title: Joe Montana

text: Montana had a prolific season in 1982. However, the regular season was shortened to nine games when members of the Player's Association went on strike. Although San Francisco failed to make the playoffs, Montana threw for 2,613 yards and 17 touchdowns during the year. He also set what was then an NFL record with five consecutive 300-yard passing games. Because the 49ers missed the playoffs, the team seriously considered trading him to the Baltimore Colts for the rights to the first overall pick in the 1983 NFL Draft (and thus, the right to draft Stanford quarterback John Elway), but the 49ers reconsidered and ultimately traded their first round pick to the San Diego Chargers (used on Billy Ray Smith Jr.) weeks before the draft.


title: Joe Montana

text: The next year, Montana threw for 3,910 yards and 26 touchdowns in 16 regular season games. The team ended the regular season with a 10–6 record and finished first in the NFC West. In the , they faced the Detroit Lions. Yet again, Montana demonstrated his ability to perform well in high-pressure situations. Despite being out-played in terms of total yardage, the 49ers trailed by just six points as the game neared its conclusion. With 1:23 remaining in regulation, the 49ers offense had the ball at the Lions 14-yard line and Montana completed a touchdown pass to wide receiver Freddie Solomon, giving San Francisco the lead on the ensuing extra-point.


title: Joe Montana

text: The victory placed the 49ers in the against the Washington Redskins. As he had done before, Montana asserted himself late in the game. The Redskins led 21–0 at the start of the fourth quarter, but Montana helped lead the 49ers back. Aided by three fourth-quarter Montana touchdown passes, the 49ers tied the game at 21. However, Redskins placekicker Mark Moseley kicked a 25-yard field goal in the waning moments of the game. Despite Montana's efforts, the team lost, 24–21.


title: Joe Montana

text: Though the Miami Dolphins finished the 1972 NFL season with no losses, the regular season at the time comprised only 14 games. Thus, when the 49ers finished the 1984 NFL season with a 15–1 record, they became the first team to win 15 games in a single regular season.


title: Joe Montana

text: Montana again had an excellent season and earned his second consecutive trip to the Pro Bowl. In their first two playoff games, the 49ers defeated the New York Giants and the Chicago Bears by a combined score of 44–10. In Super Bowl XIX, the 49ers faced the Dolphins and their quarterback, Dan Marino.


title: Joe Montana

text: In the game, Montana threw for three touchdowns and completed 24 of 35 passes. He established the Super Bowl record for most yards passing in a single game (331) and supplemented his passing with 59 yards rushing. The 49ers defeated the Dolphins 38–16 and Montana earned his second Super Bowl MVP award. After the game, 49ers head coach Bill Walsh said: "Joe Montana is the greatest quarterback today, maybe the greatest quarterback of all time."


title: Joe Montana

text: Aided in part by Montana's performance at quarterback, the 49ers advanced to the NFL Playoffs again in 1985; however, they lost in the NFC Wild card game to the New York Giants.


title: Joe Montana

text: In the 1986 season, Montana suffered a severe back injury during week one of the season. The injury was to a spinal disc in Montana's lower back and required immediate surgery. The injury was so severe that Montana's doctors suggested that Montana retire. On September 15, 1986, the 49ers placed Montana on the injured reserve list; however, he returned to the team on November 6 of that year. In his first game back from injury Montana passed for 270 yards and three touchdown passes in a 43–17 49er victory against the St. Louis Cardinals. Montana appeared in just eight games that season, and threw more interceptions than touchdown passes for the only time in his career. The 49ers finished the season with a record of 10–5–1. Montana was co-recipient (with Minnesota Vikings quarterback Tommy Kramer) of the 1986 NFL Comeback Player of the Year Award.


title: Joe Montana

text: In 1987, Montana had 31 touchdown passes, a career-high, in just 13 games. Montana crossed the picket line during the NFLPA strike and threw five touchdowns against replacement players. In 1987, he also set the NFL record for most consecutive pass attempts without an incomplete pass (22), passed for 3,054 yards, and had a passer rating of 102.1. Though the 49ers finished with the best record in the NFL, they lost in the of the playoffs to the Minnesota Vikings.


title: Joe Montana

text: Prior to the 1987 season, Bill Walsh completed a trade for Steve Young, then a quarterback with the Tampa Bay Buccaneers. Young went on to appear in eight regular season games for the team and finished the year with a passer rating of 120.8.


title: Joe Montana

text: Young's performance in 1987 was strong enough that by the time the 1988 season began, a controversy was in place as to who should get more playing time at quarterback. Young appeared in 11 games that year and rumors surfaced claiming that Montana might be traded.


title: Joe Montana

text: Despite the competition for playing time, Montana received most of the playing time during the 1988 season. After a home loss to the Los Angeles Raiders that left the 49ers with a 6–5 record, the 49ers were in danger of missing the playoffs. Montana regained the starting position and led the 49ers to a 10–6 record and the NFC Western Division title.


title: Joe Montana

text: The 49ers earned a trip to Super Bowl XXIII when they defeated the Minnesota Vikings and the Chicago Bears in the playoffs. In the NFC Divisional Playoffs, the 49ers faced Minnesota, who had eliminated them from the playoffs the year before. Montana threw three first-half touchdowns as the 49ers won, 34–9. The victory over the Bears in the is of particular note. Played at Soldier Field in Chicago, with temperatures of 17 °F (-8 °C) and a strong wind, Montana threw for 288 yards and 3 touchdowns. His first touchdown pass came on a 3rd-down play late in the first quarter in which Montana threw a perfect sideline pass to Jerry Rice and Rice outran two Bears defenders for a 61-yard score. The 49ers won 28–3 to advance to Super Bowl XXIII.


title: Joe Montana

text: In January 1989, the 49ers again faced the Cincinnati Bengals in the Super Bowl. Of his third trip to the Super Bowl, Montana told the "San Jose Mercury News": "This trip to the Super Bowl is more gratifying than the others because the road has been harder." Then, in Super Bowl XXIII, Montana had one of the best performances of his career. He completed 23 of 36 passes for a then-Super Bowl record 357 yards and two touchdowns. Despite his great performance, the 49ers found themselves trailing the Bengals 16–13 with only 3:20 left in the game and the ball on their own 8-yard line. But Montana calmly drove them down the field, completing 8 of 9 passes for 92 yards and throwing the game-winning touchdown pass to John Taylor with only 34 seconds left.


title: Joe Montana

text: 1989 proved to be successful for Montana and the 49ers. The team finished the regular season with an NFL-best 14–2 record, and their two losses were by a total of only five points. Montana threw for 3,521 yards and 26 touchdowns with only 8 interceptions, giving him what was then the highest single-season passer rating in NFL history, a mark subsequently broken by Young in 1994, and later broken again by Peyton Manning of the Indianapolis Colts in 2004 and by Aaron Rodgers 2011 season with the Packers. He also rushed for 227 yards and three touchdowns on the ground and earned the NFL Most Valuable Player Award. In a memorable comeback win in Week 4 against the Philadelphia Eagles, Montana threw four touchdown passes in the 4th quarter. He finished with 428 yards passing and five touchdown passes in the victory. The 49ers were successful in the playoffs, easily beating the Minnesota Vikings 41–13 in the divisional round and the Los Angeles Rams 30–3 in the . Montana threw for a total of 503 yards and 6 touchdowns in those 2 games without a single interception. Then in Super Bowl XXIV, Montana became the first player ever to win Super Bowl MVP honors for a third time, throwing for 297 yards and a then-Super Bowl record five touchdowns while also rushing for 15 yards as the 49ers defeated the Denver Broncos 55–10, the highest single-team and most lopsided score in Super Bowl history.


title: Joe Montana

text: In 1990, Montana once again led the 49ers to the best regular season record (14–2) in the NFL. He was named by "Sports Illustrated" as Sportsman of the Year. A highlight from the season was a rematch with the Atlanta Falcons. Intent on blitzing Montana most of the game, Atlanta's defense allowed Montana to throw for a career-best 476 yards (49ers single-game record) and six touchdown passes, five of them to Jerry Rice. He would end up throwing for 3,944 yards and 26 touchdowns, albeit while also throwing a career-high 16 interceptions. Three of those interceptions came in a November 25 home loss to the Rams, which ended the 49ers' 18-game winning streak (dating back to a home loss to the Packers in November 1989).


title: Joe Montana

text: The 49ers run game struggled in 1990: the team averaged 3.8 yards a carry, only good enough for 19th in the league. No 49er exceeded 500 yards rushing for the entire year. Fullback Tom Rathman scored the most touchdowns (7) on the ground while gaining 318 yards. Roger Craig (439 yards, 1 TD) was slowed by a knee injury suffered in week 5 at Houston. Rookie running back Dexter Carter (460 yards, 1 TD) did not help much. Carter's only touchdown came on December 17 at the Rams; his 74-yard touchdown run that clinched home-field advantage for the 49ers constituted roughly one-sixth of his productivity in terms of yardage on the ground, and he lost four fumbles at home the following Sunday in a 13–10 loss to the Saints.


title: Joe Montana

text: The 49ers looked forward to becoming the first NFL team to win three consecutive Super Bowls, and they moved through the playoffs to the to face the New York Giants. The 49ers defense was able to hold backup quarterback Jeff Hostetler and the Giants without a touchdown, but the tide of the game changed when Montana was sacked by Leonard Marshall while rolling out of the quarterback pocket; he was injured and left the game, which the Giants won, 15–13, on the last of five Giants field goals, which was set up by a fumble from 49ers running back Roger Craig.


title: Joe Montana

text: Montana missed the entire 1991 season and most of the 1992 season with an elbow injury sustained during the 1991 pre-season. In the final game of the 1992 regular season; a "Monday Night Football" matchup against the Detroit Lions, Montana stepped in and played the entire second half. Despite missing nearly two full seasons, Montana proved to be very effective, sealing the victory with "insurance points". By this time, however, Steve Young had established himself as a starter, and took over for the playoffs. Though it was not known at the time, Montana would not see another snap in a 49er uniform. He suited up for the final time as a 49er in the team's NFC Championship showdown with the Dallas Cowboys, though as third-string QB behind Young and Steve Bono.


title: Joe Montana

text: With Montana healthy and ready to play, a quarterback controversy soon emerged. Steve Young had proven his effectiveness in the two years he played while Montana was injured, and many fans and players alike felt that they had made the transition to Steve Young. Furthermore, Young did not want to play if he was used only as a backup. Nevertheless, there was also a strong sentiment that Montana was the "face of the franchise" and it would be right for him to remain so. A rift in the locker room developed, and Montana ultimately requested a trade. Young eventually led the team to another Super Bowl victory, which helped him emerge from Montana's shadow.


