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Heron's formula is a special case of Brahmagupta's formula for the area of a cyclic quadrilateral. Heron's formula and Brahmagupta's formula are both special cases of Bretschneider's formula for the area of a quadrilateral. Heron's formula can be obtained from Brahmagupta's formula or Bretschneider's formula by setting one of the sides of the ...
This formula generalizes Heron's formula for the area of a triangle. A triangle may be regarded as a quadrilateral with one side of length zero. From this perspective, as d approaches zero, a cyclic quadrilateral converges into a cyclic triangle (all triangles are cyclic), and Brahmagupta's formula simplifies to Heron's formula.
Various methods may be used in practice, depending on what is known about the triangle. Other frequently used formulas for the area of a triangle use trigonometry, side lengths (Heron's formula), vectors, coordinates, line integrals, Pick's theorem, or other properties. [3]
In geometry, a Heronian triangle (or Heron triangle) is a triangle whose side lengths a, b, and c and area A are all positive integers. [ 1 ] [ 2 ] 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 13, 14, 15 and area 84 .
Indian mathematics emerged in the Indian subcontinent [1] from 1200 BCE [2] until the end of the 18th century. In the classical period of Indian mathematics (400 CE to 1200 CE), important contributions were made by scholars like Aryabhata, Brahmagupta, Bhaskara II, Varāhamihira, and Madhava.
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 (BSS, "correctly established doctrine of Brahma", dated 628), a theoretical treatise, and the Khandakhadyaka ("edible bite", dated 665), a more practical text.
Heron–Archimedes formula. Add languages. Add links. ... Upload file; Special pages; ... Get shortened URL; Download QR code; Print/export Download as PDF; Printable ...
This formula is the same as Heron's formula, proved by Heron of Alexandria about 60 BCE, though knowledge of the formula may go back to Archimedes. As precipitation was important agriculture and food production, Qin developed precipitation gauges that was widely used in 1247 during the Mongol Empire / Southern Song dynasty to gather ...