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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 ...

Given a rectangle BCDE, draw EF=DE on an extension of BE. Bisect BF and call the midpoint G. Now draw a semicircle centered at G, and construct the extension of ED which ...

If a fixed point is added to each group of a special complete series, then the resulting series is complete.

A reflex angle is an angle of more than 180 degrees. A full angle is therefore a reflex angle, while acute, obtuse, right, and straight angles are not.

An object is reflexible if it is superposable with its image in a plane mirror. Also called amphichiral.

An automorphism which interchanges the two vertices of a regular map at each edge without interchanging the vertices.

An area-minimizing surface (rectifiable current) bounded by a smooth curve in R^3 is a smooth submanifold with boundary.

If two algebraic plane curves with only ordinary singular points and cusps are related such that the coordinates of a point on either are rational functions of a ...

Associated with an irreducible curve of curve genus p, there are p linearly independent integrals of the first sort. The roots of the integrands are groups of the canonical ...

The inverse curve of a right strophoid with parametric equations x = (1-t^2)/(t^2+1) (1) y = (t(t^2-1))/(t^2+1) (2) for an inversion circle with radius 1 and center (1,0) is ...