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The edge multiplicity of a given end vertex in a multigraph is the number of multiple edges sharing that end vertex. The maximum edge multiplicity in such a graph is known as ...

Elementary number theory is the branch of number theory in which elementary methods (i.e., arithmetic, geometry, and high school algebra) are used to solve equations with ...

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 ...

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 ...

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

The only whole number solution to the Diophantine equation y^3=x^2+2 is y=3, x=+/-5. This theorem was offered as a problem by Fermat, who suppressed his own proof.