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An equilateral triangle is a triangle with all three sides of equal length a, corresponding to what could also be known as a "regular" triangle. An equilateral triangle is ...

According to Euler's rotation theorem, any rotation may be described using three angles. If the rotations are written in terms of rotation matrices D, C, and B, then a ...

Given a Jacobi theta function, the nome is defined as q(k) = e^(piitau) (1) = e^(-piK^'(k)/K(k)) (2) = e^(-piK(sqrt(1-k^2))/K(k)) (3) (Borwein and Borwein 1987, pp. 41, 109 ...

The Penrose tiles are a pair of shapes that tile the plane only aperiodically (when the markings are constrained to match at borders). These two tiles, illustrated above, are ...

The permutation symbol (Evett 1966; Goldstein 1980, p. 172; Aris 1989, p. 16) is a three-index object sometimes called the Levi-Civita symbol (Weinberg 1972, p. 38; Misner et ...

The integer sequence defined by the recurrence P(n)=P(n-2)+P(n-3) (1) with the initial conditions P(0)=3, P(1)=0, P(2)=2. This recurrence relation is the same as that for the ...

There are (at least) three different types of points known as Steiner points. The point S of concurrence of the three lines drawn through the vertices of a triangle parallel ...

The point of concurrence K of the symmedians, sometimes also called the Lemoine point (in England and France) or the Grebe point (in Germany). Equivalently, the symmedian ...

Integrals over the unit square arising in geometric probability are int_0^1int_0^1sqrt(x^2+y^2)dxdy=1/3[sqrt(2)+sinh^(-1)(1)] int_0^1int_0^1sqrt((x-1/2)^2+(y-1/2)^2)dxdy ...

An algorithm is a specific set of instructions for carrying out a procedure or solving a problem, usually with the requirement that the procedure terminate at some point. ...