title: Joe Montana

text: Montana was traded to the Kansas City Chiefs on April 20, 1993, and signed a $10 million contract over three years. His trade was the catalyst for the subsequent Chiefs' free-agent signing of star Los Angeles Raiders running back Marcus Allen on June 9. The arrival of Montana and Allen, both former Super Bowl MVPs, generated much media attention and excitement in Kansas City. Chiefs general manager Carl Peterson had spent the 1993 off-season installing the "West Coast offense" under the direction of new offensive coordinator Paul Hackett, who at one time served as 49ers quarterbacks coach to Montana, and who would report to incumbent head coach Marty Schottenheimer.


title: Joe Montana

text: The Chiefs mailed three jerseys to Montana. One was number 3, his number from Notre Dame, which the Chiefs had retired in honor of Hall of Fame kicker Jan Stenerud, who offered to let him wear it. Another was number 19, which he wore in youth football and also briefly in training camp of the 1979 season with San Francisco, and the third was number 16, which Hall of Fame quarterback Len Dawson offered to let Montana wear since the organization had retired it. Montana declined Dawson's and Stenerud's offers and wore 19 instead. During the Chiefs' first offseason practice, the defensive players all remained behind after their session concluded to watch the offensive team practice "because they wanted to see Joe Montana play. That's what those guys thought of the trade. It gave everybody hope we could win a championship. That's why it was such a special time."


title: Joe Montana

text: Montana was injured for part of the 1993 season, but was still selected to his final Pro Bowl, as the Chiefs won their division for the first time in 22 years. Montana led the Chiefs in two come-from-behind wins in the 1993 playoffs. In their wild-card win over the Pittsburgh Steelers, he threw a 7-yard fourth-down touchdown pass to send the game into overtime. Then against the Houston Oilers, he led the team to 28 second-half points, including three touchdown passes to earn the 29th fourth-quarter comeback win of his career. In the , Kansas City lost to the Buffalo Bills 30–13, with Montana suffering a concussion during the third play of the third quarter and yielding to Dave Krieg. Including their two playoff victories that year (the Chiefs only had one prior playoff win since Super Bowl IV in 1970), the 1993 Chiefs won 13 games, which tied the franchise record for wins in a season.


title: Joe Montana

text: Montana returned healthy to the Chiefs in 1994, starting all but two games. His highlights included a classic duel with John Elway (which Montana won, 31–28) on "Monday Night Football", and a memorable game in week 2 when Montana played against his old team, the 49ers and Steve Young. In a much-anticipated match-up, Montana and the Chiefs prevailed and defeated the 49ers, 24–17. Montana led his team to a 9–7 record, sufficient for another postseason appearance, where they lost in the wild-card playoff round to the Miami Dolphins and Dan Marino, .


title: Joe Montana

text: Montana has fondly remembered the Chiefs’ home of Arrowhead Stadium with its "unbelievable roar" from field level, saying “The thing about Kansas City, it doesn’t matter whether they’re winning or losing, that fan base is ridiculous. Over the years, I don’t think that stadium’s ever been empty. Those people there support that team and that organization like none you’ve seen. And it is so loud. Even after 50 years, they’re still in there screaming every week. That fan base is probably one of the best in the NFL, one of the hardest places to play for sure". Head coach Marty Schottenheimer pulled Montana aside before his first game at Arrowhead and telling him to prepare for a volume he’d never experienced. Montana recalled ‘Come on, Marty, I’ve played in four Super Bowls. I’ve played all over the place,’ ” he said. “And Marty said, ‘Just wait.’ ” “The thing that gets you is the whole stadium, when they sing the national anthem, is when they say, ‘And the home of the … Chiefs!’ Still makes your hair stand up on your arms.”


title: Joe Montana

text: On April 18, 1995, Montana announced his retirement before a huge crowd at Justin Herman Plaza in San Francisco. The event was broadcast live on local television, and included speeches from John Madden, Eddie DeBartolo Jr., and others. Highlights from Montana's stay with San Francisco and interviews with former 49ers teammates were also shown. Bill Walsh, who had served as head coach for three of Montana's four Super Bowl victories, was the emcee for the event.


title: Joe Montana

text: Montana's replacement as starting quarterback with the Chiefs was his former backup in San Francisco, Steve Bono.


title: Joe Montana

text: Super Bowl XXX was dedicated to Montana, who ended the pregame ceremonies with the ceremonial coin toss.


title: Joe Montana

text: Former 49er teammate Harris Barton set up a fund-of-funds capital firm HRJ Capital in 1999. Montana joined HRJ as a partner from 2003 to 2005, helping invest in venture capital firms, hedge funds and private-equity funds.


title: Joe Montana

text: Montana was one of five Bay Area Super Bowl MVPs to whom Super Bowl 50 was dedicated, the others being Fred Biletnikoff, Jim Plunkett, and ex-teammates Jerry Rice and Steve Young, all five of whom were accompanied to the field by Drew Brees, Eli Manning, and Malcolm Smith for the conclusion of the pregame ceremonies; Montana again flipped the coin on their behalf.


title: Joe Montana

text: Montana was in attendance at the in Arrowhead Stadium, supporting his former team Chiefs against the New England Patriots. It was only the second time that the Chiefs contested the Conference title game; the first was when Montana quarterbacked them in the 1993 season.


title: Joe Montana

text: Super Bowl LIV between the 49ers and Chiefs was nicknamed “Joe Montana Bowl” as he played for both teams during his NFL career. Montana joked: "You heard from me first. I "guarantee" my team will win the Super Bowl!"


title: Joe Montana

text: Noted for his ability to remain calm under pressure, Montana helped his teams to 32 fourth-quarter come-from-behind victories. With 58 seconds left in the against the Dallas Cowboys, he completed a game-winning touchdown pass so memorable that it would become known simply as "The Catch". In Super Bowl XXIII against the Cincinnati Bengals, Montana threw another remarkable game-winning touchdown pass at the end of a 92-yard drive with only 36 seconds left on the game clock.


title: Joe Montana

text: During his career with the 49ers, Montana completed 2,929 of 4,600 passes for 35,142 yards with 244 touchdowns and 123 interceptions. He had thirty-five 300-yard passing games including seven in which he threw for over 400 yards. His career totals: 3,409 completions on 5,391 attempts, 273 touchdowns, 139 interceptions, and 40,551 yards passing. He also rushed for 1,676 yards and 20 touchdowns. When Montana retired, his career passer rating was 92.3, second only to his 49er successor Steve Young (96.8). He has since been surpassed by five other players, which ranks his passer rating at 7th all-time. Montana also had won 100 games faster than any other quarterback until surpassed by Tom Brady in 2008. His record as a starter was 117–47. His number 16 was retired by the 49ers on December 15, 1997, during halftime of the team's game against the Denver Broncos on "Monday Night Football". Montana also held the record for most passing yards on a Monday night game with 458 against the Los Angeles Rams in 1989.


title: Joe Montana

text: Montana is second in postseason records for most games with a passer rating over 100.0 (12), in career postseason touchdown passes (45), passing yards (5,772) and games with 300+ passing yards (six, tied with Kurt Warner). He also tied Terry Bradshaw's record for consecutive playoff games with at least two touchdown passes (seven), though this record has since been broken by Baltimore Ravens quarterback Joe Flacco and Green Bay Packers quaterback Aaron Rodgers. Undefeated in four Super Bowl appearances, Montana completed 83 of 122 passes for 1,142 yards and 11 touchdowns with no interceptions, earning him a Super Bowl record passer rating of 127.8. The first player ever to win three Super Bowl MVP awards, Montana also holds the Super Bowl record for most pass attempts (122) without throwing an interception.


title: Joe Montana

text: He was selected to the Pro Bowl eight times and selected All-Pro six times. He is also the only player to have two touchdown passes of 95+ yards.


title: Joe Montana

text: Montana earned the nickname "Joe Cool" for his ability to stay calm at key moments, and "Comeback Kid" for his history of rallying his teams from late-game deficits. His teammates in San Francisco called him "Bird Legs" due to his very thin legs and small calves. He was called "Golden Joe" because he played in California (the Golden State), and also appeared on a poster superimposed in front of the Golden Gate Bridge with the wording "The Golden Great". Two more names were provided by a "San Francisco Chronicle" nickname contest early in his NFL career: the winner was "Big Sky", but another contestant suggested that since "Joe Montana" already sounded like a nickname, Montana needed a real name, and christened him "David W. Gibson". Montana liked the Gibson name so much that he had it stenciled above his locker.


title: Joe Montana

text: Montana appears as the character "Joe Clifford" (pseudonym derived from his first and middle names) in the NFL Network's "Joe's Diner" television spots.


title: Joe Montana

text: Montana has been married three times. In 1974, he wed his hometown sweetheart, Kim Moses, during his second semester at Notre Dame; they divorced three years later. In 1981, he married Cass Castillo; they divorced in 1984. He met Jennifer Wallace, an actress and model, while the two worked on a Schick commercial; the couple married in 1985. They have four children: Alexandra (b. October 10, 1985), Elizabeth (b. December 20, 1986), Nate (b. October 3, 1989), and Nick (b. April 28, 1992). Both of his sons played football for De La Salle High School. Nate became an undrafted free agent from West Virginia Wesleyan after transferring from Notre Dame and the University of Montana, as did Nick from Tulane University (having transferred from the University of Washington and Mt. San Antonio College).


title: Joe Montana

text: In 2008, Montana sued ex-wife Moses and a Dallas auction house for "violating his 'copyright and privacy rights'" after Moses "sold a bunch of letters and memorabilia from <nowiki>[Montana's]</nowiki> college days at Notre Dame".


title: Joe Montana

text: Montana resides in San Francisco. He placed his $49 million, estate in Calistoga, California, on sale in 2009, which was reduced to $35 million in January 2012. He owns horses and produces wine under the label Montagia.


title: Candice Bergen

text: Candice Patricia Bergen (born May 9, 1946) is an American actress. She won five Primetime Emmy Awards and two Golden Globe Awards for her portrayal of the title character on the CBS sitcom "Murphy Brown" (1988–1998, 2018). She is also known for her role as Shirley Schmidt on the ABC drama "Boston Legal" (2005–2008). In films, Bergen was nominated for the Academy Award for Best Supporting Actress for "Starting Over" (1979), and for the BAFTA Award for Best Actress in a Supporting Role for "Gandhi" (1982).


