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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 ...
Three formulas have the same structure as Heron's formula but are expressed in terms of different variables. First, denoting the medians from sides a, b, and c respectively as m a, m b, and m c and their semi-sum (m a + m b + m c)/2 as σ, we have [10]
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.
Hero of Alexandria (/ ˈ h ɪər oʊ /; Ancient Greek: Ἥρων [a] ὁ Ἀλεξανδρεύς, Hērōn hò Alexandreús, also known as Heron of Alexandria / ˈ h ɛr ən /; probably 1st or 2nd century AD) was a Greek mathematician and engineer who was active in Alexandria in Egypt during the Roman era.
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 ...
"Heron", a song by Avail from their 2000 album One Wrench; Hardy Heron, the codename for the 8.04 LTS release of Ubuntu; Heron Stakes, a thoroughbred race in Great Britain; Heron's fountain, a hydraulic machine invented by physicist Heron aka "Hero of Alexandria" Heron's formula, gives the area of a triangle when the length of all three sides ...
One of the triangle area formulas involving the semiperimeter also applies to tangential quadrilaterals, which have an incircle and in which (according to Pitot's theorem) pairs of opposite sides have lengths summing to the semiperimeter—namely, the area is the product of the inradius and the semiperimeter: