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Buffon's needle problem asks to find the probability that a needle of length l will land on a line, given a floor with equally spaced parallel lines a distance d apart. The ...

The café wall illusion, sometimes also called the Münsterberg illusion (Ashton Raggatt McDougall 2006), is an optical illusion produced by a black and white rectangular ...

A catacaustic is a curve that is the envelope of rays emanating from a specified point (or a point at infinite distance producing parallel rays) for a given mirror shape. The ...

The chromatic invariant theta(G) of a connected graph G is the number of spanning trees of G that have internal activity 1 and external activity 0. For graphs other than the ...

Consider a unit circle and a radiant point located at (mu,0). There are four different regimes of caustics, illustrated above. For radiant point at mu=infty, the catacaustic ...

A circumellipse is a circumconic of a triangle that is an ellipse. There is an amazing formula for the area of a circumellipse. Let d_A be the length of the chord of the ...

Given two curves C_1 and C_2 and a fixed point O, let a line from O cut C_1 at Q and C_2 at R. Then the locus of a point P such that OP=QR is the cissoid. The word cissoid ...

The cochleoid, whose name means "snail-form" in Latin, was first considered by John Perks as referenced in Wallis et al. (1699). The cochleoid has also been called the oui-ja ...

The subset C of the Euclidean plane formed by the union of the x-axis, the line segment with interval [0,1] of the y-axis, and the sequence of segments with endpoints (1/n,0) ...

A conical frustum is a frustum created by slicing the top off a cone (with the cut made parallel to the base). For a right circular cone, let s be the slant height and R_1 ...