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32-688: The Queen Elizabeth II Great Court , commonly referred to simply as the Great Court , is the covered central quadrangle of the British Museum in London. It was redeveloped during the late 1990s to a design by Foster and Partners , from a 1970s design by Colin St John Wilson . The court was opened by Queen Elizabeth II in 2000. The court has a tessellated glass roof, engineered by Buro Happold and built by Waagner-Biro , covering

64-402: A 2 − b 2 | . {\displaystyle K={\tfrac {1}{2}}\left|\tan \theta \right|\cdot \left|a^{2}-b^{2}\right|.} Another area formula including the sides a , b , c , d is where x is the distance between the midpoints of the diagonals, and φ is the angle between the bimedians . The last trigonometric area formula including

96-417: A b ⋅ sin ⁡ A . {\displaystyle K=ab\cdot \sin {A}.} Alternatively, we can write the area in terms of the sides and the intersection angle θ of the diagonals, as long θ is not 90° : In the case of a parallelogram, the latter formula becomes K = 1 2 | tan ⁡ θ | ⋅ |

128-467: A = AB , b = BC , c = CD , d = DA , then In a convex quadrilateral ABCD with sides a = AB , b = BC , c = CD , d = DA , and where the diagonals intersect at E , where e = AE , f = BE , g = CE , and h = DE . The shape and size of a convex quadrilateral are fully determined by the lengths of its sides in sequence and of one diagonal between two specified vertices. The two diagonals p , q and

160-476: A free vector in Cartesian space equal to ( x 1 , y 1 ) and BD as ( x 2 , y 2 ) , this can be rewritten as: In the following table it is listed if the diagonals in some of the most basic quadrilaterals bisect each other, if their diagonals are perpendicular , and if their diagonals have equal length. The list applies to the most general cases, and excludes named subsets. The lengths of

192-404: A quad ) is a space or a courtyard , usually rectangular (square or oblong) in plan, the sides of which are entirely or mainly occupied by parts of a large building (or several smaller buildings). The word is probably most closely associated with college or university campus architecture, but quadrangles are also found in other buildings such as palaces . Most quadrangles are open-air, though

224-549: A quadrangle , or 4-angle. A quadrilateral with vertices A {\displaystyle A} , B {\displaystyle B} , C {\displaystyle C} and D {\displaystyle D} is sometimes denoted as ◻ A B C D {\displaystyle \square ABCD} . Quadrilaterals are either simple (not self-intersecting), or complex (self-intersecting, or crossed). Simple quadrilaterals are either convex or concave . The interior angles of

256-467: A quadrilateral is a four-sided polygon , having four edges (sides) and four corners (vertices). The word is derived from the Latin words quadri , a variant of four, and latus , meaning "side". It is also called a tetragon , derived from Greek "tetra" meaning "four" and "gon" meaning "corner" or "angle", in analogy to other polygons (e.g. pentagon ). Since "gon" means "angle", it is analogously called

288-430: A convex quadrilateral below). The four maltitudes of a convex quadrilateral are the perpendiculars to a side—through the midpoint of the opposite side. There are various general formulas for the area K of a convex quadrilateral ABCD with sides a = AB , b = BC , c = CD and d = DA . The area can be expressed in trigonometric terms as where the lengths of the diagonals are p and q and

320-446: A few have been roofed over (often with glass), to provide additional space for social meeting areas or coffee shops for students. The word quadrangle was originally synonymous with quadrilateral , but this usage is now relatively uncommon. Some modern quadrangles resemble cloister gardens of medieval monasteries , called garths , which were usually square or rectangular, enclosed by covered arcades or cloisters. However, it

352-448: A simple (and planar ) quadrilateral ABCD add up to 360 degrees , that is This is a special case of the n -gon interior angle sum formula: S = ( n − 2) × 180° (here, n=4). All non-self-crossing quadrilaterals tile the plane , by repeated rotation around the midpoints of their edges. Any quadrilateral that is not self-intersecting is a simple quadrilateral. In a convex quadrilateral all interior angles are less than 180°, and

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384-406: Is φ . Bretschneider's formula expresses the area in terms of the sides and two opposite angles: where the sides in sequence are a , b , c , d , where s is the semiperimeter, and A and C are two (in fact, any two) opposite angles. This reduces to Brahmagupta's formula for the area of a cyclic quadrilateral—when A + C = 180° . Another area formula in terms of

416-461: Is clear from the oldest examples (such as Mob Quad ) which are plain and unadorned with arcades, that the medieval colleges at Oxford and Cambridge were creating practical accommodation for college members. Grander quadrangles that look like cloisters came later, once the idea of a college was well established and benefactors or founders wished to create more monumental buildings. Although architectonically analogous, for historical reasons quads in

448-656: The Oxbridge idea, Beaux-Arts forms, and other models. All five barracks at The Citadel (military college) feature quadrangles with red-and-white squares (the colors of the South Carolina battle flag), which are used for formations by the Corps of Cadets. Quadrangles are also found in traditional Kerala houses ( Naalukettu ) and is known as the Nadumittam ("Middle Space"). Quadrilateral In geometry

480-582: The Clore Education Centre and the African galleries (which had been housed at the Museum of Mankind since 1970). The South Portico was largely rebuilt, with two new lifts incorporated for disabled access to the upper levels of the museum. A new gridshell glass roof, designed and built by Austrian specialists Waagner-Biro , was provided over the entire courtyard to create a covered space at

512-578: The Museum's global role. Upon the Great Court's opening to the public in 2000, twelve sculptures from the British Museum's collection were installed on the main floor of the concourse: There were initial plans for a new, thirteenth sculpture to be commissioned from Anish Kapoor , but these were scrapped. Quadrangle (architecture) In architecture , a quadrangle (or colloquially,

