Area is the quantity that expresses the extent of a two-dimensional figure or shape or planar lamina, in the plane. Surface area is its analog on the two-dimensional surface of a three-dimensional object. 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 volume of a solid. The area of a shape can be measured by comparing the shape to squares of a fixed size. In the International System of Units, the standard unit of area is the square metre, 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, 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 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 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 requires multivariable calculus. Area plays an 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, 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.
Area can be defined through the use of axioms, defining it as a function of a collection of certain plane figures to the set of real numbers. It can be proved. An approach to defining what is meant by "area" is through axioms. "Area" can be defined as a function from a collection M of special kind of plane figures to the set of real numbers, which satisfies the following properties: For all S in M, a ≥ 0. If S and T are in M so are S ∪ T and S ∩ T, a = a + a − a. If S and T are in M with S ⊆ T T − S is in M and a = a − a. If a set S is in M and S is congruent to T T is in M and a = a; every rectangle R is in M. If the rectangle has length h and breadth k a = hk. Let Q be a set enclosed between two step regions S and T. A step region is formed from a finite union of adjacent rectangles resting on a common base, i.e. S ⊆ Q ⊆ T. If there is a unique number c such that a ≤ c ≤ a for all such step regions S and T a = c, it can be proved that such an area function exists. Every unit of length has a corresponding unit of area, namely the area of a square with the given side length.
Thus areas can be measured in square metres, square centimetres, square millimetres, square kilometres, square feet, square yards, square miles, so forth. Algebraically, these units can be thought of as the squares of the corresponding length units; the SI unit of area is the square metre, considered an SI derived unit. Calculation of the area of a square whose length and width are 1 metre would be: 1 metre x 1 metre = 1 m2and so, a rectangle with different sides would have an area in square units that can be calculated as: 3 metres x 2 metres = 6 m2; this is equivalent to 6 million square millimetres. Other useful conversions are: 1 square kilometre = 1,000,000 square metres 1 square metre = 10,000 square centimetres = 1,000,000 square millimetres 1 square centimetre = 100 square millimetres. In non-metric units, the conversion between two square units is the square of the conversion between the corresponding length units. 1 foot = 12 inches,the relationship between square feet and square inches is 1 square foot = 144 square inches,where 144 = 122 = 12 × 12.
Similarly: 1 square yard = 9 square feet 1 square mile = 3,097,600 square yards = 27,878,400 square feetIn addition, conversion factors include: 1 square inch = 6.4516 square centimetres 1 square foot = 0.09290304 square metres 1 square yard = 0.83612736 square metres 1 square mile = 2.589988110336 square kilometres There are several other common units for area. The are was the original unit of area in the metric system, with: 1 are = 100 square metresThough the are has fallen out of use, the hectare is still used to measure land: 1 hectare = 100 ares = 10,000 square metres = 0.01 square kilometresOther uncommon metric units of area include the tetrad, the hectad, the myriad. The acre is commonly used to measure land areas, where 1 acre = 4,840 square yards = 43,560 square feet. An acre is 40% of a hectare. On the atomic scale, area is measured in units of barns, such that: 1 barn = 10−28 square meters; the barn is used in describing the cross-sectional area of interaction in nuclear physics.
