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A quartic curve with implicit equation (a^2)/(x^2)-(b^2)/(y^2)=1 (1) or a^2y^2-b^2x^2=x^2y^2 (2) and a,b>0. In parametric form, x = +/-acost (3) y = bcott. (4) The curvature ...

The catacaustic of a cardioid for a radiant point along the x-axis is complicated function of x. For x=0 (i.e., with radiant point at the cusp), however, the catacaustic for ...

A surface which is related to Cayley numbers.

The envelope of refracted rays for a given curve.

The radial curve of an epicycloid is shown above for an epicycloid with four cusps. Although it is claimed to be a rose curve by Lawrence (1972), it is not.

The epispiral is a plane curve with polar equation r=asec(ntheta). There are n sections if n is odd and 2n if n is even. A slightly more symmetric version considers instead ...

A Jordan algebra which is not isomorphic to a subalgebra.

A factorial prime is a prime number of the form n!+/-1, where n! is a factorial. n!-1 is prime for n=3, 4, 6, 7, 12, 14, 30, 32, 33, 38, 94, 166, 324, 379, 469, 546, 974, ...

The inverse curve of Fermat's spiral with the origin taken as the inversion center is the lituus.

The hippopede, also known as the horse fetter, is a curve given by the polar equation r^2=4b(a-bsin^2theta). Hippopedes are plotted above for values of a/b=0.2 to 2.0.