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Confocal conics are conic sections sharing a common focus. Any two confocal central conics are orthogonal (Ogilvy 1990, p. 77).

For a countable set of n disjoint events E_1, E_2, ..., E_n P( union _(i=1)^nE_i)=sum_(i=1)^nP(E_i).

A cube 9-compound can be constructed from the vertices of the first dodecahedron 2-compound. It will be implemented in a future version of the Wolfram Language as ...

The n-cyclohedron, also known as the Bott-Taubes polytope, is defined as the compactification of the configuration space of n points on the circle. The cyclohedron can be ...

The radial curve of the cycloid with parametric equations x = a(t-sint) (1) y = a(1-cost) (2) is the circle x_r = x_0+2asint (3) y_r = -2a+y_0+2acost. (4)

Series expansions of the parabolic cylinder functions U(a,x) and W(a,x). The formulas can be found in Abramowitz and Stegun (1972).

A decagon is a ten-sided polygon. Several special types of decagons are illustrated above. In particular, a decagon with vertices equally spaced around a circle and with all ...

An illusion due to Franz Joseph Delboeuf, a Belgian philosopher and expert on hypnosis. If the same circle is placed inside two different concentric circles, its size will ...

A curve which can be turned continuously inside an equilateral triangle. There are an infinite number of delta curves, but the simplest are the circle and lens-shaped ...

If, in an interval of x, sum_(r=1)^(n)a_r(x) is uniformly bounded with respect to n and x, and {v_r} is a sequence of positive non-increasing quantities tending to zero, then ...