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Given an arbitrary planar quadrilateral, place a square outwardly on each side, and connect the centers of opposite squares. Then van Aubel's theorem states that the two ...

A flow defined analogously to the axiom A diffeomorphism, except that instead of splitting the tangent bundle into two invariant sub-bundles, they are split into three (one ...

The parametric equations for a catenary are x = t (1) y = acosh(t/a), (2) giving the evolute as x = t-a/2sinh((2t)/a) (3) y = 2acosh(t/(2a)). (4) For t>0, the evolute has arc ...

A triangle DeltaA^'B^'C^' is said to be circumscribed in a triangle DeltaABC if A lies on B^'C^', B lies on C^'A^', and C lies on A^'B^' (Kimberling 1998, p. 185). Examples ...

A coaxal system is a system of coaxal circles. A spectacular example is the set of circles (circumcircle, nine-point circle, orthocentroidal circle, orthoptic circle of the ...

The involute of an ellipse specified parametrically by x = acost (1) y = bsint (2) is given by the parametric equations x_i = ...

For a unit speed curve on a surface, the length of the surface-tangential component of acceleration is the geodesic curvature kappa_g. Curves with kappa_g=0 are called ...

The Kampyle of Eudoxus is a curve studied by Eudoxus in relation to the classical problem of cube duplication. It is given by the polar equation r=asec^2theta, (1) and the ...

An epicycloid with n=5 cusps, named after the buttercup genus Ranunculus (Madachy 1979). Its parametric equations are x = a[6cost-cos(6t)] (1) y = a[6sint-sin(6t)]. (2) Its ...

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 ...