منابع مشابه
Primitive Heronian Triangles With Integer Inradius and Exradii
It is well known that primitive Pythagorean triangles have integer inradius and exradii. We investigate the generalization to primitive Heronian triangles. In particular, we study the special cases of isosceles triangles and triangles with sides in arithmetic progression. We also give two families of primitive Heronian triangles, one decomposable and one indecomposable, which have integer inrad...
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We study the existence of equilateral triangles of given side lengths and with integer coordinates in dimension three. We show that such a triangle exists if and only if their side lengths are of the form √ 2(m2 − mn + n2) for some integers m, n. We also show a similar characterization for the sides of a regular tetrahedron in Z: such a tetrahedron exists if and only if the sides are of the for...
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ژورنال
عنوان ژورنال: The Mathematical Gazette
سال: 2015
ISSN: 0025-5572,2056-6328
DOI: 10.1017/mag.2015.39