victories: 6, Harry Vardon (1896, 1898, 1899, 1903, 1911, 1914).
 * Most consecutive victories: 4, Young Tom Morris (1868, 1869, 1870, 1872 – there was no championship in 1871).
 * Lowest score after 36 holes: 129, Louis Oosthuizen (64-65), 2021.
 * Lowest score after 54 holes: 197, Shane Lowry (67-67-63), 2019.
 * Lowest final score (72 holes): 264, Henrik Stenson (68-65-68-63), 2016.
 * Lowest final score (72 holes) in relation to par: −20, Henrik Stenson (68-65-68-63=264), 2016; Cameron Smith (67-64-73-64=268), 2022.
 * Greatest victory margin: 13 strokes, Old Tom Morris, 1862. This remained a record for all majors until 2000, when Woods won the U.S. Open by 15 strokes at Pebble Beach. Old Tom's 13-stroke margin was achieved over 36 holes.
 * Lowest round: 62, Branden Grace, 3rd round, 2017; a record for all majors.
 * Lowest round in relation to par: −9, Paul Broadhurst, 3rd round, 1990; Rory McIlroy, 1st round, 2010.
 * Wire-to-wire winners (after 72 holes with no ties after rounds): Ted Ray in 1912, Bobby Jones in 1927, Gene Sarazen in 1932, Henry Cotton in 1934, Tom Weiskopf in 1973, Tiger Woods in 2005, and Rory McIlroy in 2014.
 * Most runner-up finishes: 7, Jack Nicklaus (1964, 1967, 1968, 1972, 1976, 1977, 1979).

Winners
Nationalities assigned above match those used in the official Open records. Source: The 148th Open 2019 Media Guide

Silver Medal winners
Since 1949, the silver medal is awarded to the leading amateur, provided that the player completes all 72 holes. In the earlier years wealthy individuals would often maintain their amateur status, and hence could win multiple times, such as Frank Stranahan who won it four times in the first five years (and was also the low amateur in 1947). In the modern era players often turn professional soon after winning the silver medal, and hence never have a chance for multiple wins. Tiger Woods and Rory McIlroy are the only silver medal winners who have gone on to win the Open.

 * 1949 – 🇺🇸 Frank Stranahan
 * 1950 – 🇺🇸 Frank Stranahan (2)
 * 1951 – 🇺🇸 Frank Stranahan (3)
 * 1952 – 🏴 Jackie Jones
 * 1953 – 🇺🇸 Frank Stranahan (4)
 * 1954 – 🇦🇺 Peter Toogood
 * 1955 – 🇺🇸 Joe Conrad
 * 1956 – 🇮🇪 Joe Carr
 * 1957 – Dickson Smith
 * 1958 – 🇮🇪 Joe Carr (2)
 * 1959 – Reid Jack
 * 1960 – 🏴 Guy Wolstenholme
 * 1961 – 🏴 Ronnie White
 * 1962 – Charlie Green
 * 1963 – none
 * 1964 – none
 * 1965 – 🏴 Michael Burgess
 * 1966 – Ronnie Shade
 * 1967 – none
 * 1968 – 🏴 Michael Bonallack
 * 1969 – 🏴 Peter Tupling
 * 1970 – 🇺🇸 Steve Melnyk
 * 1971 – 🏴 Michael Bonallack (2)
 * 1972 – none
 * 1973 – 🇺🇸 Danny Edwards
 * 1974 – none
 * 1975 – none
 * 1976 – none
 * 1977 – none
 * 1978 – 🏴 Peter McEvoy
 * 1979 – 🏴 Peter McEvoy (2)
 * 1980 – 🇺🇸 Jay Sigel
 * 1981 – 🇺🇸 Hal Sutton
 * 1982 – 🏴 Malcolm Lewis
 * 1983 – none
 * 1984 – none
 * 1985 – 🇪🇸 José María Olazábal
 * 1986 – none
 * 1987 – 🏴 Paul Mayo
 * 1988 – 🏴 Paul Broadhurst
 * 1989 – 🏴 Russell Claydon
 * 1990 – none
 * 1991 – 🏴 Jim Payne
 * 1992 – 🏴 Daren Lee
 * 1993 – 🏴 Iain Pyman
 * 1994 – 🏴 Warren Bennett
 * 1995 – 🏴 Steve Webster
 * 1996 – 🇺🇸 Tiger Woods
 * 1997 – Barclay Howard
 * 1998 – 🏴 Justin Rose
 * 1999 – none
 * 2000 – none
 * 2001 – 🏴 David Dixon
 * 2002 – none
 * 2003 – none
 * 2004 – Stuart Wilson
 * 2005 – Lloyd Saltman
 * 2006 – 🇳🇴 Marius Thorp
 * 2007 – Rory McIlroy
 * 2008 – 🏴 Chris Wood
 * 2009 – 🇮🇹 Matteo Manassero
 * 2010 – 🇰🇷 Jin Jeong
 * 2011 – 🏴 Tom Lewis
 * 2012 – none
 * 2013 – 🏴 Matt Fitzpatrick
 * 2014 – none
 * 2015 – 🇺🇸 Jordan Niebrugge
 * 2016 – none
 * 2017 – 🏴 Alfie Plant
 * 2018 – Sam Locke
 * 2019 – none
 * 2020 – no tournament
 * 2021 – 🇩🇪 Matti Schmid
 * 2022 – 🇮🇹 Filippo Celli
 * 2023 – 🇿🇦 Christo Lamprecht

Broadcasting
The distribution of The Open is provided by a partnership between R&A Productions, European Tour Productions (both run by IMG) and CTV Outside Broadcasting. The broadcasters with onsite production are Sky (UK), NBC (USA), BBC (UK), and TV Asahi (Japan).

