Area is a quantity that expresses the extent of a two-dimensional surface or shape in the plane. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat. It is the two-dimensional analog of the length of a curve (a one-dimensional concept) or the volume of a solid (a three-dimensional concept).
The area of a shape can be measured by comparing the shape to squares of a fixed size. In the International System of Units (SI), the standard unit of area is the square metre (m2), which is the area of a square whose sides are one metre long. A shape with an area of three square metres would have the same area as three such squares. In mathematics, the unit square is defined to have area one, and the area of any other shape or surface is a dimensionless real number.
There are several well-known formulas for the areas of simple shapes such as triangles, rectangles, and circles. Using these formulas, the area of any polygon can be found by dividing the polygon into triangles. For shapes with curved boundary, calculus is usually required to compute the area. Indeed, the problem of determining the area of plane figures was a major motivation for the historical development of calculus.
For a solid shape such as a sphere, cone, or cylinder, the area of its boundary surface is called the surface area. Formulas for the surface areas of simple shapes were computed by the ancient Greeks, but computing the surface area of a more complicated shape usually requires multivariable calculus.
Area plays a important role in modern mathematics. In addition to its obvious importance in geometry and calculus, area is related to the definition of determinants in linear algebra, and is a basic property of surfaces in differential geometry. In analysis, the area of a subset of the plane is defined using Lebesgue measure, though not every subset is measurable. In general, area in higher mathematics is seen as a special case of volume for two-dimensional regions.
It can be proved that such a area function actually exists. (See, for example, ''Elementary Geometry from an Advanced Standpoint'' by Edwin Moise.)
The SI unit of area is the square metre, which is considered an SI derived unit.
The acre is also commonly used to measure land areas, where
The formula for the area of a rectangle follows directly from the basic properties of area, and is sometimes taken as a definition or axiom. On the other hand, if geometry is developed before arithmetic, this formula can be used to define multiplication of real numbers.
For an example, any parallelogram can be subdivided into a trapezoid and a right triangle, as shown in figure to the left. If the triangle is moved to the other side of the trapezoid, then the resulting figure is a rectangle. It follows that the area of the parallelogram is the same as the area of the rectangle: : (parallelogram). thumb|right|180px|Two equal triangles.However, the same parallelogram can also be cut along a diagonal into two congruent triangles, as shown in the figure to the right. It follows that the area of each triangle is half the area of the parallelogram: : (triangle). Similar arguments can be used to find area formulae for the trapezoid and the rhombus, as well as more complicated polygons.
This argument is actually a simple application of the ideas of calculus. In ancient times, the method of exhaustion was used in a similar way to find the area of the circle, and this method is now recognized as a precursor to integral calculus. Using modern methods, the area of a circle can be computed using a definite integral: :
The formula for the surface area of a sphere is more difficult: because the surface of a sphere has nonzero Gaussian curvature, it cannot be flattened out. The formula for the surface area of a sphere was first obtained by Archimedes in his work ''On the Sphere and Cylinder''. The formula is : (sphere). where is the radius of the sphere. As with the formula for the area of a circle, any derivation of this formula inherently uses methods similar to calculus.
The above calculations show how to find the area of many common shapes.
The area of irregular polygons can be calculated using the "Surveyor's formula".
::
The question of the filling area of the Riemannian circle remains open.
This text is licensed under the Creative Commons CC-BY-SA License. This text was originally published on Wikipedia and was developed by the Wikipedia community.
name | Fred Rogers |
---|---|
birth name | Fred McFeely Rogers |
birth date | March 20, 1928 |
birth place | Latrobe, Pennsylvania, U.S. |
death date | February 27, 2003 |
death place | Pittsburgh, Pennsylvania, U.S. |
death cause | Stomach cancer |
religion | Presbyterian Church(ordained in 1963) |
other names | Mister RogersMr. Rogers |
spouse | Sara Joanne Byrd (1952–2003) |
occupation | Educator, minister, songwriter, television host |
years active | 1951–2002 }} |
Fred McFeely Rogers (March 20, 1928 – February 27, 2003) was an American educator, Presbyterian minister, songwriter, and television host. Rogers was most famous for creating and hosting ''Mister Rogers' Neighborhood'' (1968–2001), that featured his gentle, soft-spoken personality and directness to his audiences.