title: Candice Bergen

text: Bergen began her career as a fashion model and appeared on the cover of "Vogue" before she made her screen debut in the film "The Group" (1966). She starred in "The Sand Pebbles" (1966), "Soldier Blue" (1970), "Carnal Knowledge" (1971), and "The Wind and the Lion" (1975). She made her Broadway debut in the 1984 play "Hurlyburly" and starred in the revivals of "The Best Man" (2012) and "Love Letters" (2014). From 2002 to 2004, she appeared in three episodes of the HBO series "Sex and the City". Her other film roles include "Miss Congeniality" (2000), "Sweet Home Alabama" (2002), "The Women" (2008), "Bride Wars" (2009), "Book Club" (2018) and "Let Them All Talk" (2020).


title: Candice Bergen

text: Candice Patricia Bergen was born May 9, 1946, at Hollywood Presbyterian Hospital in Los Angeles, California. Her mother, Frances Bergen (née Westerman), was a Powers model who was known professionally as Frances Westcott. Her father, Edgar Bergen, was a ventriloquist, comedian, and actor. Her paternal grandparents were Swedish immigrants who anglicized their surname, which was originally Berggren ("mountain branch").


title: Candice Bergen

text: Bergen was raised in Beverly Hills, California, and attended the Harvard-Westlake School. As a child, she was often described as "Charlie McCarthy's little sister", which irritated her (referring to her father's star dummy).


title: Candice Bergen

text: She began appearing on her father's radio program at a young age, and in 1958, at age 11, with her father on Groucho Marx's quiz show "You Bet Your Life", as Candy Bergen. She said that when she grew up, she wanted to design clothes.


title: Candice Bergen

text: She later attended the University of Pennsylvania, where she was elected both Homecoming Queen and Miss University, but, as Bergen later acknowledged, she failed to take her education seriously and after failing two courses in art and opera, she was asked to leave at the end of her sophomore year. She ultimately received an honorary doctorate from Penn in May 1992.


title: Candice Bergen

text: She worked as a fashion model before she took up acting, featured on the covers of "Vogue". She received her acting training at HB Studio in New York City.


title: Candice Bergen

text: Bergen made her screen debut playing a university student in the ensemble film "The Group" (1966), directed by Sidney Lumet, who knew Bergen's family. The film delicately touched on the subject of lesbianism. The film was a critical and financial success.


title: Candice Bergen

text: After the film's success, Bergen left college to focus on her career. She played the role of Shirley Eckert, an assistant school teacher, in "The Sand Pebbles" (1966) with Steve McQueen. The movie was nominated for several Academy Awards and was a big financial success. It was made for 20th Century Fox.


title: Candice Bergen

text: She guest starred on an episode of "Coronet Blue", whose director Sam Wanamaker recommended her for a part in the comedy "The Day the Fish Came Out" (1967) directed by Michael Cacoyannis, distributed by Fox. The film was a box-office flop, but Fox nevertheless signed her to a long-term contract.


title: Candice Bergen

text: Bergen went to France to appear in Claude Lelouch's romantic drama "Live for Life" (1967) opposite Yves Montand, popular in France but not the US.


title: Candice Bergen

text: In 1968, she played the leading female role in "The Magus", a British mystery film for Fox starring Michael Caine and Anthony Quinn that was almost universally ridiculed on its release and was another major flop.


title: Candice Bergen

text: She was featured in a 1970 political satire, "The Adventurers", based on a novel by Harold Robbins, playing a frustrated socialite. Her salary was $200,000. The film received negative reviews, and while it did respectable business at the box office, it did not help her career. Bergen called it a "movie out of the 1940s."


title: Candice Bergen

text: Bergen played the girlfriend of Elliott Gould in "Getting Straight" (1970), a counterculture movie which drew another spate of bad reviews, but was commercially profitable. She said it took her career in "a new direction... my first experience with democratic, communal movie making."


title: Candice Bergen

text: She also starred in the controversial Western "Soldier Blue" (1970), an overseas success but a failure in its homeland, perhaps because of its unflattering portrayal of the U.S. Cavalry. The film's European success led to Bergen's being voted by British exhibitors as the seventh-most popular star at the British box office in 1971. Bergen appeared with Oliver Reed in "The Hunting Party" (1971), a violent Western which drew terrible reviews and flopped at the box office.


title: Candice Bergen

text: Bergen received some strong reviews for her support role in "Carnal Knowledge" (1971), directed by Mike Nichols. She then had the lead role in the drama "T.R. Baskin" (1971) and earned the best reviews of her career up to that time. She described the latter as the first role "that is really sort of a vehicle, where I have to act and not just be a sort of decoration" saying she'd decided "it was time for me to get serious about acting."


title: Candice Bergen

text: Bergen was absent from screens for a few years. She returned with a support part in a British heist film, "11 Harrowhouse" (1974), then did a Western with Gene Hackman and James Coburn, "Bite the Bullet" (1975). Both films were modest successes. In 1975, she replaced Faye Dunaway at the last minute to co-star with Sean Connery in "The Wind and the Lion" (1976), as a strong-willed American widow kidnapped in the Moroccan desert. The film drew mixed reviews and broke even at the box office.


title: Candice Bergen

text: Bergen was reunited with Hackman in "The Domino Principle" (1977) for Stanley Kramer, another failure.


title: Candice Bergen

text: She appeared in "A Night Full of Rain" (1978) for Lina Wertmüller and was the love interest of Ryan O'Neal's character in the "Love Story" sequel, "Oliver's Story" (1978), but both films failed critically and financially.


title: Candice Bergen

text: Bergen appeared in the Burt Reynolds romantic comedy "Starting Over" (1979), for which she received Academy Award and Golden Globe Award nominations for best supporting actress.


title: Candice Bergen

text: She portrayed a best-selling author in "Rich and Famous" (1981) with Jacqueline Bisset. A remake of the Bette Davis film "Old Acquaintance", it was not a success.


title: Candice Bergen

text: In 1982, Bergen appeared in the Oscar-winning film "Gandhi" in which she portrayed documentary photographer Margaret Bourke-White. Bergen was nominated for a BAFTA Award for Best Actress in a Supporting Role.


title: Candice Bergen

text: Beginning in the 1970s, Bergen became a frequent guest host of "Saturday Night Live". She was the first woman to host the show, and the first host to do a second show. She was also the first woman to join the Five-Timers Club, when she hosted for the fifth time in 1990. Bergen also guest-starred on "The Muppet Show" in its first year.


title: Candice Bergen

text: On television, Bergen appeared as Morgan Le Fay in "Arthur the King" (1985) and in the miniseries "Hollywood Wives" (1985). She was Burt Reynolds' romantic interest in "Stick" (1985), and for TV appeared in "Murder: By Reason of Insanity" (1985) and "Mayflower Madam" (1987).


title: Candice Bergen

text: In 1988, she took the lead role in the sitcom "Murphy Brown", in which she played a tough television reporter. The series provided her with the opportunity to show her little-seen comic talent, and although primarily a conventional sitcom, the show did tackle important issues. Murphy Brown, a recovering alcoholic, became a single mother and later battled breast cancer. In 1992, Vice President Dan Quayle criticized prime-time TV for showing the Murphy Brown character "mocking the importance of fathers by bearing a child alone and calling it just another lifestyle choice."


title: Candice Bergen

text: Quayle's disparaging remarks were subsequently written into the show, with Murphy shown watching Quayle's speech in disbelief at his insensitivity and ignorance of the reality of the lives of single mothers. A subsequent episode explored the subject of family values within a diverse set of families. The Brown character arranges for a truckload of potatoes to be dumped in front of Quayle's residence, an allusion to an infamous incident in which Quayle erroneously directed a school child to spell the word "potato" as "potatoe". In reality, Bergen agreed with at least some of Quayle's observations, saying that while the particular remark was "an arrogant and uninformed posture", as a whole, it was "a perfectly intelligent speech about fathers not being dispensable and nobody agreed with that more than I did." Bergen's run on "Murphy Brown" was extremely successful. The show ran for ten seasons and between 1989 and 1998, Bergen was nominated for an Emmy Award seven times and won five. After her fifth win, she declined future nominations for the role.


title: Candice Bergen

text: Throughout the same time frame as "Murphy Brown", Bergen also appeared as the main spokesperson for a Sprint telephone ad campaign.


title: Candice Bergen

text: After playing the role of Murphy Brown, Bergen was offered a chance to work as a real-life journalist: After the show ended in 1998, CBS approached her to cover stories for "60 Minutes". She declined the offer, saying she did not want to blur the lines between actor and journalist.


title: Candice Bergen

text: She also appeared in character roles in films, including "Miss Congeniality" (2000), where she played villainous pageant host Kathy Morningside; she also portrayed the mayor of New York in "Sweet Home Alabama" (2002) and appeared in the Gwyneth Paltrow flight-attendant comedy, "View from the Top" (2003).


title: Candice Bergen

text: She had roles in "The In-Laws" (2003), "Footsteps" (2003), a thriller, and appeared in 3 episodes of "Sex and the City" as Enid Frick, Carrie Bradshaw's editor at "Vogue".


title: Candice Bergen

text: In January 2005, Bergen joined the cast of the television series "Boston Legal" as Shirley Schmidt, a founding partner in the law firm of Crane, Poole & Schmidt. She played the role for five seasons. In 2006 and 2008, she received Emmy nominations for Outstanding Supporting Actress in a Drama Series.


title: Candice Bergen

text: She has also made guest appearances on many other TV shows, including "Seinfeld" (as herself playing Murphy Brown), "Law & Order", "Family Guy", and "Will & Grace" (playing herself). She has also featured in a long-running "Dime Lady" ad campaign for the Sprint phone company.


title: Candice Bergen

text: Bergen could be seen in "The Women" (2008) and "Bride Wars" (2009) as Marion St. Claire, New York's most sought-after wedding planner, who also serves as the narrator of the story.


title: Candice Bergen

text: From its launch in 2008, Candice Bergen was a contributor for wowOwow.com, a website for women to talk culture, politics and gossip. The website closed in 2010.


title: Candice Bergen

text: She was in "The Romantics" (2010) and had an occasional role on "House" as Lisa Cuddy's mother, starting in Season 7, including the 2011 episodes "Larger Than Life" and "Family Practice".


title: Candice Bergen

text: In 2010, she appeared in a one-night only concert: a semi-staged reading of "Evening Primrose" by Stephen Sondheim. She has also appeared on Broadway in the 2012 revival of Gore Vidal's "The Best Man" and the 2014 revival of "Love Letters".


title: Candice Bergen

text: Later performances included "A Merry Friggin' Christmas" (2014), "Beautiful & Twisted" (2015), "Rules Don't Apply" (2016),"The Meyerowitz Stories (New and Selected)" (2017), "Home Again" (2017) and "Book Club" (2018).