544-401: The angle between them is θ . In the case of an orthodiagonal quadrilateral (e.g. rhombus, square, and kite), this formula reduces to K = p q 2 {\displaystyle K={\tfrac {pq}{2}}} since θ is 90° . The area can be also expressed in terms of bimedians as where the lengths of the bimedians are m and n and the angle between them

576-472: The centre of the museum. The British Library Reading Room at the centre of the courtyard was retained and refurbished for use as the Museum library and information centre. The Reading Room had no outer wall; the book stacks came right up to the back of the Reading Room shelves. So a new outer wall was created to protect the Reading Room, to support the new roof and to conceal the ventilation ducts serving

608-647: The colleges of the University of Cambridge are always referred to as courts (such as the Trinity Great Court ). In North America, Thomas Jefferson 's design for the University of Virginia centered the housing and academic buildings in a Palladian form around three sides of the Lawn , a huge grassy expanse. Later, some American college and university planners imitated the Jeffersonian plan,

640-451: The crossing (two acute and two reflex , all on the left or all on the right as the figure is traced out) add up to 720°. The two diagonals of a convex quadrilateral are the line segments that connect opposite vertices. The two bimedians of a convex quadrilateral are the line segments that connect the midpoints of opposite sides. They intersect at the "vertex centroid" of the quadrilateral (see § Remarkable points and lines in

672-552: The cyclic quadrilateral case, since then pq = ac + bd . The area can also be expressed in terms of the bimedians m , n and the diagonals p , q : In fact, any three of the four values m , n , p , and q suffice for determination of the area, since in any quadrilateral the four values are related by p 2 + q 2 = 2 ( m 2 + n 2 ) . {\displaystyle p^{2}+q^{2}=2(m^{2}+n^{2}).} The corresponding expressions are: if

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704-437: The diagonals in a convex quadrilateral This relation can be considered to be a law of cosines for a quadrilateral. In a cyclic quadrilateral , where A + C = 180° , it reduces to pq = ac + bd . Since cos   ( A + C ) ≥ −1 , it also gives a proof of Ptolemy's inequality. If X and Y are the feet of the normals from B and D to the diagonal AC = p in a convex quadrilateral ABCD with sides

736-407: The diagonals in a convex quadrilateral ABCD can be calculated using the law of cosines on each triangle formed by one diagonal and two sides of the quadrilateral. Thus and Other, more symmetric formulas for the lengths of the diagonals, are and In any convex quadrilateral ABCD , the sum of the squares of the four sides is equal to the sum of the squares of the two diagonals plus four times

768-476: The entire court, and surrounds the original circular British Museum Reading Room in the centre, now a museum. It is the largest covered square in Europe . The glass and steel roof is made up of 4,878 unique steel members connected at 1,566 unique nodes and 1,656 pairs of glass windowpanes making up 6,100 m of glazing; each of a unique shape because of the undulating nature of the roof. Controversially, some of

800-461: The entire courtyard was filled with bookshelves, three storeys high (the "book stacks"). To get from one side of the museum to the other, visitors had to go around. Once the Library had moved out, the book stacks were cleared and the Great Court constructed in this central courtyard. A new 'ground' level was created, a story higher than the original courtyard, with the space below used to accommodate

832-476: The lengths of two bimedians and one diagonal are given, and if the lengths of two diagonals and one bimedian are given. The area of a quadrilateral ABCD can be calculated using vectors . Let vectors AC and BD form the diagonals from A to C and from B to D . The area of the quadrilateral is then which is half the magnitude of the cross product of vectors AC and BD . In two-dimensional Euclidean space, expressing vector AC as

864-453: The sides a , b , c , d and the angle α (between a and b ) is: which can also be used for the area of a concave quadrilateral (having the concave part opposite to angle α ), by just changing the first sign + to - . The following two formulas express the area in terms of the sides a , b , c and d , the semiperimeter s , and the diagonals p , q : The first reduces to Brahmagupta's formula in

896-488: The sides and angles, with angle C being between sides b and c , and A being between sides a and d , is In the case of a cyclic quadrilateral, the latter formula becomes K = 1 2 ( a d + b c ) sin ⁡ A . {\displaystyle K={\tfrac {1}{2}}(ad+bc)\sin {A}.} In a parallelogram, where both pairs of opposite sides and angles are equal, this formula reduces to K =

928-467: The spaces below. North of the Reading Room there is a block with a museum shop at ground level, a gallery for temporary exhibitions above and a restaurant above that, just below the glass roof. The Clore Education Centre is housed in the lower level of the Great Court. It comprises the: Nelson Mandela spoke at the inauguration of the BP Lecture Theatre on 16 November 2000. He supported

960-407: The square of the line segment connecting the midpoints of the diagonals. Thus where x is the distance between the midpoints of the diagonals. This is sometimes known as Euler's quadrilateral theorem and is a generalization of the parallelogram law . The German mathematician Carl Anton Bretschneider derived in 1842 the following generalization of Ptolemy's theorem , regarding the product of

992-575: The stone in the court is from France , rather than being Portland stone from southern England as agreed in the original contract with the masons. Within the Great Court, there are shops and a café. The court acts as a central linking point for the museum, somewhat like I. M. Pei 's Louvre Pyramid in Paris . The central courtyard of the British Museum was occupied by the British Library until 1997, when it moved to St Pancras . At that time

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1024-441: The two diagonals both lie inside the quadrilateral. [REDACTED] In a concave quadrilateral, one interior angle is bigger than 180°, and one of the two diagonals lies outside the quadrilateral. A self-intersecting quadrilateral is called variously a cross-quadrilateral , crossed quadrilateral , butterfly quadrilateral or bow-tie quadrilateral . In a crossed quadrilateral, the four "interior" angles on either side of

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