Many non-British broadcasters referred to the Open as the "British" Open in their coverage until 2010, when The R&A introduced use of contractual terms in their media contracts, similar to the Masters, and now rights holders are obliged to refer to the tournament as "The Open". On 7 November 2018, the parent company of the U.S. rights holder, NBC, completed a takeover of the U.K. rights holder, Sky. This means the media rights in the two primary markets are owned by the same company, albeit produced separately by two different subsidiaries. There are over 170 cameras on site during the tournament, including cameras in the face of the Open's pot bunkers.

Ivor Robson was the announcer for 41 years; he died in October 2023.

United Kingdom
The BBC first started to broadcast the Open in 1955, with Peter Alliss involved since 1961, and having the role of lead commentator since 1978. With the growth of pay television, and the increasing value of sporting rights, the BBC's golf portfolio began to reduce. The loss of the rights to the Scottish Open, and BMW PGA Championship in 2012 left the BBC's only golf coverage as the Open, and the final two days of the Masters (which it shared with Sky). With so little golf, the BBC was accused of neglecting investment in production and was criticised about its 'quality of coverage and innovation' compared to Sky, which held the rights to most golf events. The tournament is considered a Category B event under the Ofcom Code on Sports and Other Listed and Designated Events, which allows its rights to be held by a pay television broadcaster as long as sufficient secondary coverage is provided by a free-to-air broadcaster.

Many were hoping that a deal similar to the Masters would be reached, where Sky had coverage of all four days, and the BBC also provided live weekend coverage, but Sky were not keen on this and won the full rights in 2015. Some were angered about the demise of golf on terrestrial television, and the impact that could have on the interest in golf in the U.K., whilst others were pleased about the perceived improved coverage that Sky would give. Despite Peter Alliss promising on air that the BBC would cover the 2016 event, the BBC reached a deal for Sky to take the coverage. The BBC still covers the tournament, showing highlights from 8pm–10pm on tournament days and radio coverage on Radio 5 Live. The deal with Sky required the broadcaster to restrict its advertisement breaks to 4 minutes every hour, similar to the Masters. Sky also offers complete coverage online through NOW to non-subscribers, which is £7.99 for one day, or £12.99 for a weeks access.

Timeline of U.K. broadcasting rights
Ref:

United States
ABC began broadcasting the Open in 1962, with taped highlights on Wide World of Sports. In the pre-digital age the coverage had to be converted from the U.K.'s PAL colour encoding system, to the U.S.'s NTSC, which meant picture quality could be impacted, especially in the early years. The coverage expanded over the years, and as is common in America, there was a different early round rights holder, which was ESPN until 2003 when TNT took over. Co-owned ESPN became responsible for ABC's sports coverage in 2006; it won the rights to cover all four days of the championship in 2010, and concurrently moved coverage to its channels. The Open became the first golf major to be covered exclusively on pay television in America, as ESPN left only highlights for its partner broadcast network.

After losing the rights to the U.S. Open in 2015, NBC bid aggressively to win the rights to the Open, and become a broadcaster of a golf major again. NBC also had a track record of broadcasting European sporting events successfully in the morning U.S. time with the Premier League, Formula One, and "Breakfast at Wimbledon", and was able to place early round coverage on its subsidiary Golf Channel. NBC won the rights from 2017 to 2028. ESPN also sold them the rights for 2016.

The 2019 edition of the Open Championship had a total of 49 hours of coverage in the United States, with 29 hours being on Thursday and Friday, and 20 hours being on Saturday and Sunday; the Golf Channel cable network had a total of 34 hours of coverage, with 29 hours on Thursday and Friday, and 5 hours on Saturday and Sunday. The NBC broadcast network had a total of 15 hours of coverage on the weekend, with 8 hours Saturday, and 7 hours Sunday. The 49 total hours of coverage on Golf Channel and NBC is down 30 minutes from 2018; the difference is that NBC's Sunday coverage is down 30 minutes, from 7.5 hours in 2018, to 7 hours in 2019.

Timeline of U.S. broadcasting rights
Ref:

TheOpen.com
The Open provides limited coverage for free on its website including highlights, featured groups, featured holes, and radio coverage. The Open's local rights holders usually provide these feeds as part of their broadcast package.

Rest of the world
The Open produces a 'world feed' for use by international broadcasters if they require. The other large golf markets in a similar time zone as the U.K. are the rest of Europe (where Sky, the U.K. broadcast company often has a presence), and South Africa where it is covered by SuperSport.

Japan, South Korea, Australia, New Zealand and increasingly China are markets with high media interest in golf and the Open, but the time zone means the prime coverage is shown in the early hours of the morning.

title: The Open Championship


text:
Anarchists (film)

Anarchists is a 2000 South Korean action film directed by Yoo Young-sik and co-written by Park Chan-wook. Set in Shanghai in 1924, the film is about the Heroic Corps: a covert cell of insurrectionist anarchists who attempt to overthrow the Japanese government's occupation of Korea through propaganda of the deed. Told from the perspective of the youngest member, Sang-gu, years after the fact, the story is a sympathetic look at a group of revolutionaries through the eyes of one of their own.

Plot
In the opening scene the protagonist begins to reminisce about his youth and remembers the day he was saved from execution in a raid performed by the anarchist cell he would later join. After reaching a safe house the group begins to teach him the tricks of their trade. He later takes part in several missions, though he continues to have difficulty throughout the film with the violence of his new job.

Eventually a string of tragic events strike the team. One of their members is fatally betrayed during a mission, leading to their covers being blown during the next. Now wanted by the Japanese and Chinese authorities, their funders turn away from them and instead choose to support socialist electoral politics to further their cause. This angers the group, and they leave the larger organization, attempting to survive on their own by earning money through gambling and bank robbery. Over time the group becomes agitated with simply scraping by and several voice a desire to return to their old ways of clandestine warfare. They collectively decide to strike at the Japanese government in a high-profile attack, leading up to a dramatic finale.