title: Candice Bergen

text: On January 24, 2018, it was announced that Candice Bergen would be reprising her role as Murphy Brown. The reboot aired on CBS in fall 2018 for 13 episodes. On May 10, 2019, the reboot was canceled by CBS.


title: Candice Bergen

text: In addition to acting, Bergen studied photography and worked as a photojournalist. She has written numerous articles and a play, as well as two memoirs, "Knock Wood" in 1984, and "A Fine Romance" in 2015.


title: Candice Bergen

text: In 2016, Bergen began hand painting, with paint pens, on handbags, with the business overseen by her daughter, Chloé Malle, and the proceeds benefiting charity.


title: Candice Bergen

text: Bergen is a political activist who once accepted a date with Henry Kissinger. In 1967, she participated in a Yippie prank when she, Abbie Hoffman, and others threw dollar bills onto the floor of the New York Stock Exchange, leading to its temporary shutdown. In the late 1960's Bergen was in a relationship with Doris Day's son Terry Melcher. In 1972, she served as a fundraiser and organizer for George McGovern's presidential campaign.


title: Candice Bergen

text: From 1971 to circa 1975, Bergen was in a relationship with late Hollywood producer and writer Bert Schneider.


title: Candice Bergen

text: Bergen's father died in 1978. In her memoir "A Fine Romance", she mentions that she was left out of his will, while he bequeathed $10,000 to his dummy, Charlie McCarthy, adding that she felt her father had a stronger bond with Charlie than with her. She later said:


title: Candice Bergen

text: On September 27, 1980, she married French film director Louis Malle. They had one child, a daughter named Chloe Françoise, in 1985. The couple were married until Malle's death from cancer on Thanksgiving Day in 1995. Bergen and Malle were introduced at Diane von Fürstenberg's home, Cloudwalk Farm, located in the Merryall area of New Milford, Connecticut.


title: Names of large numbers

text: Two naming scales for large numbers have been used in English and other European languages since the early modern era: the long and short scales. Most English variants use the short scale today, but the long scale remains dominant in many non-English-speaking areas, including continental Europe and Spanish-speaking countries in Latin America. These naming procedures are based on taking the number "n" occurring in 10 (short scale) or 10 (long scale) and concatenating Latin roots for its units, tens, and hundreds place, together with the suffix "-illion".


title: Names of large numbers

text: Names of numbers above a trillion are rarely used in practice; such large numbers have practical usage primarily in the scientific domain, where powers of ten are expressed as "10" with a numeric superscript.


title: Names of large numbers

text: Indian English does not use millions, but has its own system of large numbers including lakhs and crores. English also has many words, such as "zillion", used informally to mean large but unspecified amounts; see indefinite and fictitious numbers.


title: Names of large numbers

text: Apart from "million", the words in this list ending with -"illion" are all derived by adding prefixes ("bi"-, "tri"-, etc., derived from Latin) to the stem -"illion". "Centillion" appears to be the highest name ending in -"illion" that is included in these dictionaries. "Trigintillion", often cited as a word in discussions of names of large numbers, is not included in any of them, nor are any of the names that can easily be created by extending the naming pattern ("unvigintillion", "duovigintillion", "duoquinquagintillion", etc.).


title: Names of large numbers

text: All of the dictionaries included "googol" and "googolplex", generally crediting it to the Kasner and Newman book and to Kasner's nephew. None include any higher names in the googol family (googolduplex, etc.). The "Oxford English Dictionary" comments that "googol" and "googolplex" are "not in formal mathematical use".


title: Names of large numbers

text: Some names of large numbers, such as "million", "billion", and "trillion", have real referents in human experience, and are encountered in many contexts. At times, the names of large numbers have been forced into common usage as a result of hyperinflation. The highest numerical value banknote ever printed was a note for 1 sextillion pengő (10 or 1 milliard bilpengő as printed) printed in Hungary in 1946. In 2009, Zimbabwe printed a 100 trillion (10) Zimbabwean dollar note, which at the time of printing was worth about US$30.


title: Names of large numbers

text: Names of larger numbers, however, have a tenuous, artificial existence, rarely found outside definitions, lists, and discussions of how large numbers are named. Even well-established names like "sextillion" are rarely used, since in the context of science, including astronomy, where such large numbers often occur, they are nearly always written using scientific notation. In this notation, powers of ten are expressed as "10" with a numeric superscript, e.g. "The X-ray emission of the radio galaxy is ." When a number such as 10 needs to be referred to in words, it is simply read out as "ten to the forty-fifth". This is easier to say and less ambiguous than "quattuordecillion", which means something different in the long scale and the short scale.


title: Names of large numbers

text: When a number represents a quantity rather than a count, SI prefixes can be used—thus "femtosecond", not "one quadrillionth of a second"—although often powers of ten are used instead of some of the very high and very low prefixes. In some cases, specialized units are used, such as the astronomer's parsec and light year or the particle physicist's barn.


title: Names of large numbers

text: Nevertheless, large numbers have an intellectual fascination and are of mathematical interest, and giving them names is one way people try to conceptualize and understand them.


title: Names of large numbers

text: One of the earliest examples of this is "The Sand Reckoner", in which Archimedes gave a system for naming large numbers. To do this, he called the numbers up to a myriad myriad (10) "first numbers" and called 10 itself the "unit of the second numbers". Multiples of this unit then became the second numbers, up to this unit taken a myriad myriad times, 10·10=10. This became the "unit of the third numbers", whose multiples were the third numbers, and so on. Archimedes continued naming numbers in this way up to a myriad myriad times the unit of the 10-th numbers, i.e. formula_1 and embedded this construction within another copy of itself to produce names for numbers up to formula_2 Archimedes then estimated the number of grains of sand that would be required to fill the known universe, and found that it was no more than "one thousand myriad of the eighth numbers" (10).


title: Names of large numbers

text: Since then, many others have engaged in the pursuit of conceptualizing and naming numbers that have no existence outside the imagination. One motivation for such a pursuit is that attributed to the inventor of the word "googol", who was certain that any finite number "had to have a name". Another possible motivation is competition between students in computer programming courses, where a common exercise is that of writing a program to output numbers in the form of English words.


title: Names of large numbers

text: Most names proposed for large numbers belong to systematic schemes which are extensible. Thus, many names for large numbers are simply the result of following a naming system to its logical conclusion—or extending it further.


title: Names of large numbers

text: The words "bymillion" and "trimillion" were first recorded in 1475 in a manuscript of Jehan Adam. Subsequently, Nicolas Chuquet wrote a book "Triparty en la science des nombres" which was not published during Chuquet's lifetime. However, most of it was copied by Estienne de La Roche for a portion of his 1520 book, "L'arismetique". Chuquet's book contains a passage in which he shows a large number marked off into groups of six digits, with the comment:


title: Names of large numbers

text: Ou qui veult le premier point peult signiffier million Le second point byllion Le tiers point tryllion Le quart quadrillion Le cinq quyllion Le six sixlion Le sept. septyllion Le huyt ottyllion Le neuf nonyllion et ainsi des ault' se plus oultre on vouloit preceder


title: Names of large numbers

text: (Or if you prefer the first mark can signify million, the second mark byllion, the third mark tryllion, the fourth quadrillion, the fifth quyillion, the sixth sixlion, the seventh septyllion, the eighth ottyllion, the ninth nonyllion and so on with others as far as you wish to go).


title: Names of large numbers

text: Adam and Chuquet used the long scale of powers of a million; that is, Adam's "bymillion" (Chuquet's "byllion") denoted 10, and Adam's "trimillion" (Chuquet's "tryllion") denoted 10.


title: Names of large numbers

text: The names "googol" and "googolplex" were invented by Edward Kasner's nephew Milton Sirotta and introduced in Kasner and Newman's 1940 book "Mathematics and the Imagination" in the following passage:


title: Names of large numbers

text: John Horton Conway and Richard K. Guy have suggested that "N-plex" be used as a name for 10. This gives rise to the name "googolplexplex" for 10 = 10. Conway and Guy have proposed that "N-minex" be used as a name for 10, giving rise to the name "googolminex" for the reciprocal of a googolplex. None of these names are in wide use, nor are any currently found in dictionaries.


title: Names of large numbers

text: The names "googol" and "googolplex" inspired the name of the Internet company Google and its corporate headquarters, the Googleplex, respectively.


title: Names of large numbers

text: This section illustrates several systems for naming large numbers, and shows how they can be extended past "vigintillion".


title: Names of large numbers

text: Traditional British usage assigned new names for each power of one million (the long scale): ; ; ; and so on. It was adapted from French usage, and is similar to the system that was documented or invented by Chuquet.


title: Names of large numbers

text: Traditional American usage (which was also adapted from French usage but at a later date), Canadian, and modern British usage assign new names for each power of one thousand (the short scale.) Thus, a "billion" is 1000 × 1000 = 10; a "trillion" is 1000 × 1000 = 10; and so forth. Due to its dominance in the financial world (and by the US dollar), this was adopted for official United Nations documents.


title: Names of large numbers

text: Traditional French usage has varied; in 1948, France, which had originally popularized the short scale worldwide, reverted to the long scale.


title: Names of large numbers

text: The term "milliard" is unambiguous and always means 10. It is seldom seen in American usage and rarely in British usage, but frequently in continental European usage. The term is sometimes attributed to French mathematician Jacques Peletier du Mans circa 1550 (for this reason, the long scale is also known as the "Chuquet-Peletier" system), but the Oxford English Dictionary states that the term derives from post-Classical Latin term "milliartum", which became "milliare" and then "milliart" and finally our modern term.


title: Names of large numbers

text: Concerning names ending in -illiard for numbers 10, "milliard" is certainly in widespread use in languages other than English, but the degree of actual use of the larger terms is questionable. The terms "Milliarde" in German, "miljard" in Dutch, "milyar" in Turkish, and "миллиард," milliard (transliterated) in Russian, are standard usage when discussing financial topics.


