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Brahmagupta Triangle
A Brahmagupta triangle is a triangle whose side lengths are consecutive positive integers and area is a positive integer. The triangle whose side lengths are 3, 4, 5 is a Brahmagupta triangle and so also is the triangle whose side lengths are 13, 14, 15. The Brahmagupta triangle is a special case of the Heronian triangle which is a triangle whose side lengths and area are all positive integers but the side lengths need not necessarily be consecutive integers. A Brahmagupta triangle is called as such in honor of the Indian astronomer and mathematician Brahmagupta (c. 598 – c. 668 CE) who gave a list of the first eight such triangles without explaining the method by which he computed that list. A Brahmagupta triangle is also called a Fleenor-Heronian triangle in honor of Charles R. Fleenor who discussed the concept in a paper published in 1996. Some of the other names by which Brahmagupta triangles are known are super-Heronian triangle and almost-equilateral Heronian triangle. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Triangle
A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called ''vertices'', are zero-dimensional points while the sides connecting them, also called ''edges'', are one-dimensional line segments. A triangle has three internal angles, each one bounded by a pair of adjacent edges; the sum of angles of a triangle always equals a straight angle (180 degrees or π radians). The triangle is a plane figure and its interior is a planar region. Sometimes an arbitrary edge is chosen to be the ''base'', in which case the opposite vertex is called the ''apex''; the shortest segment between the base and apex is the ''height''. The area of a triangle equals one-half the product of height and base length. In Euclidean geometry, any two points determine a unique line segment situated within a unique straight line, and any three points that do not all lie on the same straight line determine a unique triangle situated w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heronian Triangle
In geometry, a Heronian triangle (or Heron triangle) is a triangle whose side lengths , , and and area are all positive integers. Heronian triangles are named after Heron of Alexandria, based on their relation to Heron's formula which Heron demonstrated with the example triangle of sides and area . Heron's formula implies that the Heronian triangles are exactly the positive integer solutions of the Diophantine equation :16\,A^2=(a+b+c)(a+b-c)(b+c-a)(c+a-b); that is, the side lengths and area of any Heronian triangle satisfy the equation, and any positive integer solution of the equation describes a Heronian triangle. If the three side lengths are setwise coprime (meaning that the greatest common divisor of all three sides is 1), the Heronian triangle is called ''primitive''. Triangles whose side lengths and areas are all rational numbers (positive rational solutions of the above equation) are sometimes also called ''Heronian triangles'' or ''rational triangles''; in this art ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brahmagupta
Brahmagupta ( – ) was an Indian Indian mathematics, mathematician and Indian astronomy, astronomer. He is the author of two early works on mathematics and astronomy: the ''Brāhmasphuṭasiddhānta'' (BSS, "correctly established Siddhanta, doctrine of Brahma", dated 628), a theoretical treatise, and the ''Khandakhadyaka'' ("edible bite", dated 665), a more practical text. In 628 CE, Brahmagupta first described gravity as an attractive force, and used the term "gurutvākarṣaṇam (गुरुत्वाकर्षणम्)" in Sanskrit to describe it. He is also credited with the first clear description of the quadratic formula (the solution of the quadratic equation)Bradley, Michael. ''The Birth of Mathematics: Ancient Times to 1300'', p. 86 (Infobase Publishing 2006) in his main work, the ''Brāhma-sphuṭa-siddhānta''. Life and career Brahmagupta, according to his own statement, was born in 598 CE. Born in ''Bhillamāla'' in Gurjaradesa (modern Bhinmal in Rajasthan, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
