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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 ...
A method analogous to piece-wise linear approximation but using only arithmetic instead of algebraic equations, uses the multiplication tables in reverse: the square root of a number between 1 and 100 is between 1 and 10, so if we know 25 is a perfect square (5 × 5), and 36 is a perfect square (6 × 6), then the square root of a number greater than or equal to 25 but less than 36, begins with ...
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.
Yes, Hero's Formula and Heron's Formula are the same. The spellings "Hero of Alexandria" and "Heron of Alexandria" are both used, and neither is correct, although the Greek language purists would probably prefer the version with the n. -- ♦Ian Ma c M♦ (talk to me) 08:11, 27 November 2007 (UTC) [ reply ]
they can be expressed in terms of smaller integers d and e using Euclid's formula u = 2de v = d 2 − e 2 x = d 2 + e 2. Since u = 2m 2 = 2de, and since d and e are coprime, they must be squares themselves, d = g 2 and e = h 2. This gives the equation v = d 2 − e 2 = g 4 − h 4 = k 2. The solution (g, h, k) is another solution to the ...
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