title: Names of large numbers

text: The naming procedure for large numbers is based on taking the number "n" occurring in 10 (short scale) or 10 (long scale) and concatenating Latin roots for its units, tens, and hundreds place, together with the suffix "-illion". In this way, numbers up to 10 = 10 (short scale) or 10 = 10 (long scale) may be named. The choice of roots and the concatenation procedure is that of the standard dictionary numbers if "n" is 9 or smaller. For larger "n" (between 10 and 999), prefixes can be constructed based on a system described by Conway and Guy. Today, sexdecillion and novemdecillion are standard dictionary numbers and, using the same reasoning as Conway and Guy did for the numbers up to nonillion, could probably be used to form acceptable prefixes. The Conway–Guy system for forming prefixes:


title: Names of large numbers

text: Since the system of using Latin prefixes will become ambiguous for numbers with exponents of a size which the Romans rarely counted to, like 10, Conway and Guy co-devised with Allan Wechsler the following set of consistent conventions that permit, in principle, the extension of this system indefinitely to provide English short-scale names for any integer whatsoever. The name of a number 10, where "n" is greater than or equal to 1000, is formed by concatenating the names of the numbers of the form 10, where "m" represents each group of comma-separated digits of "n", with each but the last "-illion" trimmed to "-illi-", or, in the case of "m" = 0, either "-nilli-" or "-nillion". For example, 10, the 1,000,003rd "-illion" number, equals one "millinillitrillion"; 10, the 11,000,670,036th "-illion" number, equals one "undecillinilliseptuagintasescentillisestrigintillion"; and 10, the 9,876,543,210th "-illion" number, equals one "nonilliseseptuagintaoctingentillitresquadragintaquingentillideciducentillion".


title: Names of large numbers

text: The following table shows number names generated by the system described by Conway and Guy for the short and long scales.


title: Names of large numbers

text: The International System of Quantities (ISQ) defines a series of prefixes denoting integer powers of 1024 between 1024 and 1024.


title: Tagalog language

text: Tagalog (, ; ; "Baybayin": ) is an Austronesian language spoken as a first language by the ethnic Tagalog people, who make up a quarter of the population of the Philippines, and as a second language by the majority. Its standardized form, officially named "Filipino", is the national language of the Philippines, and is one of two official languages, alongside English.


title: Tagalog language

text: Tagalog is closely related to other Philippine languages, such as the Bikol languages, Ilocano, the Bisayan languages, Kapampangan, and Pangasinan, and more distantly to other Austronesian languages, such as the Formosan languages of Taiwan, Indonesian, Malay, Hawaiian, Māori, and Malagasy.


title: Tagalog language

text: Tagalog is a Central Philippine language within the Austronesian language family. Being Malayo-Polynesian, it is related to other Austronesian languages, such as Malagasy, Javanese, Indonesian, Malay, Tetum (of Timor), and Yami (of Taiwan). It is closely related to the languages spoken in the Bicol Region and the Visayas islands, such as the Bikol group and the Visayan group, including Waray-Waray, Hiligaynon and Cebuano.


title: Tagalog language

text: Tagalog differs from its Central Philippine counterparts with its treatment of the Proto-Philippine schwa vowel . In most Bikol and Visayan languages, this sound merged with and . In Tagalog, it has merged with . For example, Proto-Philippine (adhere, stick) is Tagalog "dikít" and Visayan & Bikol "dukot".


title: Tagalog language

text: Proto-Philippine , , and merged with but is between vowels. Proto-Philippine (name) and (kiss) became Tagalog "ngalan" and "halík".


title: Tagalog language

text: The word "Tagalog" is derived from the endonym "taga-ilog" ("river dweller"), composed of "tagá-" ("native of" or "from") and "ilog" ("river"). Linguists such as David Zorc and Robert Blust speculate that the Tagalogs and other Central Philippine ethno-linguistic groups originated in Northeastern Mindanao or the Eastern Visayas.


title: Tagalog language

text: Possible words of Old Tagalog origin are attested in the Laguna Copperplate Inscription from the tenth century, which is largely written in Old Malay. The first known complete book to be written in Tagalog is the "Doctrina Christiana" (Christian Doctrine), printed in 1593. The "Doctrina" was written in Spanish and two transcriptions of Tagalog; one in the ancient, then-current Baybayin script and the other in an early Spanish attempt at a Latin orthography for the language.


title: Tagalog language

text: Throughout the 333 years of Spanish rule, various grammars and dictionaries were written by Spanish clergymen. In 1610, the Dominican priest Francisco Blancas de San Jose published the "Arte y reglas de la lengua tagala" (which was subsequently revised with two editions in 1752 and 1832) in Bataan. In 1613, the Franciscan priest Pedro de San Buenaventura published the first Tagalog dictionary, his "Vocabulario de la lengua tagala" in Pila, Laguna.


title: Tagalog language

text: The first substantial dictionary of the Tagalog language was written by the Czech Jesuit missionary Pablo Clain in the beginning of the 18th century. Clain spoke Tagalog and used it actively in several of his books. He prepared the dictionary, which he later passed over to Francisco Jansens and José Hernandez. Further compilation of his substantial work was prepared by P. Juan de Noceda and P. Pedro de Sanlucar and published as "Vocabulario de la lengua tagala" in Manila in 1754 and then repeatedly reedited, with the last edition being in 2013 in Manila.


title: Tagalog language

text: Among others, "Arte de la lengua tagala y manual tagalog para la administración de los Santos Sacramentos" (1850) in addition to early studies of the language.


title: Tagalog language

text: The indigenous poet Francisco Balagtas (1788–1862) is known as the foremost Tagalog writer, his most notable work being the 19th-century epic "Florante at Laura".


title: Tagalog language

text: Tagalog was declared the official language by the first revolutionary constitution in the Philippines, the in 1897.


title: Tagalog language

text: In 1935, the Philippine constitution designated English and Spanish as official languages, but mandated the development and adoption of a common national language based on one of the existing native languages. After study and deliberation, the National Language Institute, a committee composed of seven members who represented various regions in the Philippines, chose Tagalog as the basis for the evolution and adoption of the national language of the Philippines. President Manuel L. Quezon then, on December 30, 1937, proclaimed the selection of the Tagalog language to be used as the basis for the evolution and adoption of the national language of the Philippines. In 1939, President Quezon renamed the proposed Tagalog-based national language as "Wikang Pambansâ" (national language). Under the Japanese puppet government during World War II, Tagalog as a national language was strongly promoted; the 1943 Constitution specifying: The government shall take steps toward the development and propagation of Tagalog as the national language.".


title: Tagalog language

text: In 1959, the language was further renamed as "Pilipino". Along with English, the national language has had official status under the 1973 constitution (as "Pilipino") and the present 1987 constitution (as Filipino).


title: Tagalog language

text: The adoption of Tagalog in 1937 as basis for a national language is not without its own controversies. Instead of specifying Tagalog, the national language was designated as "Wikang Pambansâ" ("National Language") in 1939. Twenty years later, in 1959, it was renamed by then Secretary of Education, José Romero, as "Pilipino" to give it a national rather than ethnic label and connotation. The changing of the name did not, however, result in acceptance among non-Tagalogs, especially Cebuanos who had not accepted the selection.


title: Tagalog language

text: The national language issue was revived once more during the 1971 Constitutional Convention. The majority of the delegates were even in favor of scrapping the idea of a "national language" altogether. A compromise solution was worked out—a "universalist" approach to the national language, to be called "Filipino" rather than "Pilipino". The 1973 constitution makes no mention of Tagalog. When a new constitution was drawn up in 1987, it named Filipino as the national language. The constitution specified that as the Filipino language evolves, it shall be further developed and enriched on the basis of existing Philippine and other languages. However, more than two decades after the institution of the "universalist" approach, there seems to be little if any difference between Tagalog and Filipino.


title: Tagalog language

text: Many of the older generation in the Philippines feel that the replacement of English by Tagalog in the popular visual media has had dire economic effects regarding the competitiveness of the Philippines in trade and overseas remittances.


title: Tagalog language

text: Upon the issuance of "Executive Order No. 134", Tagalog was declared as basis of the National Language. On April 12, 1940, "Executive No. 263" was issued ordering the teaching of the national language in all public and private schools in the country.


title: Tagalog language

text: In 2009, the Department of Education promulgated an order institutionalizing a system of mother-tongue based multilingual education ("MLE"), wherein instruction is conducted primarily in a student's mother tongue (one of the various regional Philippine languages) until at least grade three, with additional languages such as Filipino and English being introduced as separate subjects no earlier than grade two. In secondary school, Filipino and English become the primary languages of instruction, with the learner's first language taking on an auxiliary role. After pilot tests in selected schools, the MLE program was implemented nationwide from School Year (SY) 2012–2013.


title: Tagalog language

text: Tagalog is the first language of a quarter of the population of the Philippines (particularly in Central and Southern Luzon) and the second language for the majority.


title: Tagalog language

text: According to the Philippine Statistics Authority, as of 2014, there were 100 million people living in the Philippines, where the vast majority have some basic level of understanding of the language. The Tagalog homeland, Katagalugan, covers roughly much of the central to southern parts of the island of Luzon—particularly in Aurora, Bataan, Batangas, Bulacan, Cavite, Laguna, Metro Manila, Nueva Ecija, Quezon, and Rizal. Tagalog is also spoken natively by inhabitants living on the islands of Marinduque and Mindoro, as well as Palawan to a lesser extent. Significant minorities are found in the other Central Luzon provinces of Pampanga and Tarlac, Ambos Camarines in Bicol Region, and the Cordillera city of Baguio. Tagalog is also the predominant language of Cotabato City in Mindanao, making it the only place outside of Luzon with a native Tagalog-speaking majority.


title: Tagalog language

text: At the 2000 Philippines Census, it is spoken by approximately 57.3 million Filipinos, 96% of the household population who were able to attend school; slightly over 22 million, or 28% of the total Philippine population, speak it as a native language.


title: Tagalog language

text: The following regions and provinces of the Philippines are majority Tagalog-speaking (from north to south):


title: Tagalog language

text: Tagalog speakers are also found in other parts of the Philippines and through its standardized form of Filipino, the language serves the national "lingua franca" of the country.


title: Tagalog language

text: Tagalog serves as the common language among Overseas Filipinos, though its use overseas is usually limited to communication between Filipino ethnic groups. The largest concentration of Tagalog speakers outside the Philippines is found in the United States, wherein 2013, the United States Census Bureau reported (based on data collected in 2011) that it was the fourth most-spoken non-English language at home with almost 1.6 million speakers, behind Spanish, French (including Patois, Cajun, Creole), and Chinese (with figures for Cantonese and Mandarin combined). In urban areas, Tagalog ranked as the third most spoken non-English language, behind Spanish and Chinese varieties but ahead of French.


title: Tagalog language

text: A study based on data from the United States Census Bureau’s 2015 American Consumer Survey shows that Tagalog is the most commonly spoken non-English language after Spanish in California, Nevada, and Washington states.


title: Tagalog language

text: Tagalog is one of three recognized languages in San Francisco, California, along with Spanish and Chinese, making all essential city services be communicated using these languages along with English. Meanwhile, Tagalog and Ilocano (which is primarily spoken in northern Philippines) are among the non-official languages of Hawaii that its state offices and state-funded entities are required to provide oral and written translations to its residents. Election ballots in Nevada include instructions written in Tagalog, which was first introduced in the 2020 United States presidential elections.


