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The angular twist theta of a shaft with given cross section is given by theta=(TL)/(KG) (1) (Roark 1954, p. 174), where T is the twisting moment (commonly measured in units ...

The area Delta (sometimes also denoted sigma) of a triangle DeltaABC with side lengths a, b, c and corresponding angles A, B, and C is given by Delta = 1/2bcsinA (1) = ...

A triangle center function (sometimes simply called a center function) is a nonzero function f(a,b,c) that is homogeneous f(ta,tb,tc)=t^nf(a,b,c) (1) bisymmetry in b and c, ...

The problem of finding the mean triangle area of a triangle with vertices picked inside a triangle with unit area was proposed by Watson (1865) and solved by Sylvester. It ...

Angle addition formulas express trigonometric functions of sums of angles alpha+/-beta in terms of functions of alpha and beta. The fundamental formulas of angle addition in ...

A twin Pythagorean triple is a Pythagorean triple (a,b,c) for which two values are consecutive integers. By definition, twin triplets are therefore primitive triples. Of the ...

Wang's conjecture states that if a set of tiles can tile the plane, then they can always be arranged to do so periodically (Wang 1961). The conjecture was refuted when Berger ...

The regular polygon of 17 sides is called the heptadecagon, or sometimes the heptakaidecagon. Gauss proved in 1796 (when he was 19 years old) that the heptadecagon is ...

In two dimensions, there are two periodic circle packings for identical circles: square lattice and hexagonal lattice. In 1940, Fejes Tóth proved that the hexagonal lattice ...

The word polyhedron has slightly different meanings in geometry and algebraic geometry. In geometry, a polyhedron is simply a three-dimensional solid which consists of a ...