geometry, a Heronian triangle (or Heron triangle) is a triangle whose side lengths a, b, and c and area A are all positive integers. Heronian triangles are named...
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to mean a Heronian triangle (a triangle with integral or rational side lengths and area); Conway and Guy (1996) define a rational triangle as one with...
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Pythagorean triple (redirect from Pythagorean triangle)
problem Brahmagupta triangle Congruum Diophantus II.VIII Eisenstein triple Euler brick Heronian triangle Hilbert's theorem 90 Integer triangle Modular arithmetic...
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integers. The faces must therefore all be Heronian triangles (named for Hero of Alexandria). Every Heronian tetrahedron can be arranged in Euclidean space...
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Brahmagupta triangle and so also is the triangle whose side lengths are 13, 14, 15. The Brahmagupta triangle is a special case of the Heronian triangle which...
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almost-equilateral Heronian triangle, the number of n-queens problem solutions for n = 10, 725 = 52 × 29, side length of an almost-equilateral Heronian triangle 726...
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Heronian triangle Integer triangle Pythagorean triple Eisenstein triple Bermuda Triangle Historic Triangle Lithium Triangle Parliamentary Triangle, Canberra...
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road signs, including the yield sign. Almost-equilateral Heronian triangle Isosceles triangle Ternary plot Trilinear coordinates Bencze, Mihály; Wu, Hui-Hua;...
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triangle Heronian triangle Pythagorean triangle Isosceles heronian triangle Right triangle 30-60-90 triangle Isosceles right triangle Kepler triangle Scalene...
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Heron's formula (category Theorems about triangles)
this example, the side lengths and area are integers, making it a Heronian triangle. However, Heron's formula works equally well in cases where one or...
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3 : 4 : 5 triangles are the only right triangles with edges in arithmetic progression. Triangles based on Pythagorean triples are Heronian, meaning they...
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Concyclic points (section Triangles)
of their side lengths are positive integers. Triangles with this property are called Heronian triangles; cyclic quadrilaterals with this property (and...
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888 (number) (section Heronian tetrahedron)
side of a primitive Heronian tetrahedron (after 203, and preceding 1804) with four congruent triangle faces (this primitive Heronian tetrahedron is a tetrahedron...
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Area (section Triangle area)
map Heronian triangle, a triangle with integer sides and integer area. List of triangle inequalities One-seventh area triangle, an inner triangle with...
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trapezoid Triangle Acute and obtuse triangles Equilateral triangle Euler's line Heron's formula Integer triangle Heronian triangle Isosceles triangle List...
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{\displaystyle g} , then The triangle with the side lengths ( d 2 , e 2 , f 2 ) {\displaystyle (d^{2},e^{2},f^{2})} is a Heronian triangle an area a b c g {\displaystyle...
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addition and subtraction formulas for tangents) and the triangle can be scaled to a Heronian triangle. Generally, if K is a subfield of the complex numbers...
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Herodian – Herod the Great (as in Herodian dynasty) Heronian – Hero of Alexandria (as in Heronian triangle) Hilbertian – David Hilbert (as in Hilbertian field)...
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triple which generates a distinct right triangle, a Pythagorean quadruple will generate a distinct Heronian triangle. If a, b, c, d is a Pythagorean quadruple...
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area of a triangle in terms of its side lengths. Hero also reported on a method for calculating cube roots. In solid geometry, the Heronian mean may be...
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Heron's formula, gives the area of a triangle when the length of all three sides are known. Heronian triangle, a triangle with integer side-lengths and integer...
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arithmetic progression is, but allowing several possible differences Heronian triangles with sides in arithmetic progression Problems involving arithmetic...
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Pythagorean triangles with a side or area that is a square or cube, connecting this problem to Fermat's Last Theorem. After a chapter on Heronian triangles, Chapter...
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Integer quadruples of this type are also closely related to Heronian triangles, triangles with integer sides and area. Starting with any four mutually...
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called Heronian tetrahedra. One example has one edge of 896, the opposite edge of 990 and the other four edges of 1073; two faces are isosceles triangles with...
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generally, the problem of finding all equable triangles with integer sides (that is, equable Heronian triangles) was considered by B. Yates in 1858. As W...
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Elementary symmetric mean Geometric-harmonic mean Grand mean Heinz mean Heronian mean Identric mean Lehmer mean Logarithmic mean Moving average Neuman–Sándor...
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found applications in tiling problems and in the problem of finding Heronian triangles in which the lengths of the sides are consecutive integers. In algebra...
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the 5-Con triangles would be congruent. There are no integer 5-Con triangles that are Heronian because the sides of integer 5-Con triangles are in a geometric...
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heart attack. Blichfeldt made his first mathematical publication, on Heronian triangles, as an undergraduate in 1896.[A1] Blichfeldt's work in group theory...
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