Cast

 * Jang Dong-gun as Sergei
 * Jung Joon-ho as Lee Geun
 * Kim Sang-joong as Han Myung-gon
 * Lee Beom-soo as Dol-suk
 * Kim In-kwon as Sang-gu
 * Ye Ji-won as Kaneko

Production notes and historical significance
Anarchists was the first Korean and Chinese co-production in the history of Korean cinema. The project was put together through the efforts of the Korean Film Commission and the international exchange division of the city of Busan, using connections they had been developing in Shanghai. The film was shot entirely in China over a period of three months in Shanghai and in towns nearby, with a budget of US$3,000,000. For Anarchists, the production team worked with a Chinese-based A-level staff who participated in the production of Chen Kaige's Farewell My Concubine and Temptress Moon. The actors and the core production staff came from Korea, while the production design, elaborate sets, supporting talent and hundreds of extras were supplied by the Shanghai Film Studio.

The film was co-winner of the audience choice award at the 2001 Cinequest Film Festival.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Anarchists (film)


text:
Scent hound

Scent hounds (or scenthounds) are a type of hound that primarily hunts by scent rather than sight. These breeds are hunting dogs and are generally regarded as having some of the most sensitive noses among dogs. Scent hounds specialize in following scent or smells. Most of them tend to have long, drooping ears and large nasal cavities to enhance smell sensitivity. They need to have relatively high endurance to be able to keep track of scent over long distances and rough terrain. It is believed that they were first bred by the Celts by crossbreeding mastiff-type dogs with sighthounds. The first established scent hounds were St. Hubert Hounds (the ancestor of today's Bloodhound) bred by monks in Belgium during the Middle Ages.

Description
Hounds are hunting dogs that either hunt by following the scent of a game animal (scent hounds) or by following the animal by sight (sighthounds). There are many breeds in the scent hound type, and scent hounds may do other work as well, so exactly which breeds should be called scent hound can be controversial. Kennel clubs assign breeds of dogs to Groups, which are loosely based on breed types. Each kennel club determines which breeds it will place in a given group.

Scent hounds specialize in following a smell or scent. Most of these breeds have long, drooping ears. One theory says that this trait helps to collect scent from the air and keep it near the dog's face and nose. They also have large nasal cavities, which helps them scent better. Their typically loose, moist lips are said to assist in trapping scent particles.

Because scent hounds tend to walk or run with their noses to the ground, many scent hound breeds have been developed such that the dog will hold their tail upright when on a scent. In addition, some breeds (e.g. beagle) also have been bred to have white hair on the tip of their tails. These traits allow the dog's master to identify him when at a distance or in longer grassland.

Scent hounds do not need to be as fast as sighthounds, because they do not need to keep prey in sight, but they need endurance so that they can stick with a scent and follow it for long distances over rough terrain. The best scent hounds can follow a scent trail even across running water and even when it is several days old. Most scent hounds are used for hunting in packs of multiple dogs. Longer-legged hounds run more quickly and usually require that the hunters follow on horseback; shorter-legged hounds allow hunters to follow on foot. Hunting with some breeds, such as German Bracke, American Foxhounds, or coonhounds, involves allowing the pack of dogs to run freely while the hunters wait in a fixed spot until the dogs' baying announces that the game has been "treed". The hunters then go to the spot on foot, following the sound of the dogs' baying.

Vocalization
Most scent hounds have a range of vocalizations, which can vary depending upon the situation the dog finds himself in. Their baying voice - most often used when excited and is useful in informing their master that they are following a scent trail - is deep and booming and can be distinct from their barking voice; which itself can have variations in tone from excited to nervous or fearful.

As they are bred to 'give voice' when excited, scent hounds may bark much more frequently than other dog breeds. Although this can be a nuisance in settled areas, it is a valuable trait that allows the dog's handler to follow the dog or pack of dogs during a hunt even when they are out of sight, such as when following a fox or raccoon through woodland

Classification
The Fédération Cynologique Internationale (FCI) places scent hounds into their classification "Group 6". This includes a subdivision, "Section 2, Leash Hounds", some examples of which are the Bavarian Mountain Hound (Bayrischer Gebirgsschweisshund, no. 217), the Hanover Hound (Hannover'scher Schweisshund, no. 213), and the Alpine Dachsbracke (Alpenländische Dachsbracke, no. 254). In addition, the Dalmatian and the Rhodesian Ridgeback are placed in Group 6 as "Related breeds".

Genetic history
Genetic studies indicate that the scent hounds are more closely related to each other than they are with other branches on the dog family tree.

Breeds
The scent hound type includes the following breeds:

