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Consider the family of ellipses (x^2)/(c^2)+(y^2)/((1-c)^2)-1=0 (1) for c in [0,1]. The partial derivative with respect to c is -(2x^2)/(c^3)+(2y^2)/((1-c)^3)=0 (2) ...

A catastrophe which can occur for three control factors and two behavior axes. The elliptical umbilic is catastrophe of codimension 3 that has the equation ...

Johnson solid J_(41).

A 1-cusped epicycloid has b=a, so n=1. The radius measured from the center of the large circle for a 1-cusped epicycloid is given by epicycloid equation (◇) with n=1 so r^2 = ...

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 quantity is said to be exact if it has a precise and well-defined value. J. W. Tukey remarked in 1962, "Far better an approximate answer to the right question, which is ...

The excentral-hexyl ellipse is the ellipse passing through vertices of the excentral and hexyl triangles (P. Moses, pers. comm., Jan. 29, 2005). It has center at the ...

Exponential decay is the decrease in a quantity N according to the law N(t)=N_0e^(-lambdat) (1) for a parameter t and constant lambda (known as the decay constant), where e^x ...

The Cartesian product of a finite or infinite set of modules over a ring with only finitely many nonzero entries in each sequence.

The closed plane curve that crosses itself once and consists of one lobe on each side of the intersection. It can be viewed as a circle with a half twist. The fundamental ...