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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 .
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.
This is an accepted version of this page This is the latest accepted revision, reviewed on 18 February 2025. Indian mathematician and astronomer (598–668) Brahmagupta Born c. 598 CE Bhillamala, Gurjaradesa, Chavda kingdom (modern day Bhinmal, Rajasthan, India) Died c. 668 CE (aged c. 69–70) Ujjain, Chalukya Empire (modern day Madhya Pradesh, India) Known for Rules for computing with Zero ...
Solution of triangles (Latin: solutio triangulorum) is the main trigonometric problem of finding the characteristics of a triangle (angles and lengths of sides), when some of these are known. The triangle can be located on a plane or on a sphere. Applications requiring triangle solutions include geodesy, astronomy, construction, and navigation.
Heron was the flag bearer for Team Panama at the Olympics opening ceremony. She is one of eight Panamanian athletes, and the only gymnast from the country, to participate in the 2024 Paris Olympics.
Shoelace scheme for determining the area of a polygon with point coordinates (,),..., (,). The shoelace formula, also known as Gauss's area formula and the surveyor's formula, [1] is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane. [2]