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...

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...

problem Brahmagupta triangle Congruum Diophantus II.VIII Eisenstein triple Euler brick Heronian triangle Hilbert's theorem 90 Integer triangle Modular arithmetic...

integers. The faces must therefore all be Heronian triangles (named for Hero of Alexandria). Every Heronian tetrahedron can be arranged in Euclidean space...

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...

Rational triangle Heronian triangle Pythagorean triangle Isosceles heronian triangle Primitive Heronian triangle Right triangle 30-60-90 triangle Isosceles right...

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...

Heronian triangle Integer triangle Pythagorean triple Eisenstein triple Bermuda Triangle Historic Triangle Lithium Triangle Parliamentary Triangle, Canberra...

this instance of the Thomson problem is unknown. Almost-equilateral Heronian triangle Malfatti circles Ternary plot Trilinear coordinates Stahl (2003),...

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...

3 : 4 : 5 triangles are the only right triangles with edges in arithmetic progression. Triangles based on Pythagorean triples are Heronian, meaning they...

of their side lengths are positive integers. Triangles with this property are called Heronian triangles; cyclic quadrilaterals with this property (and...

map Heronian triangle, a triangle with integer sides and integer area. List of triangle inequalities One-seventh area triangle, an inner triangle with...

side of a primitive Heronian tetrahedron (after 203, and preceding 1804) with four congruent triangle faces (this primitive Heronian tetrahedron is a tetrahedron...

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...

trapezoid Triangle Acute and obtuse triangles Equilateral triangle Euler's line Heron's formula Integer triangle Heronian triangle Isosceles triangle List...

Herodian – Herod the Great (as in Herodian dynasty) Heronian – Hero of Alexandria (as in Heronian triangle) Hilbertian – David Hilbert (as in Hilbertian field)...

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...

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...

{\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...

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...

arithmetic progression is, but allowing several possible differences Heronian triangles with sides in arithmetic progression Problems involving arithmetic...

partitioned into three Heronian triangles by cutting it along any two non-crossing diagonals, or into five Heronian triangles by cutting it along the...

Integer quadruples of this type are also closely related to Heronian triangles, triangles with integer sides and area. Starting with any four mutually...

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...

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...

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...

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...

Elementary symmetric mean Geometric-harmonic mean Grand mean Heinz mean Heronian mean Identric mean Lehmer mean Logarithmic mean Moving average Neuman–Sándor...

expression for all triangles with consecutive integer sides and rational area, also known as almost-equilateral Heronian triangles. He is sometimes credited...