In India, 20 dhurki = 1 dhur 20 dhur = 1 khatha 20 khata = 1 bigha 32 khata = 1 acre In the 5th century BCE, Hippocrates of Chios was the first to show that the area of a disk is proportional to the square of its diameter, as part of his quadrature of the lune of
The following is a list of squads for each nation competing at the 2008 European Women's Handball Championship in the Republic of Macedonia. The tournament started on 2 December and the final took place in Skopje on 14 December; each nation had to submit an initial squad of 28 players, 12 of them became reserves when the final squad of 16 players was announced on 1 December. Appearances and ages as of 1 December 2008. Head coach: Jan Pytlick Head coach: Olivier Krumbholz Head coach:Vilmos Imre Head coach: Radu Voina Head coach: Marit Breivik Head coach: Jorge Dueñas Head coach: Paula Castro Head coach: Leonid Yevtushenko Head coach: Herbert Müller Head coach: Konstantin Charovarov Head coach: Evgeny Trefilov Head coach: Ulf Schefvert Head coach: Zdravko Zovko Head coach: Armin Emrich Head coach: Vladimir Gligorov Head coach: Časlav Dinčić "Official squads"
Lincoln Junior College, located in Fort Pierce, opened its doors in 1960, at the same time as Indian River Junior College, restricted to white students. It was designed to serve Indian River, Okeechobee, St. Lucie counties, it was one of eleven black community colleges which were founded, at the urging of the Florida Legislature, in the late 1950s and early 1960s to show that a "separate but equal" educational system for blacks existed in Florida. At the time, there was no nearby college for Negroes, the distances and lack of funding closed off most local blacks from college. Initial classes used the facilities of Lincoln Park Academy. In 1962, a new building added classroom facilities, faculty offices, science laboratories, an administrative unit, a fine arts building, a student union. Leroy S. Floyd, principal of Lincoln Park Academy, was selected as president of the new institution. With one exception, all the initial administrators and faculty were employed in the K-12 school system in St. Lucie County prior to the College's opening.
Offerings included a college parallel program. The adult program was a part of the evening high school program prior to the College. However, when it became part of the College, enrollment quadrupled from 115 to 446. Initial enrollment was 98 students. Peak enrollment in its final year, 1964–65, was 667 students, of which 221 were in the college parallel program. In 1964-65 it became apparent that the black institution would soon be merged with Indian River Junior College, it was planned that the Lincoln facility would remain a center of Indian River, but "local political leaders were not ready to promote integrated facilities for the college in the Black community". Uniquely among the twelve black junior colleges, all the full-time faculty became "members of the merged faculty" at Indian River. President Floyd became Dean of Students at Indian River Junior College. Booker T. Washington Junior College Roosevelt Junior College Jackson Junior College Carver Junior College Hampton Junior College Gibbs Junior College Rosenwald Junior College Volusia County Community College Suwannee River Junior College Collier-Blocker Junior College Jackson Junior College Johnson Junior College
This is a complete list of the operettas written by the Austrian composer Johann Strauss II. With the exceptions of Eine Nacht in Venedig and three incomplete works, all premieres took place in Vienna. La reine Indigo, opérette in 3 acts La tzigane, opérette in 3 acts Wiener Blut, Operette in 3 acts, arranged by Adolf Müller Gräfin Pepi, Operette in 3 acts, arranged by E Reiterer Tausend und eine Nacht, Operette in a prelude and 2 acts, arranged by E Reiterer Reiche Mädchen, Operette in 3 acts Der blaue Held, Operette in 3 acts Faschingshochzeit, Operette arranged by J Klein Casanova, Operette in 7 scenes, arranged by Ralph Benatzky Walzer aus Wien, Singspiel in 2 acts, arranged by Julius Bittner and Erich Wolfgang Korngold SourcesLamb, Andrew,'Strauss, Johann' in The New Grove Dictionary of Opera, ed. Stanley Sadie ISBN 0-333-73432-7
Chinese Puzzle is a 2013 French comedy-drama film written and directed by Cédric Klapisch. It is the third chapter of the Spanish Apartment trilogy, after L'Auberge Espagnole and Les Poupées russes. Ten years have passed, the once happy lovers, Xavier Rousseau and Wendy, have split; when she moves with their two children to New York City, he moves to there to be near the children. Wendy now lives with John in a luxury apartment overlooking Central Park. Xavier stays with Isabelle and Ju, a lesbian couple whose child he fathered, but he soon finds his own apartment above a Chinese bakery where he works on a new novel assisted by brief visions of Arthur Schopenhauer and Georg Wilhelm Friedrich Hegel. Having no work visa, Xavier is advised by his lawyer to seek illegal employment and marry for a green card. After saving his taxicab driver from a vicious beating, the driver's grateful Chinese-American family agrees to have Xavier marry one of their relations, amenable and complicit, his former French girlfriend, visits him while on a business trip and returns a second time with her own two children on spring break.
