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...

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

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

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

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

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

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

century Indian mathematician Brahmagupta. In his Brāhmasphuṭasiddhānta, Brahmagupta expresses the circumradius of a triangle as the product of two sides...

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

integers: 9:12:15, which is a 3:4:5 right triangle that is a Pythagorean, a Heronian, and a Brahmagupta triangle. As a regular number, 54 is a divisor of...

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

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...

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...

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

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...

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...

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

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

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

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...

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

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...

Euclidean plane geometry. For example, the sum of the interior angles of any triangle is always greater than 180°. Elliptic geometry may be derived from spherical...

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...

right-handed triangles, the general law of sines, and the solution of a spherical triangle by means of the polar triangle. The book On Triangles by Regiomontanus...

an equilateral triangle, 1 12 3 , {\displaystyle {\frac {1}{12{\sqrt {3}}}},} is larger than that for any other triangle. Brahmagupta quadrilateral, a...

1200 CE), important contributions were made by scholars like Aryabhata, Brahmagupta, Bhaskara II, Varāhamihira, and Madhava. The decimal number system in...

Among others are the following. Concepts in mathematics and computing Brahmagupta–Fibonacci identity Fibonacci coding Fibonacci cube Fibonacci heap Fibonacci...

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...