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{\displaystyle \omega } . The area K of a cyclic quadrilateral with sides a, b, c, d is given by Brahmagupta's formula: p.24  K = ( s − a ) ( s − b ) ( s −...

Brahmagupta (c. 598 – c. 668 CE) was an Indian mathematician and astronomer. He is the author of two early works on mathematics and astronomy: the Brāhmasphuṭasiddhānta...

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...

In geometry, Brahmagupta's theorem states that if a cyclic quadrilateral is orthodiagonal (that is, has perpendicular diagonals), then the perpendicular...

Euclidean geometry, Brahmagupta's formula, named after the 7th century Indian mathematician, is used to find the area of any cyclic quadrilateral (one that can...

A Brahmagupta triangle is a triangle whose side lengths are consecutive positive integers and area is a positive integer. The triangle whose side lengths...

quadrilaterals with this property (and that the diagonals that connect opposite vertices have integer length) are called Brahmagupta quadrilaterals;...

have integral standard deviation. Heronian tetrahedron Brahmagupta quadrilateral Brahmagupta triangle Robbins pentagon Integer triangle#Heronian triangles...

century CE, Brahmagupta developed a formula, now known as Brahmagupta's formula, for the area of a cyclic quadrilateral (a quadrilateral inscribed in...

point where the diagonals intersect. Brahmagupta's theorem states that for a cyclic orthodiagonal quadrilateral, the perpendicular from any side through...

at) a common point called the "anticenter". Brahmagupta's theorem states that if a cyclic quadrilateral is orthodiagonal (that is, has perpendicular...

special case of Brahmagupta's formula. It can also be derived directly from the trigonometric formula for the area of a tangential quadrilateral. Note that...

meet at a common point called the "anticenter". Brahmagupta's theorem states that if a cyclic quadrilateral is orthodiagonal (that is, has perpendicular...

American English, or trapezium (/trəˈpiːziəm/) in British English, is a quadrilateral that has one pair of parallel sides. The parallel sides are called the...

al-Haytham, Khayyam and al-Tusi on quadrilaterals, including the Lambert quadrilateral and Saccheri quadrilateral, were "the first few theorems of the...

include the square, the rhombus, and the kite. By Brahmagupta's theorem, in an orthodiagonal quadrilateral that is also cyclic, a line through the midpoint...

regarded as a quadrilateral with one side of length zero. From this perspective, as d {\displaystyle d} approaches zero, a cyclic quadrilateral converges...

asinorum Quadrilateral Bicentric quadrilateral Cyclic quadrilateral Equidiagonal quadrilateral Kite (geometry) Orthodiagonal quadrilateral Rhombus Rectangle...

centroid and the orthocenter. In addition to the sides and diagonals of a quadrilateral, some important segments are the two bimedians (connecting the midpoints...

{\displaystyle K=rs.} The simplest form of Brahmagupta's formula for the area of a cyclic quadrilateral has a form similar to that of Heron's formula...