 * Alpine Dachsbracke
 * American Leopard Hound
 * Anglo-French hounds (French hounds crossed with English Foxhounds)
 * Anglo-Français de Petite Vénerie
 * Grand Anglo-Français Blanc et Noir
 * Grand Anglo-Français Blanc et Orange
 * Grand Anglo-Français Tricolore
 * Ariegeois
 * Artois Hound
 * Austrian Black and Tan Hound
 * Basset Artésien Normand
 * Basset Bleu de Gascogne
 * Basset Fauve de Bretagne
 * Basset Hound
 * Bavarian Mountain Hound
 * Beagle
 * Beagle-Harrier
 * Billy
 * Black Mouth Cur
 * Bloodhound
 * Blue Lacy
 * Bosnian Broken-haired Hound
 * Briquet Griffon Vendéen
 * Catahoula Leopard Dog
 * Coonhounds
 * Black and Tan Coonhound
 * Bluetick Coonhound
 * English Coonhound (a.k.a. American English Coonhound and Redtick Coonhound)
 * Redbone Coonhound
 * Treeing Walker Coonhound
 * Cretan Hound
 * Dachshund
 * Deutsche Bracke
 * Drever (Swedish Dachsbracke)
 * Dunker (Norwegian Hound)
 * Estonian Hound
 * Finnish Hound
 * Foxhounds
 * American Foxhound
 * English Foxhound
 * Dumfriesshire Black and Tan Foxhound (extinct)
 * Welsh Foxhound
 * French hounds
 * Chien Français Blanc et Noir
 * Chien Français Blanc et Orange
 * Chien Français Tricolore
 * Grand Basset Griffon Vendéen
 * Grand Bleu de Gascogne
 * Grand Gascon Saintongeois
 * Grand Griffon Vendéen
 * Greek Harehound
 * Griffon Bleu de Gascogne
 * Griffon Fauve de Bretagne
 * Hamiltonstövare
 * Hanover Hound
 * Harrier
 * Istrian Coarse-haired Hound
 * Istrian Shorthaired Hound
 * Kerry Beagle
 * Limer (obsolete term)
 * Montenegrin Mountain Hound
 * Mountain Cur
 * North Country Beagle (Northern Hound) (extinct)
 * Otterhound
 * Petit Basset Griffon Vendéen
 * Petit Bleu de Gascogne
 * Petit Gascon Saintongeois
 * Plott Hound
 * Polish Hound (pl. Ogar Polski)
 * Polish Hunting Dog (pl. Gończy Polski)
 * Porcelaine
 * Posavac Hound
 * Rache (obsolete term)
 * Sabueso Español (Spanish Scenthound)
 * Sabueso fino Colombiano
 * St. Hubert Jura Hound
 * Schillerstövare
 * Segugio dell'Appennino
 * Segugio Italiano a pelo forte
 * Segugio Italiano a pelo raso
 * Segugio Maremmano
 * Serbian Hound
 * Serbian Tricolour Hound
 * Schweizer Laufhund
 * Schweizerischer Niederlaufhund
 * Slovenský Kopov (Slovakian Hound)
 * Smalandstövare
 * Southern Hound (extinct)
 * Stephens Cur
 * Styrian Coarse-haired Hound
 * Talbot Hound (extinct)
 * Transylvanian Hound
 * Treeing Cur
 * Treeing Tennessee Brindle
 * Trigg Hound
 * Tyrolean Hound
 * Westphalian Dachsbracke

United Kennel Club (US) Scenthound Group
The Scenthound Group is the group category used by the United Kennel Club (US), which it divides into two categories. The first includes the American hunting dogs known as coonhounds and the European hounds from which they were developed. These are referred to as Tree Hounds. The category also includes curs, American dogs bred for hunting a variety of game, such as squirrels, raccoons, opossums, bobcats, cougars, American black bears and feral pigs. The second category is referred to as Trailing Scenthounds, and includes dogs used for tracking of humans, reputedly descended from the St. Hubert Hounds.

title: Scent hound


text:
Cylindrical coordinate system

A cylindrical coordinate system is a three-dimensional coordinate system that specifies point positions by the distance from a chosen reference axis (axis L in the image opposite), the direction from the axis relative to a chosen reference direction (axis A), and the distance from a chosen reference plane perpendicular to the axis (plane containing the purple section). The latter distance is given as a positive or negative number depending on which side of the reference plane faces the point.

The origin of the system is the point where all three coordinates can be given as zero. This is the intersection between the reference plane and the axis. The axis is variously called the cylindrical or longitudinal axis, to differentiate it from the polar axis, which is the ray that lies in the reference plane, starting at the origin and pointing in the reference direction. Other directions perpendicular to the longitudinal axis are called radial lines.

The distance from the axis may be called the radial distance or radius, while the angular coordinate is sometimes referred to as the angular position or as the azimuth. The radius and the azimuth are together called the polar coordinates, as they correspond to a two-dimensional polar coordinate system in the plane through the point, parallel to the reference plane. The third coordinate may be called the height or altitude (if the reference plane is considered horizontal), longitudinal position, or axial position.

Cylindrical coordinates are useful in connection with objects and phenomena that have some rotational symmetry about the longitudinal axis, such as water flow in a straight pipe with round cross-section, heat distribution in a metal cylinder, electromagnetic fields produced by an electric current in a long, straight wire, accretion disks in astronomy, and so on.

They are sometimes called "cylindrical polar coordinates" and "polar cylindrical coordinates", and are sometimes used to specify the position of stars in a galaxy ("galactocentric cylindrical polar coordinates").

Definition
The three coordinates ($O$, $A$, $L$) of a point $r$ are defined as:
 * The radial distance $θ$ is the Euclidean distance from the $z$-axis to the point $ρ$.
 * The azimuth $φ$ is the angle between the reference direction on the chosen plane and the line from the origin to the projection of $z$ on the plane.
 * The axial coordinate or height $P$ is the signed distance from the chosen plane to the point $ρ$.

Unique cylindrical coordinates
As in polar coordinates, the same point with cylindrical coordinates $ρ = 4$ has infinitely many equivalent coordinates, namely $φ = 130°$ and $z = 4$ where $z$ is any integer. Moreover, if the radius $P$ is zero, the azimuth is arbitrary.

In situations where someone wants a unique set of coordinates for each point, one may restrict the radius to be non-negative ($(r,θ,z)$) and the azimuth $φ$ to lie in a specific interval spanning 360°, such as $Z = v_{bz}t$ or $(ρ, φ, z)$.