Initially educated to be a minister, Rogers was displeased with the way television addressed children and made an effort to change this when he began to write for and perform on local Pittsburgh area shows dedicated to youth. The Public Broadcasting System developed his own nationally aired show in 1968 and over the course of three decades on television, he became an indelible American icon of children's entertainment and education, as well as a symbol of compassion, patience, and morality. He was also known for his advocacy of various public causes. He testified to the U.S. Supreme Court on time shifting; and he gave a now-famous speech before the U.S. Senate, advocating government funding for children's television.
Rogers was honored extensively for his life work in children's education. He received the Presidential Medal of Freedom, the United States' highest civilian honor, a Peabody Award for his career, and was inducted into the Television Hall of Fame. Two resolutions recognizing his work were unanimously passed by U.S. Congress, one of his trademark sweaters was acquired and is on display at the Smithsonian Institution, and several buildings and works of art in Pennsylvania are dedicated to his memory.
Rogers graduated from Latrobe High School (1946). He studied at Dartmouth College (1946–48) in Hanover, New Hampshire, and transferred to Rollins College in Winter Park, Florida, where he received a Bachelor of Arts in Music Composition (1951).
At Rollins, Rogers met Sara Joanne Byrd, an Oakland, Florida, native; and they married on June 9, 1952. They had two sons, James (b. 1959) and John (b. 1961), and three grandsons, the third (Ian McFeely Rogers) born twelve days after Rogers' death. In 1963, Rogers graduated from Pittsburgh Theological Seminary and was ordained a minister in the Presbyterian Church. During the course of his career, he garnered forty honorary degrees. Rogers was red-green color blind, swam every morning, was a vegetarian, and neither smoked nor drank.
Rogers had an apartment in New York City and a summer home on Nantucket island in Massachusetts.
He thus applied for a job at NBC in New York City in 1951 and was hired because of his Music degree. Rogers spent three years working on the production staffs for such music-centered programming as ''NBC Opera Theater''. He also worked on Gabby Hayes' show for children. Ultimately, Rogers decided that commercial television's reliance on advertisement and merchandising undermined its ability to educate or enrich young audiences, so he quit NBC.
In 1954, he began working at WQED, a Pittsburgh public television station, as a puppeteer on a local children's show ''The Children's Corner''. For the next seven years, he worked with host Josie Carey in unscripted live TV, developing many of the puppets, characters, and music used in his later work, such as King Friday XIII, and Curious X the Owl.
Rogers began wearing his famous sneakers when he found them to be quieter than his work shoes as he moved about behind the set. He was also the voices of King Friday XIII and Queen Sara Saturday (named after his wife), rulers of the neighborhood, as well as X the Owl, Henrietta Pussycat, Daniel Striped Tiger, Lady Elaine Fairchild, and Larry Horse. The show won a Sylvania Award for best children's show, and was briefly broadcast nationally on NBC.
During these eight years, he would leave the WQED studios during his lunch breaks to study theology at the nearby Pittsburgh Theological Seminary. Rogers, however, was not interested in preaching; and, after his ordination, he was specifically charged to continue his work with Children's Television. He had also done work at the University of Pittsburgh's program in Child Development and Child Care.
In 1963, Rogers moved to Toronto, where he was contracted by the Canadian Broadcasting Corporation (CBC) to develop a 15-minute children's television program: ''Misterogers'', which would be his debut in front of the camera. The show was a hit with children but lasted for only three seasons. Many of his famous set pieces—Trolley, Eiffel Tower, the 'tree', and 'castle'—were created by CBC designers. While in Canada, Rogers brought his friend and understudy Ernie Coombs, who would go on to create ''Mr. Dressup'', a very successful and long-running children's show in Canada, and similar in many ways to ''Mister Rogers' Neighborhood''. ''Mr. Dressup'' also used some of the songs that would be featured on Rogers' later program.In 1966, Rogers acquired the rights to his program from the CBC and moved the show to WQED in Pittsburgh, where he had worked on ''The Children's Corner''. He developed the new show for the Eastern Educational Network. Stations that carried the program were limited but did include educational stations in Boston, Washington, D.C., and New York City.
After returning to Pittsburgh, Rogers attended and participated in activities at the Sixth Presbyterian church in the Squirrel Hill neighborhood of Pittsburgh, a More Light congregation which he attended until his death.
Distribution of ''Mister Rogers' Neighborhood'' began on February 19, 1968. The following year, the show moved to PBS (Public Broadcasting Service). In 1971, Rogers formed Family Communications, Inc. (FCI), and the company established offices in the WQED building in Pittsburgh. Initially, the company served solely as the production arm of ''Mister Rogers' Neighborhood'', but now develops and produces an array of children's programming and educational materials.
