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For an ellipse given by the parametric equations x = acost (1) y = bsint, (2) the catacaustic is a complicated expression for generic radiant point (x_r,y_r). However, it ...

A transformation from one reference frame to another moving with a constant velocity v with respect to the first for classical motion. However, special relativity shows that ...

A geometric sequence is a sequence {a_k}, k=0, 1, ..., such that each term is given by a multiple r of the previous one. Another equivalent definition is that a sequence is ...

A pyramid with a hexagonal base. The edge length of a hexagonal pyramid of height h is a special case of the formula for a regular n-gonal pyramid with n=6, given by ...

An isozonohedron is a zonohedron whose faces consist of n(n-1) congruent rhombi (Fedorov 1953, pp. 256-266; Chilton and Coxeter 1963). The following table summarizes some of ...

Let the center B of a circle of radius a move along a line BA. Let O be a fixed point located a distance c away from AB. Draw a secant line through O and D, the midpoint of ...

The nonagon, also known as an enneagon, is a 9-sided polygon. Although the term "enneagon" is perhaps preferable (since it uses the Greek prefix and suffix instead of the ...

The contravariant four-vector arising in special and general relativity, x^mu=[x^0; x^1; x^2; x^3]=[ct; x; y; z], (1) where c is the speed of light and t is time. ...

The sum of reciprocal multifactorials can be given in closed form by the beautiful formula m(n) = sum_(n=0)^(infty)1/(n!...!_()_(k)) (1) = ...

The m×n rook complement graph K_m square K_n^_ is the graph complement of the m×n rook graph. It has vertex count mn and edge count 2(m; 2)(n; 2), where (n; k) is a binomial ...