title: Tagalog language

text: Other countries with significant concentrations of overseas Filipinos and Tagalog speakers include Saudi Arabia with 938,490, Canada with 676,775, Japan with 313,588, United Arab Emirates with 541,593, Kuwait with 187,067, and Malaysia with 620,043.


title: Tagalog language

text: At present, no comprehensive dialectology has been done in the Tagalog-speaking regions, though there have been descriptions in the form of dictionaries and grammars of various Tagalog dialects. Ethnologue lists Manila, Lubang, Marinduque, Bataan (Western Central Luzon), Batangas, Bulacan (Eastern Central Luzon), Tanay-Paete (Rizal-Laguna), and Tayabas (Quezon and Aurora) as dialects of Tagalog; however, there appear to be four main dialects, of which the aforementioned are a part: Northern (exemplified by the Bulacan dialect), Central (including Manila), Southern (exemplified by Batangas), and Marinduque.


title: Tagalog language

text: Perhaps the most divergent Tagalog dialects are those spoken in Marinduque. Linguist Rosa Soberano identifies two dialects, western and eastern, with the former being closer to the Tagalog dialects spoken in the provinces of Batangas and Quezon.


title: Tagalog language

text: One example is the verb conjugation paradigms. While some of the affixes are different, Marinduque also preserves the imperative affixes, also found in Visayan and Bikol languages, that have mostly disappeared from most Tagalog early 20th century; they have since merged with the infinitive.


title: Tagalog language

text: Tagalog has 33 phonemes: 19 of them are consonants and 14 are vowels. Syllable structure is relatively simple, being maximally CrVC, where Cr only occurs in borrowed words such as "trak" "truck" or "sombréro" "hat".


title: Tagalog language

text: Tagalog has ten simple vowels, five long and five short, and four diphthongs. Before appearing in the area north of the Pasig river, Tagalog had three vowel qualities: , , and . This was later expanded to five with the introduction of Spanish words.


title: Tagalog language

text: Nevertheless, simplification of pairs and is likely to take place, especially in some Tagalog as second language, remote location and working class registers.


title: Tagalog language

text: The four diphthongs are , , , and . Long vowels are not written apart from pedagogical texts, where an acute accent is used: "á é í ó ú."


title: Tagalog language

text: The table above shows all the possible realizations for each of the five vowel sounds depending on the speaker's origin or proficiency. The five general vowels are in bold.


title: Tagalog language

text: Below is a chart of Tagalog consonants. All the stops are unaspirated. The velar nasal occurs in all positions including at the beginning of a word. Loanword variants using these phonemes are italicized inside the angle brackets.


title: Tagalog language

text: Stress is a distinctive feature in Tagalog. Primary stress occurs on either the final or the penultimate syllable of a word. Vowel lengthening accompanies primary or secondary stress except when stress occurs at the end of a word.


title: Tagalog language

text: Tagalog words are often distinguished from one another by the position of the stress and/or the presence of a final glottal stop. In formal or academic settings, stress placement and the glottal stop are indicated by a diacritic ("tuldík") above the final vowel. The penultimate primary stress position ("malumay") is the default stress type and so is left unwritten except in dictionaries.


title: Tagalog language

text: Tagalog, like other Philippines languages today, is written using the Latin alphabet. Prior to the arrival of the Spanish in 1521 and the beginning of their colonization in 1565, Tagalog was written in an abugida—or alphasyllabary—called Baybayin. This system of writing gradually gave way to the use and propagation of the Latin alphabet as introduced by the Spanish. As the Spanish began to record and create grammars and dictionaries for the various languages of the Philippine archipelago, they adopted systems of writing closely following the orthographic customs of the Spanish language and were refined over the years. Until the first half of the 20th century, most Philippine languages were widely written in a variety of ways based on Spanish orthography.


title: Tagalog language

text: In the late 19th century, a number of educated Filipinos began proposing for revising the spelling system used for Tagalog at the time. In 1884, Filipino doctor and student of languages Trinidad Pardo de Tavera published his study on the ancient Tagalog script "Contribucion para el Estudio de los Antiguos Alfabetos Filipinos" and in 1887, published his essay "El Sanscrito en la lengua Tagalog" which made use of a new writing system developed by him. Meanwhile, Jose Rizal, inspired by Pardo de Tavera's 1884 work, also began developing a new system of orthography (unaware at first of Pardo de Tavera's own orthography). A major noticeable change in these proposed orthographies was the use of the letter ⟨k⟩ rather than ⟨c⟩ and ⟨q⟩ to represent the phoneme .


title: Tagalog language

text: In 1889, the new bilingual Spanish-Tagalog "La España Oriental" newspaper, of which Isabelo de los Reyes was an editor, began publishing using the new orthography stating in a footnote that it would "use the orthography recently introduced by ... learned Orientalis". This new orthography, while having its supporters, was also not initially accepted by several writers. Soon after the first issue of "La España", Pascual H. Poblete's "Revista Católica de Filipina" began a series of articles attacking the new orthography and its proponents. A fellow writer, Pablo Tecson was also critical. Among the attacks was the use of the letters "k" and "w" as they were deemed to be of German origin and thus its proponents were deemed as "unpatriotic". The publishers of these two papers would eventually merge as "La Lectura Popular" in January 1890 and would eventually make use of both spelling systems in its articles. Pedro Laktaw, a schoolteacher, published the first Spanish-Tagalog dictionary using the new orthography in 1890.


title: Tagalog language

text: In April 1890, Jose Rizal authored an article "Sobre la Nueva Ortografia de la Lengua Tagalog" in the Madrid-based periodical La Solidaridad. In it, he addressed the criticisms of the new writing system by writers like Pobrete and Tecson and the simplicity, in his opinion, of the new orthography. Rizal described the orthography promoted by Pardo de Tavera as "more perfect" than what he himself had developed. The new orthography was however not broadly adopted initially and was used inconsistently in the bilingual periodicals of Manila until the early 20th century. The revolutionary society Kataás-taasan, Kagalang-galang Katipunan ng̃ mg̃á Anak ng̃ Bayan or Katipunan made use of the k-orthography and the letter k featured prominently on many of its flags and insignias.


title: Tagalog language

text: In 1937, Tagalog was selected to serve as basis for the country's national language. In 1940, the "Balarílà ng Wikang Pambansâ" () of grammarian Lope K. Santos introduced the Abakada alphabet. This alphabet consists of 20 letters and became the standard alphabet of the national language. The orthography as used by Tagalog would eventually influence and spread to the systems of writing used by other Philippine languages (which had been using variants of the Spanish-based system of writing). In 1987, the ABAKADA was dropped and in its place is the expanded Filipino alphabet.


title: Tagalog language

text: Tagalog was written in an abugida (alphasyllabary) called Baybayin prior to the Spanish colonial period in the Philippines, in the 16th century. This particular writing system was composed of symbols representing three vowels and 14 consonants. Belonging to the Brahmic family of scripts, it shares similarities with the Old Kawi script of Java and is believed to be descended from the script used by the Bugis in Sulawesi.


title: Tagalog language

text: Although it enjoyed a relatively high level of literacy, Baybayin gradually fell into disuse in favor of the Latin alphabet taught by the Spaniards during their rule.


title: Tagalog language

text: There has been confusion of how to use Baybayin, which is actually an abugida, or an alphasyllabary, rather than an alphabet. Not every letter in the Latin alphabet is represented with one of those in the Baybayin alphasyllabary. Rather than letters being put together to make sounds as in Western languages, Baybayin uses symbols to represent syllables.


title: Tagalog language

text: A "kudlit" resembling an apostrophe is used above or below a symbol to change the vowel sound after its consonant. If the kudlit is used above, the vowel is an "E" or "I" sound. If the kudlit is used below, the vowel is an "O" or "U" sound. A special kudlit was later added by Spanish missionaries in which a cross placed below the symbol to get rid of the vowel sound all together, leaving a consonant. Previously, the consonant without a following vowel was simply left out (for example, "bundok" being rendered as "budo"), forcing the reader to use context when reading such words.


title: Tagalog language

text: Until the first half of the 20th century, Tagalog was widely written in a variety of ways based on Spanish orthography consisting of 32 letters called 'ABECEDARIO' (Spanish for "alphabet"). The additional letters from the 26-letter English alphabet are: ch, ll, ng, ñ, n͠g / ñg, and rr.


title: Tagalog language

text: When the national language was based on Tagalog, grammarian Lope K. Santos introduced a new alphabet consisting of 20 letters called "ABAKADA" in school grammar books called "balarilà". The only letter not in the English alphabet is ng.


title: Tagalog language

text: In 1987, the Department of Education, Culture and Sports issued a memo stating that the Philippine alphabet had changed from the Pilipino-Tagalog Abakada version to a new 28-letter alphabet to make room for loans, especially family names from Spanish and English. The additional letters from the 26-letter English alphabet are: ñ, ng.


title: Tagalog language

text: The genitive marker "ng" and the plural marker "mga" (e.g. "Iyan ang mga damit ko." (Those are my clothes)) are abbreviations that are pronounced "nang" and "mangá" . "Ng", in most cases, roughly translates to "of" (ex. "Siya ay kapatid ng nanay ko." She is the sibling "of" my mother) while "nang" usually means "when" or can describe how something is done or to what extent (equivalent to the suffix "-ly" in English adverbs), among other uses.


title: Tagalog language

text: In the first example, "nang" is used in lieu of the word "noong" (when; "Noong si Hudas ay madulas"). In the second, "nang" describes that the person woke up ("gumising") early ("maaga"); "gumising nang maaga". In the third, "nang" described up to what extent that Juan improved ("gumaling"), which is "greatly" ("nang "). In the latter two examples, the ligature "na" and its variants "-ng" and "-g" may also be used ("Gumising na maaga/Maagang gumising"; "Gumaling na /Todong gumaling").


title: Tagalog language

text: The words "pô/hô" originated from the word "Panginoon." and "Poon." ("Lord."). When combined with the basic affirmative "Oo" "yes" (from Proto-Malayo-Polynesian *heqe), the resulting forms are "opò" and "ohò".


title: Tagalog language

text: "Pô" and "opò" are specifically used to denote a high level of respect when addressing older persons of close affinity like parents, relatives, teachers and family friends. "Hô" and "ohò" are generally used to politely address older neighbours, strangers, public officials, bosses and nannies, and may suggest a distance in societal relationship and respect determined by the addressee's social rank and not their age. However, "pô" and "opò" can be used in any case in order to express an elevation of respect.


