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

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...

exists an inscribing circle for this quadrilateral. Butterfly theorem Brahmagupta triangle Cyclic polygon Power of a point Ptolemy's table of chords Robbins...

deviation. Heronian tetrahedron Brahmagupta quadrilateral Brahmagupta triangle Robbins pentagon Integer triangle#Heronian triangles Carlson, John R. (1970),...

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

problem of finding Heronian triangles in which the lengths of the sides are consecutive integers. In algebra, Brahmagupta's identity says that, for given...

problem Brahmagupta triangle Congruum Diophantus II.VIII Eisenstein triple Euler brick Heronian triangle Hilbert's theorem 90 Integer triangle Modular...

cyclic triangle (all triangles are cyclic), and Brahmagupta's formula simplifies to Heron's formula. If the semiperimeter is not used, Brahmagupta's formula...

for triangles and Brahmagupta's formula for cyclic quadrilaterals. Either diagonal of a rhombus divides it into two congruent isosceles triangles. Similarly...

assertion needs modern highly non-trivial mathematics. Brahmagupta triangle, a Heronian triangle in which the side lengths are consecutive integers Robbins...

none of them are. If the five diagonals are rational (the case called a Brahmagupta pentagon by Sastry (2005)), then the radius of its circumscribed circle...

fundamental relation in Euclidean geometry between the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse (the...

this work, Colebrooke translates Brahmagupta's statement of the sine rule as: The product of the two sides of a triangle, divided by twice the perpendicular...

(trígōnon) 'triangle', and μέτρον (métron) 'measure') is a branch of mathematics concerned with relationships between angles and side lengths of triangles. In...

endpoints, such as in AB. Examples of line segments include the sides of a triangle or square. More generally, when both of the segment's end points are vertices...

Polynomial SOS, polynomials that are sums of squares of other polynomials The Brahmagupta–Fibonacci identity, representing the product of sums of two squares of...

angles of a triangle and the lengths of the opposing sides. In Figure 1, a, b, and c are the lengths of the three sides of the triangle, and α, β, and...

Aryabhata: every astronomical text spells his name thus, including Brahmagupta's references to him "in more than a hundred places by name". Furthermore...

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

of the triangle, or as a special case of De Gua's theorem (for the particular case of acute triangles), or as a special case of Brahmagupta's formula...

angles θ2, ..., θn for the remaining n − 1 sides. Every Heronian triangle and every Brahmagupta quadrilateral has a rational value for the tangent of the quarter...

concurrent at (all meet at) a common point called the "anticenter". Brahmagupta's theorem states that if a cyclic quadrilateral is orthodiagonal (that...

simplest form of Brahmagupta's formula for the area of a cyclic quadrilateral has a form similar to that of Heron's formula for the triangle area: K = ( s...

Homothety Shear mapping 2D computer graphics 2D geometric model Altitude Brahmagupta's formula Bretschneider's formula Compass and straightedge constructions...

Pell's equation. 628: Brahmagupta provides an explicit solution to the quadratic equation. 628: Brahmagupta discovers Brahmagupta's formula, a generalization...

Mollweide's formula is a pair of relationships between sides and angles in a triangle. A variant in more geometrical style was first published by Isaac Newton...

hyperbolic triangle has an incircle. In hyperbolic geometry, if all three of its vertices lie on a horocycle or hypercycle, then the triangle has no circumscribed...

n equal triangles with height h and base s, thus equals 1⁄2nhs. But since h < r and ns < c, the polygon area must be less than the triangle area, 1⁄2cr...

law of cotangents is a relationship among the lengths of the sides of a triangle and the cotangents of the halves of the three angles. Just as three quantities...

and areas, parallelism, the sum of the angles in a triangle, and the three cases in which triangles are "equal" (have the same area), among many other...