Conventions
The notation for cylindrical coordinates is not uniform. The ISO standard 31-11 recommends $(ρ, φ ± n×360°, z)$, where $P$ is the radial coordinate, $z$ the azimuth, and $P$ the height. However, the radius is also often denoted $n$ or $ρ$, the azimuth by $φ$ or $ρ$, and the third coordinate by $φ$ or (if the cylindrical axis is considered horizontal) $z$, or any context-specific letter.

In concrete situations, and in many mathematical illustrations, a positive angular coordinate is measured counterclockwise as seen from any point with positive height.

Coordinate system conversions
The cylindrical coordinate system is one of many three-dimensional coordinate systems. The following formulae may be used to convert between them.

Cartesian coordinates
For the conversion between cylindrical and Cartesian coordinates, it is convenient to assume that the reference plane of the former is the Cartesian $r$-plane (with equation $(−ρ, φ ± (2n + 1)×180°, z),$), and the cylindrical axis is the Cartesian $s$-axis. Then the $θ$-coordinate is the same in both systems, and the correspondence between cylindrical $ρ ≥ 0$ and Cartesian $[−180°,+180°]$ are the same as for polar coordinates, namely $$ \begin{align} x &= \rho \cos \varphi \\ y &= \rho \sin \varphi \\ z &= z \end{align} $$ in one direction, and $$\begin{align} \rho &= \sqrt{x^2+y^2} \\ \varphi &= \begin{cases} \text{indeterminate} & \text{if } x = 0 \text{ and } y = 0\\ \arcsin\left(\frac{y}{\rho}\right) & \text{if } x \geq 0 \\ -\arcsin\left(\frac{y}{\rho}\right) + \pi & \mbox{if } x < 0 \text{ and } y \ge 0\\ -\arcsin\left(\frac{y}{\rho}\right) + \pi & \mbox{if } x < 0 \text{ and } y < 0 \end{cases} \end{align}$$ in the other. The arcsine function is the inverse of the sine function, and is assumed to return an angle in the range $[0,360°]$ = $(ρ, φ, z)$. These formulas yield an azimuth $t$ in the range $(ρ, φ, z)$.

By using the arctangent function that returns also an angle in the range $ρ = 2$ = $z = 1$, one may also compute $$\varphi$$ without computing $$\rho$$ first $$\begin{align} \varphi &= \begin{cases} \text{indeterminate} & \text{if } x = 0 \text{ and } y = 0\\ \frac\pi2\frac y{|y|} & \text{if } x = 0 \text{ and } y \ne 0\\ \arctan\left(\frac{y}{x}\right) & \mbox{if } x > 0 \\ \arctan\left(\frac{y}{x}\right)+\pi & \mbox{if } x < 0 \text{ and } y \ge 0\\ \arctan\left(\frac{y}{x}\right)-\pi & \mbox{if } x < 0 \text{ and } y < 0 \end{cases} \end{align}$$ For other formulas, see the article Polar coordinate system.

Many modern programming languages provide a function that will compute the correct azimuth $h$, in the range $φ = −60°$, given x and y, without the need to perform a case analysis as above. For example, this function is called by atan2(y, x) in the C programming language, and (atan y x) in Common Lisp.

Spherical coordinates
Spherical coordinates (radius $x$, elevation or inclination $z$, azimuth $x$), may be converted to or from cylindrical coordinates, depending on whether $P$ represents elevation or inclination, by the following:

Line and volume elements
In many problems involving cylindrical polar coordinates, it is useful to know the line and volume elements; these are used in integration to solve problems involving paths and volumes.

The line element is $$\mathrm{d}\boldsymbol{r} = \mathrm{d}\rho\,\boldsymbol{\hat{\rho}} + \rho\,\mathrm{d}\varphi\,\boldsymbol{\hat{\varphi}} + \mathrm{d}z\,\boldsymbol{\hat{z}}.$$

The volume element is $$\mathrm{d}V = \rho\,\mathrm{d}\rho\,\mathrm{d}\varphi\,\mathrm{d}z.$$

The surface element in a surface of constant radius $P$ (a vertical cylinder) is $$\mathrm{d}S_\rho = \rho\,\mathrm{d}\varphi\,\mathrm{d}z.$$

The surface element in a surface of constant azimuth $ρ$ (a vertical half-plane) is $$\mathrm{d}S_\varphi = \mathrm{d}\rho\,\mathrm{d}z.$$

The surface element in a surface of constant height $φ$ (a horizontal plane) is $$\mathrm{d}S_z = \rho\,\mathrm{d}\rho\,\mathrm{d}\varphi.$$

The del operator in this system leads to the following expressions for gradient, divergence, curl and Laplacian: $$\begin{align} \nabla f &= \frac{\partial f}{\partial \rho}\boldsymbol{\hat{\rho}} + \frac{1}{\rho}\frac{\partial f}{\partial \varphi}\boldsymbol{\hat{\varphi}} + \frac{\partial f}{\partial z}\boldsymbol{\hat{z}} \\[8px]

\nabla \cdot \boldsymbol{A} &= \frac{1}{\rho}\frac{\partial}{\partial \rho}\left(\rho A_\rho\right) + \frac{1}{\rho} \frac{\partial A_\varphi}{\partial \varphi} + \frac{\partial A_z}{\partial z} \\[8px]

\nabla \times \boldsymbol{A} &= \left(\frac{1}{\rho}\frac{\partial A_z}{\partial \varphi} - \frac{\partial A_\varphi}{\partial z}\right)\boldsymbol{\hat{\rho}} + \left(\frac{\partial A_\rho}{\partial z} - \frac{\partial A_z}{\partial \rho}\right)\boldsymbol{\hat{\varphi}} + \frac{1}{\rho}\left(\frac{\partial}{\partial \rho}\left(\rho A_\varphi\right) - \frac{\partial A_\rho}{\partial \varphi}\right) \boldsymbol{\hat{z}} \\[8px]

\nabla^2 f &= \frac{1}{\rho} \frac{\partial}{\partial \rho} \left(\rho \frac{\partial f}{\partial \rho}\right) + \frac{1}{\rho^2} \frac{\partial^2 f}{\partial \varphi^2} + \frac{\partial^2 f}{\partial z^2} \end{align}$$

Cylindrical harmonics
The solutions to the Laplace equation in a system with cylindrical symmetry are called cylindrical harmonics.