title: Tagalog language

text: Tagalog vocabulary is mostly of native Austronesian or Tagalog origin, such as most of the words that end with the diphthong -iw, (e.g. giliw) and words that exhibit reduplication (e.g. halo-halo, patpat, etc.). Besides inherited cognates, this also accounts for innovations in Tagalog vocabulary, especially traditional ones within its dialects. Tagalog has also incorporated many Spanish and English loanwords; the necessity of which increases in more technical parlance.


title: Tagalog language

text: In precolonial times, Trade Malay was widely known and spoken throughout Maritime Southeast Asia, contributing a significant number of Malay vocabulary into the Tagalog language. Malay loanwords, identifiable or not, may often already be considered native as these have existed in the language before colonisation.


title: Tagalog language

text: Tagalog also includes loanwords from Indian languages (Sanskrit and Tamil, mostly through Malay), Chinese languages (mostly Hokkien, followed by Cantonese, Mandarin, etc.), Japanese, Arabic and Persian.


title: Tagalog language

text: Due to the colonial trade with Mexico using the Manila galleons from the 16th to the 19th centuries, some words from several Amerindian languages such as Nahuatl (Aztec), Quechua, and Taino were introduced to Tagalog.


title: Tagalog language

text: English has borrowed some words from Tagalog, such as abaca, barong, balisong, boondocks, jeepney, Manila hemp, pancit, ylang-ylang, and yaya. Some of these loanwords are more often used in Philippine English.


title: Tagalog language

text: Tagalog has contributed several words to Philippine Spanish, like "barangay" (from "balan͠gay," meaning "barrio"), the "abacá", "cogon", "palay", "dalaga" etc.


title: Tagalog language

text: "Taglish" and "Englog" are names given to a mix of English and Tagalog. The amount of English vs. Tagalog varies from the occasional use of English loan words to changing language in mid-sentence. Such code-switching is prevalent throughout the Philippines and in various languages of the Philippines other than Tagalog.


title: Tagalog language

text: Code-mixing also entails the use of foreign words that are "Filipinized" by reforming them using Filipino rules, such as verb conjugations. Users typically use Filipino or English words, whichever comes to mind first or whichever is easier to use.


title: Tagalog language

text: The practice is common in television, radio, and print media as well. Advertisements from companies like Wells Fargo, Wal-Mart, Albertsons, McDonald's and Western Union have contained Taglish.


title: Tagalog language

text: Religious literature remains one of the most dynamic components to Tagalog literature. The first Bible in Tagalog, then called "Ang Biblia" ("the Bible") and now called "Ang Dating Biblia" ("the Old Bible"), was published in 1905. In 1970, the Philippine Bible Society translated the Bible into modern Tagalog. Even before the Second Vatican Council, devotional materials in Tagalog had been in circulation. There are at least four circulating Tagalog translations of the Bible


title: Tagalog language

text: When the Second Vatican Council, (specifically the Sacrosanctum Concilium) permitted the universal prayers to be translated into vernacular languages, the Catholic Bishops' Conference of the Philippines was one of the first to translate the Roman Missal into Tagalog. The Roman Missal in Tagalog was published as early as 1982.


title: Tagalog language

text: Jehovah's Witnesses were printing Tagalog literature at least as early as 1941 and "The Watchtower" (the primary magazine of Jehovah's Witnesses) has been published in Tagalog since at least the 1950s. New releases are now regularly released simultaneously in a number of languages, including Tagalog. The official website of Jehovah's Witnesses also has some publications available online in Tagalog. The revised bible edition, the "New World Translation of the Holy Scriptures," was released in Tagalog on 2019 and it is distributed without charge both printed and online versions.


title: Tagalog language

text: Tagalog is quite a stable language, and very few revisions have been made to Catholic Bible translations. Also, as Protestantism in the Philippines is relatively young, liturgical prayers tend to be more ecumenical.


title: Tagalog language

text: This is Article 1 of the Universal Declaration of Human Rights ("Pángkalahatáng Pagpapahayag ng Karapatáng Pantao")


title: Tagalog language

text: Numbers ("mga bilang/mga numero") in Tagalog follow two systems. The first consists of native Tagalog words and the other are Spanish-derived. (This may be compared to other East Asian languages, except with the second set of numbers borrowed from Spanish instead of Chinese.) For example, when a person refers to the number "seven", it can be translated into Tagalog as ""pito"" or ""siyete"" (Spanish: "siete").


title: Tagalog language

text: Months and days in Tagalog are also localised forms of Spanish months and days. "Month" in Tagalog is "buwán" (also the word for moon) and "day" is "araw" (the word also means sun). Unlike Spanish, however, months and days in Tagalog are always capitalised.


title: Tagalog language

text: Time expressions in Tagalog are also Tagalized forms of the corresponding Spanish. "Time" in Tagalog is "panahón" or "oras".


title: Tagalog language

text: "Ang hindî marunong lumingón sa pinánggalingan ay hindî makaráratíng sa paroroonan". (José Rizal)One who knows not how to look back from whence he came, will never get to where he is going.


title: Tagalog language

text: "Tao ka nang humarap, bilang tao kitang haharapin."(A proverb in Southern Tagalog that made people aware the significance of sincerity in Tagalog communities. It says, "As a human you reach me, I treat you as a human and never act as a traitor.")


title: Tagalog language

text: "Hulí man daw (raw) at magalíng, nakáhahábol pa rin."If one is behind but capable, one will still be able to catch up.


title: Tagalog language

text: "Magbirô ka na sa lasíng, huwág lang sa bagong gising."Make fun of someone drunk, if you must, but never one who has just awakened.


title: Tagalog language

text: "Ang sakít ng kalingkingan, damdám ng buóng katawán."The pain in the pinkie is felt by the whole body.


title: Tagalog language

text: "Pagkáhabà-habà man ng prusisyón, sa simbahan pa rin ang tulóy."The procession may stretch on and on, but it still ends up at the church.


title: Tagalog language

text: "Kung 'dî mádaán sa santóng dasalan, daanin sa santóng paspasan."If it cannot be got through holy prayer, get it through blessed force.


title: Logarithm

text: In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number  to the base  is the exponent to which must be raised, to produce . For example, since , the "logarithm base" 10 of is , or . The logarithm of to "base"  is denoted as , or without parentheses, , or even without the explicit base, , when no confusion is possible, or when the base does not matter such as in big O notation.


title: Logarithm

text: The logarithm base is called the decimal or common logarithm and is commonly used in science and engineering. The natural logarithm has the number  as its base; its use is widespread in mathematics and physics, because of its very simple derivative. The binary logarithm uses base and is frequently used in computer science.


title: Logarithm

text: Logarithms were introduced by John Napier in 1614 as a means of simplifying calculations. They were rapidly adopted by navigators, scientists, engineers, surveyors and others to perform high-accuracy computations more easily. Using logarithm tables, tedious multi-digit multiplication steps can be replaced by table look-ups and simpler addition. This is possible because the logarithm of a product is the sum of the logarithms of the factors:


title: Logarithm

text: provided that , and are all positive and . The slide rule, also based on logarithms, allows quick calculations without tables, but at lower precision. The present-day notion of logarithms comes from Leonhard Euler, who connected them to the exponential function in the 18th century, and who also introduced the letter as the base of natural logarithms.


title: Logarithm

text: Logarithmic scales reduce wide-ranging quantities to smaller scopes. For example, the decibel (dB) is a unit used to express ratio as logarithms, mostly for signal power and amplitude (of which sound pressure is a common example). In chemistry, pH is a logarithmic measure for the acidity of an aqueous solution. Logarithms are commonplace in scientific formulae, and in measurements of the complexity of algorithms and of geometric objects called fractals. They help to describe frequency ratios of musical intervals, appear in formulas counting prime numbers or approximating factorials, inform some models in psychophysics, and can aid in forensic accounting.


title: Logarithm

text: The concept of logarithm as the inverse of exponentiation extends to other mathematical structures as well. However, in general settings, the logarithm tends to be a multi-valued function. For example, the complex logarithm is the multi-valued inverse of the complex exponential function. Similarly, the discrete logarithm is the multi-valued inverse of the exponential function in finite groups; it has uses in public-key cryptography.


title: Logarithm

text: Addition, multiplication, and exponentiation are three of the most fundamental arithmetic operations. The inverse of addition is subtraction, and the inverse of multiplication is division. Similarly, a logarithm is the inverse operation of exponentiation. Exponentiation is when a number , the "base", is raised to a certain power , the "exponent", to give a value ; this is denoted


title: Logarithm

text: The logarithm of base is the inverse operation, that provides the output from the input . That is, formula_4 is equivalent to formula_5 if is a positive real number. (If is not a positive real number, both exponentiation and logarithm can be defined but may take several values, which makes definitions much more complicated.)


title: Logarithm

text: which allowed (before the invention of computers) reducing computation of multiplications and divisions to additions, subtractions and logarithm table looking.


title: Logarithm

text: Given a positive real number such that , the "logarithm" of a positive real number with respect to base  is the exponent by which must be raised to yield . In other words, the logarithm of to base  is the unique real number  such that formula_7.


title: Logarithm

text: The logarithm is denoted "" (pronounced as "the logarithm of to base ", "the logarithm of ", or most commonly "the log, base , of ").


title: Logarithm

text: An equivalent and more succinct definition is that the function is the inverse function to the function formula_8.


title: Logarithm

text: Several important formulas, sometimes called "logarithmic identities" or "logarithmic laws", relate logarithms to one another.


title: Logarithm

text: The logarithm of a product is the sum of the logarithms of the numbers being multiplied; the logarithm of the ratio of two numbers is the difference of the logarithms. The logarithm of the -th power of a number is " "times the logarithm of the number itself; the logarithm of a -th root is the logarithm of the number divided by . The following table lists these identities with examples. Each of the identities can be derived after substitution of the logarithm definitions formula_11 or formula_12 in the left hand sides.


title: Logarithm

text: The logarithm can be computed from the logarithms of and with respect to an arbitrary base  using the following formula:


title: Logarithm

text: showing the conversion factor from given formula_18-values to their corresponding formula_19-values to be formula_20


title: Logarithm

text: Typical scientific calculators calculate the logarithms to bases 10 and . Logarithms with respect to any base  can be determined using either of these two logarithms by the previous formula:


title: Logarithm

text: Among all choices for the base, three are particularly common. These are , (the irrational mathematical constant ≈ 2.71828), and (the binary logarithm). In mathematical analysis, the logarithm base is widespread because of analytical properties explained below. On the other hand, logarithms are easy to use for manual calculations in the decimal number system:


title: Logarithm

text: Thus, is related to the number of decimal digits of a positive integer : the number of digits is the smallest integer strictly bigger than . For example, is approximately 3.15. The next integer is 4, which is the number of digits of 1430. Both the natural logarithm and the logarithm to base two are used in information theory, corresponding to the use of nats or bits as the fundamental units of information, respectively. Binary logarithms are also used in computer science, where the binary system is ubiquitous; in music theory, where a pitch ratio of two (the octave) is ubiquitous and the number of cents between any two pitches is the binary logarithm, times 1200, of their ratio (that is, 100 cents per equal-temperament semitone); and in photography to measure exposure values, light levels, exposure times, apertures, and film speeds in "stops".


