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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 ...
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 .
He is mostly remembered for Heron's formula; a way to calculate the area of a triangle using only the lengths of its sides. [6] Much of Hero's original writings and designs have been lost, but some of his works were preserved in manuscripts from the Byzantine Empire and, to a lesser extent, in Latin or Arabic translations.
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.
Heron's fountain is a hydraulic machine invented by the 1st century AD inventor, mathematician, and physicist Heron (or Hero) of Alexandria. [ 1 ] Heron studied the pressure of air and steam, described the first steam engine , and built toys that would spurt water, one of them known as Heron's fountain.
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