Kinematics
In a cylindrical coordinate system, the position of a particle can be written as $$\boldsymbol{r} = \rho\,\boldsymbol{\hat \rho} + z\,\boldsymbol{\hat z}.$$ The velocity of the particle is the time derivative of its position, $$\boldsymbol{v} = \frac{\mathrm{d}\boldsymbol{r}}{\mathrm{d}t} = \dot{\rho}\,\boldsymbol{\hat \rho} + \rho\,\dot\varphi\,\hat{\boldsymbol{\varphi}} + \dot{z}\,\hat{\boldsymbol{z}},$$ where the term $$\rho \dot\varphi\hat\varphi$$ comes from the Poisson formula $$\frac{\mathrm d\hat\rho}{\mathrm dt} = \dot\varphi\hat z\times \hat\rho $$. Its acceleration is $$ \boldsymbol{a} = \frac{\mathrm{d}\boldsymbol{v}}{\mathrm{d}t} = \left( \ddot{\rho} - \rho\,\dot\varphi^2 \right)\boldsymbol{\hat \rho} + \left( 2\dot{\rho}\,\dot\varphi + \rho\,\ddot\varphi \right) \hat{\boldsymbol\varphi } + \ddot{z}\,\hat{\boldsymbol{z}} $$

title: Cylindrical coordinate system


text:
User:Bonum Melior

Background: B.A. in Philosophy, several years in finance then MBA, now working for HM Treasury on PFI.

title: User:Bonum Melior


text:
Neolithic architecture

Neolithic architecture refers to structures encompassing housing and shelter from approximately 10,000 to 2,000 BC, the Neolithic period. In southwest Asia, Neolithic cultures appear soon after 10,000 BC, initially in the Levant (Pre-Pottery Neolithic A and Pre-Pottery Neolithic B) and from there into the east and west. Early Neolithic structures and buildings can be found in southeast Anatolia, Syria, and Iraq by 8,000 BC with agriculture societies first appearing in southeast Europe by 6,500 BC, and central Europe by ca. 5,500 BC (of which the earliest cultural complexes include the Starčevo-Koros (Cris), Linearbandkeramic, and Vinča.

Architectural advances are an important part of the Neolithic period (10,000-2000 BC), during which some of the major innovations of human history occurred. The domestication of plants and animals, for example, led to both new economics and a new relationship between people and the world, an increase in community size and permanence, a massive development of material culture, and new social and ritual solutions to enable people to live together in these communities. New styles of individual structures and their combination into settlements provided the buildings required for the new lifestyle and economy, and were also an essential element of change.

Housing
The Neolithic people in the Levant, Anatolia, Syria, northern Mesopotamia and central Asia were great builders, utilising mud-brick to construct houses and villages. At Çatalhöyük, houses were plastered and painted with elaborate scenes of humans and animals.

In Europe, the Neolithic long house with a timber frame, pitched, thatched roof, and walls finished in wattle and daub could be very large, presumably housing a whole extended family. Villages might comprise only a few such houses.

Neolithic pile dwellings have been excavated in Sweden (Alvastra pile dwelling) and in the circum-Alpine area, with remains being found at the Mondsee and Attersee lakes in Upper Austria. Early archaeologists like Ferdinand Keller thought they formed artificial islands, much like the Scottish crannogs, but today it is clear that the majority of settlements was located on the shores of lakes and were only inundated later on. Reconstructed pile dwellings are shown in open-air museums in Unteruhldingen and Zürich (Pfahlbauland).

In Romania, Moldova, and Ukraine, Neolithic settlements included wattle-and-daub structures with thatched roofs and floors made of logs covered in clay. This is also when the burdei pit-house (below-ground) style of house construction was developed, which was still used by Romanians and Ukrainians until the 20th century.

Neolithic settlements and "cities" include:
 * Göbekli Tepe in Turkey, ca. 9,000 BC
 * Tell es-Sultan (Jericho) in the Levant, Neolithic from around 8,350 BC, arising from the earlier Epipaleolithic Natufian culture
 * Nevali Cori in Turkey, ca. 8,000 BC
 * Çatalhöyük in Turkey, 7,500 BC
 * Mehrgarh in Pakistan, 7,000 BC
 * Knap of Howar and Skara Brae, the Orkney Islands, Scotland, from 3,500 BC
 * over 3,000 settlements of the Cucuteni-Trypillian culture, some with populations up to 15,000 residents, flourished in present-day Romania, Moldova and Ukraine from 5,400 to 2,800 BC.

Tombs and ritual monuments
Elaborate tombs for the dead were also built. These tombs are particularly numerous in Ireland, where there are many thousand still in existence. Neolithic people in the British Isles built long barrows and chamber tombs for their dead and causewayed camps, henges and cursus monuments.

Megalithic architecture
Megaliths found in Europe and the Mediterranean were also erected in the Neolithic period. These monuments include megalithic tombs, temples and several structures of unknown function. Tomb architecture is normally easily distinguished by the presence of human remains that had originally been buried, often with recognizable intent. Other structures may have had a mixed use, now often characterised as religious, ritual, astronomical or political. The modern distinction between various architectural functions with which we are familiar today, now makes it difficult for us to think of some megalithic structures as multi-purpose socio-cultural centre points. Such structures would have served a mixture of socio-economic, ideological, political functions and indeed aesthetic ideals.