title: Logarithm

text: The following table lists common notations for logarithms to these bases and the fields where they are used. Many disciplines write instead of , when the intended base can be determined from the context. The notation also occurs. The "ISO notation" column lists designations suggested by the International Organization for Standardization (ISO 80000-2). Because the notation has been used for all three bases (or when the base is indeterminate or immaterial), the intended base must often be inferred based on context or discipline. In computer science, usually refers to , and in mathematics usually refers to . In other contexts, often means .


title: Logarithm

text: The history of logarithms in seventeenth-century Europe is the discovery of a new function that extended the realm of analysis beyond the scope of algebraic methods. The method of logarithms was publicly propounded by John Napier in 1614, in a book titled "Mirifici Logarithmorum Canonis Descriptio" ("Description of the Wonderful Rule of Logarithms"). Prior to Napier's invention, there had been other techniques of similar scopes, such as the prosthaphaeresis or the use of tables of progressions, extensively developed by Jost Bürgi around 1600. Napier coined the term for logarithm in Middle Latin, “logarithmus,” derived from the Greek, literally meaning, “ratio-number,” from "logos" “proportion, ratio, word” + "arithmos" “number”.


title: Logarithm

text: The common logarithm of a number is the index of that power of ten which equals the number. Speaking of a number as requiring so many figures is a rough allusion to common logarithm, and was referred to by Archimedes as the “order of a number”. The first real logarithms were heuristic methods to turn multiplication into addition, thus facilitating rapid computation. Some of these methods used tables derived from trigonometric identities. Such methods are called prosthaphaeresis.


title: Logarithm

text: Invention of the function now known as the natural logarithm began as an attempt to perform a quadrature of a rectangular hyperbola by Grégoire de Saint-Vincent, a Belgian Jesuit residing in Prague. Archimedes had written "The Quadrature of the Parabola" in the third century BC, but a quadrature for the hyperbola eluded all efforts until Saint-Vincent published his results in 1647. The relation that the logarithm provides between a geometric progression in its argument and an arithmetic progression of values, prompted A. A. de Sarasa to make the connection of Saint-Vincent's quadrature and the tradition of logarithms in prosthaphaeresis, leading to the term “hyperbolic logarithm”, a synonym for natural logarithm. Soon the new function was appreciated by Christiaan Huygens, and James Gregory. The notation Log y was adopted by Leibniz in 1675, and the next year he connected it to the integral formula_26


title: Logarithm

text: Before Euler developed his modern conception of complex natural logarithms, Roger Cotes had a nearly equivalent result when he showed in 1714 that


title: Logarithm

text: By simplifying difficult calculations before calculators and computers became available, logarithms contributed to the advance of science, especially astronomy. They were critical to advances in surveying, celestial navigation, and other domains. Pierre-Simon Laplace called logarithms


title: Logarithm

text: As the function is the inverse function of , it has been called an antilogarithm. Nowadays, this function is more commonly called an exponential function.


title: Logarithm

text: A key tool that enabled the practical use of logarithms was the "table of logarithms". The first such table was compiled by Henry Briggs in 1617, immediately after Napier's invention but with the innovation of using 10 as the base. Briggs' first table contained the common logarithms of all integers in the range from 1 to 1000, with a precision of 14 digits. Subsequently, tables with increasing scope were written. These tables listed the values of for any number  in a certain range, at a certain precision. Base-10 logarithms were universally used for computation, hence the name common logarithm, since numbers that differ by factors of 10 have logarithms that differ by integers. The common logarithm of can be separated into an integer part and a fractional part, known as the characteristic and mantissa. Tables of logarithms need only include the mantissa, as the characteristic can be easily determined by counting digits from the decimal point. The characteristic of is one plus the characteristic of , and their mantissas are the same. Thus using a three-digit log table, the logarithm of 3542 is approximated by


title: Logarithm

text: The value of can be determined by reverse look up in the same table, since the logarithm is a monotonic function.


title: Logarithm

text: The product and quotient of two positive numbers and "" were routinely calculated as the sum and difference of their logarithms. The product  or quotient  came from looking up the antilogarithm of the sum or difference, via the same table:


title: Logarithm

text: For manual calculations that demand any appreciable precision, performing the lookups of the two logarithms, calculating their sum or difference, and looking up the antilogarithm is much faster than performing the multiplication by earlier methods such as prosthaphaeresis, which relies on trigonometric identities.


title: Logarithm

text: Trigonometric calculations were facilitated by tables that contained the common logarithms of trigonometric functions.


title: Logarithm

text: Another critical application was the slide rule, a pair of logarithmically divided scales used for calculation. The non-sliding logarithmic scale, Gunter's rule, was invented shortly after Napier's invention. William Oughtred enhanced it to create the slide rule—a pair of logarithmic scales movable with respect to each other. Numbers are placed on sliding scales at distances proportional to the differences between their logarithms. Sliding the upper scale appropriately amounts to mechanically adding logarithms, as illustrated here:


title: Logarithm

text: For example, adding the distance from 1 to 2 on the lower scale to the distance from 1 to 3 on the upper scale yields a product of 6, which is read off at the lower part. The slide rule was an essential calculating tool for engineers and scientists until the 1970s, because it allows, at the expense of precision, much faster computation than techniques based on tables.


title: Logarithm

text: A deeper study of logarithms requires the concept of a "function". A function is a rule that, given one number, produces another number. An example is the function producing the -th power of from any real number , where the base  is a fixed number. This function is written as . When is positive and unequal to 1, we show below that is invertible when considered as a function from the reals to the positive reals.


title: Logarithm

text: It is a standard result in real analysis that any continuous strictly monotonic function is bijective between its domain and range. This fact follows from the intermediate value theorem. Now, is strictly increasing (for ), or strictly decreasing (for ), is continuous, has domain formula_34, and has range formula_35. Therefore, is a bijection from formula_34 to formula_37. In other words, for each positive real number , there is exactly one real number such that formula_38.


title: Logarithm

text: We let formula_39 denote the inverse of . That is, is the unique real number such that formula_38. This function is called the base- "logarithm function" or "logarithmic function" (or just "logarithm").


title: Logarithm

text: More precisely, the logarithm to any base is the only increasing function "f" from the positive reals to the reals satisfying and


title: Logarithm

text: As discussed above, the function is the inverse to the exponential function formula_8. Therefore, Their graphs correspond to each other upon exchanging the - and the -coordinates (or upon reflection at the diagonal line ), as shown at the right: a point on the graph of yields a point on the graph of the logarithm and vice versa. As a consequence, diverges to infinity (gets bigger than any given number) if grows to infinity, provided that is greater than one. In that case, is an increasing function. For , tends to minus infinity instead. When approaches zero, goes to minus infinity for (plus infinity for , respectively).


title: Logarithm

text: Analytic properties of functions pass to their inverses. Thus, as is a continuous and differentiable function, so is . Roughly, a continuous function is differentiable if its graph has no sharp "corners". Moreover, as the derivative of evaluates to by the properties of the exponential function, the chain rule implies that the derivative of is given by


title: Logarithm

text: The derivative of is ; this implies that is the unique antiderivative of that has the value 0 for . It is this very simple formula that motivated to qualify as "natural" the natural logarithm; this is also one of the main reasons of the importance of the constant .


title: Logarithm

text: The quotient at the right hand side is called the logarithmic derivative of ". Computing by means of the derivative of is known as logarithmic differentiation. The antiderivative of the natural logarithm is:


title: Logarithm

text: Related formulas, such as antiderivatives of logarithms to other bases can be derived from this equation using the change of bases.


title: Logarithm

text: This definition has the advantage that it does not rely on the exponential function or any trigonometric functions; the definition is in terms of an integral of a simple reciprocal. As an integral, equals the area between the -axis and the graph of the function , ranging from to . This is a consequence of the fundamental theorem of calculus and the fact that the derivative of is . Product and power logarithm formulas can be derived from this definition. For example, the product formula is deduced as:


title: Logarithm

text: The equality (1) splits the integral into two parts, while the equality (2) is a change of variable (). In the illustration below, the splitting corresponds to dividing the area into the yellow and blue parts. Rescaling the left hand blue area vertically by the factor  and shrinking it by the same factor horizontally does not change its size. Moving it appropriately, the area fits the graph of the function again. Therefore, the left hand blue area, which is the integral of from to is the same as the integral from 1 to . This justifies the equality (2) with a more geometric proof.


title: Logarithm

text: is called the harmonic series. It is closely tied to the natural logarithm: as tends to infinity, the difference,


title: Logarithm

text: converges (i.e. gets arbitrarily close) to a number known as the Euler–Mascheroni constant . This relation aids in analyzing the performance of algorithms such as quicksort.


title: Logarithm

text: Real numbers that are not algebraic are called transcendental; for example, and "e" are such numbers, but formula_52 is not. Almost all real numbers are transcendental. The logarithm is an example of a transcendental function. The Gelfond–Schneider theorem asserts that logarithms usually take transcendental, i.e. "difficult" values.


title: Logarithm

text: Logarithms are easy to compute in some cases, such as . In general, logarithms can be calculated using power series or the arithmetic–geometric mean, or be retrieved from a precalculated logarithm table that provides a fixed precision. Newton's method, an iterative method to solve equations approximately, can also be used to calculate the logarithm, because its inverse function, the exponential function, can be computed efficiently. Using look-up tables, CORDIC-like methods can be used to compute logarithms by using only the operations of addition and bit shifts. Moreover, the binary logarithm algorithm calculates recursively, based on repeated squarings of , taking advantage of the relation


title: Logarithm

text: This is a shorthand for saying that can be approximated to a more and more accurate value by the following expressions:


title: Logarithm

text: For example, with the third approximation yields 0.4167, which is about 0.011 greater than . This series approximates with arbitrary precision, provided the number of summands is large enough. In elementary calculus, is therefore the limit of this series. It is the Taylor series of the natural logarithm at . The Taylor series of provides a particularly useful approximation to when is small, , since then


title: Logarithm

text: For example, with the first-order approximation gives , which is less than 5% off the correct value 0.0953.