''Mister Rogers' Neighborhood'' began airing in 1968 and ran for 895 episodes; the last set of new episodes was taped in December 2000 and began airing in August 2001. At its peak, in 1985, 8% of U.S households tuned in to the show.
Visually, the presentation of the show was very simple, and it did not feature the animation or fast pace of other children's shows, which Rogers thought of as "bombardment". Rogers also believed in not acting out a different persona on camera compared to how he acted off camera, stating that "One of the greatest gifts you can give anybody is the gift of your honest self. I also believe that kids can spot a phony a mile away." Rogers composed almost all of the music on the program. He wanted to teach children to love themselves and others, and he addressed common childhood fears with comforting songs and skits. For example, one of his famous songs explains how a child cannot be pulled down the bathtub drain because he or she will not fit. He even once took a trip to the Children's Hospital of Pittsburgh to show children that a hospital is not a place to fear. During the Gulf War (1990–91), he assured his audience that all children in the neighborhood would be well cared for and asked parents to promise to take care of their own children. The message was aired again by PBS during the media storm that preceded the 2003 invasion of Iraq.
For a time Rogers produced specials for parents as a precursor to the subject of the week on the Neighborhood called "Mister Rogers Talks To Parents About ''[topic]''". Rogers didn't host those specials though as other people like Joan Lunden, who hosted the Conflict special, and other news announcers played MC duties in front of a gallery of parents while Rogers answered questions from them. These specials were made to prep the parents for any questions the children might ask after watching the episodes on that topic of the week.
The only time Rogers appeared on television as someone other than himself was in 1996, when he played a preacher on one episode of ''Dr. Quinn, Medicine Woman.''
In the mid-1980s, the Burger King fast-food chain lampooned Rogers' image with an actor called "Mr. Rodney", imitating Rogers' television character. Rogers found the character's pitching fast food as confusing to children, and called a press conference in which he stated that he did not endorse the company's use of his character or likeness (Rogers did no commercial endorsements of any kind throughout his career, though he acted as a pitchman for several non-profit organizations dedicated to learning over the years). The chain publicly apologized for the ''faux pas'', and pulled the ads. By contrast, Fred Rogers found Eddie Murphy's parody of his show on ''Saturday Night Live'', "Mr. Robinson's Neighborhood," amusing and affectionate, which was also initially broadcast at a time of night when his own child audience was not likely to see it.
During the 1997 Daytime Emmys, the Lifetime Achievement Award was presented to Rogers. The following is an excerpt from ''Esquire's'' coverage of the gala, written by Tom Junod:
The chairman of the subcommittee, John O. Pastore, was not previously familiar with Rogers' work, and was sometimes described as impatient. However, he reported that the testimony had given him goosebumps, and declared, "I think it's wonderful. Looks like you just earned the $20 million." The subsequent congressional appropriation, for 1971, increased PBS funding from $9 million to $22 million.
The Supreme Court considered the testimony of Rogers in its decision that held that the Betamax video recorder did not infringe copyright. The Court stated that his views were a notable piece of evidence "that many [television] producers are willing to allow private time-shifting to continue" and even quoted his testimony in a footnote:
}}
Rogers was diagnosed with stomach cancer in December 2002, not long after his retirement. He underwent surgery on January 6, 2003, which was unsuccessful. A week earlier, he served as grand marshal of the Tournament of Roses Parade, with Art Linkletter and Bill Cosby.
Rogers died on February 27, 2003 at his home with his wife by his side, less than a month before he would have turned 75. His death was such a significant event in Pittsburgh that the front page of the ''Pittsburgh Post-Gazette'' published the next day devoted its coverage to him. The Reverend William P. Barker presided over a public memorial in Pittsburgh. More than 2,700 people attended the memorial at Heinz Hall, including former ''Good Morning America'' host David Hartman, Teresa Heinz Kerry, philanthropist Elsie Hillman, PBS President Pat Mitchell, ''Arthur'' creator Marc Brown, and ''The Very Hungry Caterpillar'' author-illustrator Eric Carle. Speakers remembered Rogers' love of children, devotion to his religion, enthusiasm for music, and quirks. Teresa Heinz Kerry said of Rogers, "He never condescended, just invited us into his conversation. He spoke to us as the people we were, not as the people others wished we were." Rogers is interred at Unity Cemetery in Latrobe.