The megalithic structures of Ġgantija, Tarxien, Ħaġar Qim, Mnajdra, Ta' Ħaġrat, Skorba and smaller satellite buildings on Malta and Gozo, first appearing in their current form around 3600 BC, represent one of the earliest examples of a fully developed architectural statement in which aesthetics, location, design and engineering fused into free-standing monuments. Stonehenge, the other well-known building from the Neolithic would later, 2600 and 2400 BC for the sarsen stones, and perhaps 3000 BC for the blue stones, be transformed into the form that we know so well. At its height Neolithic architecture marked geographic space; their durable monumentality embodied a past, perhaps made up of memories and remembrance.

In the Central Mediterranean, Malta also became home of a subterranean skeuomorphised form of architecture around 3600 BC. At the Ħal-Saflieni Hypogeum, the inhabitants of Malta carved out an underground burial complex in which surface architectural elements were used to embellish a series of chambers and entrances. It is at the Neolithic Ħal-Saflieni Hypogeum that the earliest known skeuomorphism first occurred in the world. This architectural device served to define the aesthetics of the underworld in terms that well known in the larger megaliths. On Malta and Gozo, surface and subterranean architecture defined two worlds, which later, in the Greek world, would manifest themselves in the myth of Hades and the world of the living. In Malta, therefore, we encounter Neolithic architecture which is demonstrably not purely functional, but which was conceptual in design and purpose.

Other structures
Early Neolithic water wells from the Linear Pottery culture have been found in central Germany near Leipzig. These structures are built in timber with complicated woodworking joints at the edges and are dated between 5,200 and 5,100 BC.

The world's oldest known engineered roadway, the Sweet Track in England, also dates from this time.

title: Neolithic architecture


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HM Treasury

His Majesty's Treasury (HM Treasury), occasionally referred to as the Exchequer, or more informally the Treasury, is a ministerial department of the Government of the United Kingdom. It is responsible for developing and executing the government's public finance policy and economic policy. The Treasury maintains the Online System for Central Accounting and Reporting, the replacement for the Combined Online Information System, which itemises departmental spending under thousands of category headings, and from which the Whole of Government Accounts annual financial statements are produced.

History
The origins of the Treasury of England have been traced by some to an individual known as Henry the Treasurer, a servant to King William the Conqueror. This claim is based on an entry in the Domesday Book showing the individual Henry "the treasurer" as a landowner in Winchester, where the royal treasure was stored.

The UK Treasury traces its origins to the Treasury of the Kingdom of England, founded by 1126, in the reign of King Henry I. The Treasury emerged from the Royal Household. It was where the king kept his treasures, such as in The King's Chamber. The head of the Treasury was called the Lord Treasurer. Starting in Tudor times, the Lord Treasurer became one of the chief officers of state, and competed with the Lord Chancellor for the principal place. Thomas Cromwell transformed the financial administration of the country, restoring authority to the Exchequer and making the King's Chamber, of central importance under Henry VII, back into a small spending department overseeing the Royal Household. The fact that Cromwell had a key post in the old Chamber system as well as being Chancellor of the Exchequer shows how he did this. For the majority of the medieval period the office of the Treasury was within the Exchequer (responsible for managing the royal revenue in addition to collecting and issuing money). As is often the case, wars are expensive and in 1433 war with France led to a deficit of £30,000 - the equivalent of over £100 billion today. Money that the Treasury received was recorded by using tallies. These were sticks with notches marked on them according to the amount of money involved. The stick was cut in two and one half given to the Sheriff as receipt for the money. They were in use until 1834 when a fire destroyed the Palace of Westminster. By 1584, the deficit had been turned into a surplus equivalent to one year's revenue. Monarchs tended to bypass the Exchequer because of its ineffectiveness until it was reformed by Lord Treasurer Winchester and his successor, Lord Burghley, under Elizabeth I.

In contrast, the Stuarts failed to enforce limits on inflation, war, corruption and extravagant tendencies and were forced into debt again. In 1667, King Charles II was responsible for appointing George Downing, the builder of Downing Street, to radically reform the Treasury and the collection of taxes. The Treasury was first put in commission (placed under the control of several people instead of only one) in May or June 1660. The first commissioners were the Duke of Albemarle, Lord Ashley, (Sir) W. Coventry, (Sir) J. Duncomb, and (Sir) T. Clifford. From the middle of the 17th century the need for a national bank became pressing. England and, in particular, London was greatly changing due to fast expansion of The Empire's trade, not least N.America, but also entrepot trade that grew to over one third of trade and with Continental Europe, however, what was needed was a "fund of money," or a term familiar today, but by which is really meant either precious metals or 'hard' currency such as US dollars mainly that grew in importance after WW1 to pay external trade bills i.e. questions of financial liquidity or circulation needed to maintain and grow the nation's national income and trade, but above all to honour the nation's foreign obligations. Failures to do so can lead to casus belli.

The early 1700s saw the meteoric rise of the banking and financial markets, with the emerging stock market revolving around government funds. The ability to raise money by means of creating debt through the issue of bills and bonds heralded the beginning of the National Debt. Improved controls over public spending ensured that creditors were more willing to lend money to the government. By the 1730s an early version of the public spending survey and the annual Budget had been established. In its evolution the Treasury had to learn some valuable lessons. In 1711, the Treasury established a scheme whereby it secured government debt by the authorisation of its subscription into the capital of the South Sea Company, with government creditors in return holding stock in the company. After 1714, the Treasury was always in commission. The commissioners were referred to as the Lords of the Treasury and were given a number based on their seniority. In 1720 the South Sea bubble burst and thousands of investors were affected; such was the outrage that the Chancellor of the Exchequer was sent to the Tower of London. Eventually the First Lord of the Treasury came, however, to be seen as the natural head of government, and from Robert Walpole on, the holder of the office became known, unofficially, as the Prime Minister. Until 1827, the First Lord of the Treasury, when a commoner, also held the office of Chancellor of the Exchequer, while if the First Lord was a peer, the Second Lord usually served as Chancellor. Since 1827, however, the Chancellor of the Exchequer has always been Second Lord of the Treasury.