Xavier and Martine attempt to rekindle their relationship. The film climaxes when the Immigration and Naturalization Service performs a surprise inspection of Xavier's apartment while Isabelle is using it to cheat on Ju with their babysitter; as Martine is departing for home with her kids, Xavier races on foot to catch her shuttle bus, confess his love, ask her to stay and live with him. She agrees; the film concludes with the cast of characters walking in a celebratory parade down a Chinatown street. Romain Duris as Xavier Rousseau Kelly Reilly as Wendy Audrey Tautou as Martine Cécile de France as Isabelle Sandrine Holt as Ju Flore Bonaventura as Isabelle the babysitter Jochen Hägele as Hegel Benoît Jacquot as Xavier's father Martine Demaret as Xavier's mother Dominique Besnehard as the editor Zinedine Soualem as Mr. Boubaker Peter Hermann as John Jason Kravits as Xavier's lawyer Vanessa Guide as the nurse Kyan Khojandi as Antoine Garceau Li Jun Li as Nancy Pablo Mugnier-Jacob as Tom Margaux Mansart as Mia Adrian Martinez as Le patron coursier Peter McRobbie as L'agent bureau immigration Larry Fessenden as Le premier rocker The film garnered favourable reviews.
It scored a 78%'certified fresh' rating on review aggregation website Rotten Tomatoes, based on 64 reviews, with a weighted average of 6.52/10. The site's consensus states: "Pleasantly easygoing and funny, Chinese Puzzle offers a suitably endearing conclusion to Cédric Klapisch's Trilogy of Xavier." At Metacritic, it has a score of 64, based on 24 critics, indicating "Generally favorable reviews". The film was nominated for the Best Music award at the 39th César Awards, came second for the Audience Award for Best Narrative Feature at the 57th San Francisco International Film Festival. Chinese Puzzle on IMDb Chinese Puzzle at Box Office Mojo Chinese Puzzle at Rotten Tomatoes Chinese Puzzle at Metacritic Official US trailer Official US site
The Viva la Vida Tour was the fourth concert tour by British band Coldplay. The tour was in support All His Friends; the tour was a massive commercial and critical success visiting Europe, the Americas and Australasia. The tour further established the band as one the concert industry's biggest draws and as one of the world's most popular bands. According to Pollstar from 2008 to 2010, the tour grossed $209.4 million The stage setup consisted of a stripped-down main stage and two catwalks. Instead of a giant video screen on-stage, the band opted for six hanging giant PufferSpheres that displayed images and streamed closeups. Lead singer Chris Martin dubbed the fixtures as their "magic balls". During the tour, The Blue Danube by Johann Strauss II, was played on all concerts, as an intro, right before the band coming into the stage. Coldplay were accompanied by David Gibbin during the tour. Volunteers were stationed at each venue to tell concertgoers. On 23 July 2008 Coldplay performed their second in two shows at the United Center arena in Chicago.
In each of the two shows, the band shot the music video for "Lost!" by performing the song twice. On 19 September 2008, Chris Martin was accompanied by A-ha pianist Magne Furuholmen in the encore at the Oslo Spektrum, Oslo, to play a cover of the A-Ha song "Hunting High and Low"; the intro of the concert would begin in space before turning to show the Earth and zooming to aerial views of the continent, country and stadium that the show would take place. The idea was to make each show being a spectacle in its own, rather than just part of the tour; the cosmic theme is repeated across a number of the visuals like "Speed of Sound" and "Glass of Water". This takes the gig-goers on a journey through a solar system where the stars coalesce to form an eye shape that goes supernova and engulfs the screen in flames. However, other sections of the show were different. "Lovers in Japan", one of the highlights in visual terms, uses a series of archive footage and animations across the screen at the back of the stage and in the end thousands of confetti butterflies would rain all over the venue.
For the show's closing number, "Life in Technicolor II", the paintings created for the album artwork from Viva La Vida was treated with sprocket and projection effects to create a vibrant and immersive colorful effect. There were 34 supporting acts for the tour, they are: Notes Citations Coldplay Viva La Vida Tour