On New Years Day of 2004, Michael Keaton hosted the PBS TV special "Mr. Rogers: America's Favorite Neighbor". It was released on DVD September 28 that year. Keaton was a former stagehand on the show before he quit to become an actor. To mark what would have been his 80th birthday, Rogers' production company sponsored several events to memorialize him, including "Won't You Wear a Sweater Day", during which fans and neighbors were asked to wear their favorite sweaters in celebration.
The television industry honored Rogers with a George Foster Peabody Award "in recognition of 25 years of beautiful days in the neighborhood" in 1987, the same year he was initiated as an honorary member of Phi Mu Alpha Sinfonia Fraternity, the national fraternity for men of music. Rogers was a National Patron of Delta Omicron, an international professional music fraternity. He was inducted into the Television Hall of Fame in 1999. One of Rogers' iconic sweaters was acquired by the Smithsonian Institution, which displays it as a "Treasure of American History". In 2002 Rogers received the PNC Commonwealth Award in Mass Communications.
He was furthermore awarded the Presidential Medal of Freedom in 2002, for his contributions to children's education, justified by President George W. Bush, who said, "Fred Rogers has proven that television can soothe the soul and nurture the spirit and teach the very young". A year later, the U.S. Senate unanimously passed Resolution 16 to commemorate the life of Fred Rogers. It read, in part, "Through his spirituality and placid nature, Mr. Rogers was able to reach out to our nation's children and encourage each of them to understand the important role they play in their communities and as part of their families. More importantly, he did not shy away from dealing with difficult issues of death and divorce but rather encouraged children to express their emotions in a healthy, constructive manner, often providing a simple answer to life's hardships."
Following Rogers' death, the U.S. House of Representatives in 2003 unanimously passed Resolution 111 honoring Rogers for "his legendary service to the improvement of the lives of children, his steadfast commitment to demonstrating the power of compassion, and his dedication to spreading kindness through example."
The same year the U.S. Presbyterian Church approved an overture "to observe a memorial time for the Reverend Fred M. Rogers" at its General Assembly. The rationale for the recognition of Rogers reads, "The Reverend Fred Rogers, a member of the Presbytery of Pittsburgh, as host of Mister Rogers’ Neighborhood since 1968, had a profound effect on the lives of millions of people across the country through his ministry to children and families. Mister Rogers promoted and supported Christian values in the public media with his demonstration of unconditional love. His ability to communicate with children and to help them understand and deal with difficult questions in their lives will be greatly missed."Several buildings, monuments, and works of art are dedicated to Rogers' memory, including a mural sponsored by the Pittsburgh-based Sprout Fund in 2006, "Interpretations of Oakland," by John Laidacker that featured Mr. Rogers. Saint Vincent College in (Latrobe, Pennsylvania) completed construction of The Fred M. Rogers Center for Early Learning and Children's Media in 2008. The Fred Rogers Memorial Statue on the North Shore near Heinz Field in Pittsburgh was created by Robert Berks and dedicated in 2009.
The asteroid 26858 Misterrogers is named after Rogers. This naming, by the International Astronomical Union, was announced on May 2, 2003 by the director of the Henry Buhl Jr. Planetarium & Observatory at the Carnegie Science Center in Pittsburgh. The science center worked with Rogers' Family Communications, Inc. to produce a planetarium show for preschoolers called "The Sky Above Mister Rogers' Neighborhood", which plays at planetariums across the United States.
Category:1928 births Category:2003 deaths Category:People from Latrobe, Pennsylvania Category:American Presbyterian clergy Category:Actors from Pittsburgh, Pennsylvania Category:American puppeteers Category:American television actors Category:American television personalities Category:American vegetarians Category:Christian vegetarians Category:Cancer deaths in Pennsylvania Category:Christianity in Pittsburgh, Pennsylvania Category:Dartmouth College alumni Category:Daytime Emmy Award winners Category:Deaths from stomach cancer Category:PBS people Category:Peabody Award winners Category:Presidential Medal of Freedom recipients Category:Rollins College alumni
eo:Fred Rogers fa:فرد راجرز fr:Fred Rogers id:Fred Rogers pt:Fred Rogers simple:Fred Rogers sh:Mister RogersThis text is licensed under the Creative Commons CC-BY-SA License. This text was originally published on Wikipedia and was developed by the Wikipedia community.
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