If important lessons were learnt that the National Debt (and public finances) require prudent management, when The Exchequer was abolished in 1833, The HM Treasury became the ministerial department under the Chancellor of the Exchequer. When The Treasury was under commission, junior Lords were each paid £1,600 a year. It is insensible to consider The Treasury's history without The Bank of England set up in the 17th century. The argument for England's bank grew after the “Glorious Revolution” of 1688 when William of Orange and Queen Mary ascended to England's throne. London-based Scottish entrepreneur, William Paterson proposed a “Bank of England” with a “fund for perpetual Interest” (not yet bonds or bills) that was passed by Parliament, supported by Charles Montagu, Chancellor of the Exchequer and Michael Godfrey, another leading City merchant. The public were invited to invest subscriptions totalling £1.2 million forming the initial capital stock onward loaned to the Government in return for a Royal Charter. At the same time the National Debt was born, paper money came into existence.

Chancellor of the Exchequer
Although the Kingdoms of Great Britain and Ireland had been united by the Acts of Union 1800, the exchequers of the two kingdoms were not consolidated until 1817 under the Consolidated Fund Act 1816 (56 Geo. 3. c. 98). For the holders of the Irish office before this date, see Chancellor of the Exchequer of Ireland.

Current Treasury Ministers
As of 5 July 2024, the Treasury Ministers are as follows, with cabinet ministers in bold:

Whips
Some of the government whips are also associated in name with the Treasury: the Chief Whip is nominally Parliamentary Secretary to the Treasury and traditionally had an office in 12 Downing Street. Some of the other whips are nominally Lords Commissioners of the Treasury, though they are all members of the House of Commons. Being a whip is a party, rather than a government, position; the appointments to the Treasury are sinecure positions which allow the whips to be paid ministerial salaries. This has led to the Government front bench in the Commons being known as the Treasury Bench. However, since the whips no longer have any effective ministerial roles in the Treasury, they are usually not listed as Treasury ministers.

Permanent secretaries
The position of Permanent Secretary to the Treasury is generally regarded as the second most influential in the British Civil Service; two recent incumbents have gone on to be Cabinet Secretary, the only post outranking it.

From October 2022, the Permanent Secretary to the Treasury is James Bowler and there are two Second Permanent Secretaries: Cat Little and Beth Russell. The previous Permanent Secretary, Sir Tom Scholar, was sacked by Chancellor Kwasi Kwarteng and Prime Minister Liz Truss shortly after they took office.

Guidance
The Treasury publishes cross-government guidance including Managing Public Money and The Green Book: Central Government Guidance on appraisal and evaluation, current version dated 2020. Managing Public Money includes a definition of "value for money":"Value for money ... means securing the best mix of quality and effectiveness for the least outlay over the period of use of the goods or services bought. It is not about minimising up front prices." The Green Book includes the historic five case model, which requires consideration of the policy, economic, commercial, financial and management dimensions of a proposed project.

Banknote issue
Banknotes in the UK are normally issued by the Bank of England and a number of commercial banks (see Banknotes of the pound sterling). At the start of the First World War, the Currency and Bank Notes Act 1914 was passed, giving the Treasury temporary powers to issue banknotes in two denominations, one at £1 and another at 10 shillings, in the UK. Treasury notes had full legal tender status and were not convertible for gold through the Bank of England. They replaced the gold coin in circulation to prevent a run on sterling and to enable purchases of raw materials for armaments production. These notes featured an image of King George V (Bank of England notes did not begin to display an image of the monarch until 1960). The wording on each note was UNITED KINGDOM OF GREAT BRITAIN AND IRELAND — Currency notes are Legal Tender for the payment of any amount by the Lords Commissioners of His Majesty's Treasury under the Authority of Act of Parliament (4 & 5 Geo. V c.14). Notes issued after the partition of Ireland from 1922 had the wording changed to read "United Kingdom of Great Britain and Northern Ireland".

The promise (never adhered to) was that they would be removed from circulation after the war had ended. In fact, the notes were issued until 1928, when the Currency and Bank Notes Act 1928 returned note-issuing powers to the banks.

Executive agencies of HM Treasury

 * UK Debt Management Office, reporting to the Economic Secretary to the Treasury, is responsible for government borrowing operations.
 * National Savings and Investments

Other bodies reporting to Treasury ministers

 * HM Revenue & Customs, a non-ministerial government department for which the responsible minister is the Exchequer Secretary
 * Valuation Office Agency, an executive agency of HM Revenue and Customs
 * Office for Budget Responsibility, a non-departmental public body of HM Treasury
 * Office of Tax Simplification, an independent office of HM Treasury
 * Royal Mint, a Treasury-owned coinage company
 * UK Government Investments, a Treasury-owned holding company

History of the Treasury Main Building
The Treasury Main Building at 1 Horse Guards Road, often referred to as the Government Offices, Great George Street (GOGGS), was designed by John Brydon following a competition. Construction took place in two phases. The West end was completed in 1908 and the East end was completed in 1917. It was originally built as offices for the Board of Education, the Local Government Board, and the Ministry of Works Office; HM Treasury moved into the building in 1940. A major refurbishment of the building was procured under a Private Finance Initiative contract in 2000. The works, which were designed by Foster and Partners together with Feilden and Mawson and carried out by Bovis Lend Lease at a cost of £140 million, were completed in 2002.

title: HM Treasury