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Partial differential equation boundary conditions which give the value of the function on a surface, e.g., T=f(r,t).

Two cones placed apex to apex. The double cone is given by algebraic equation (z^2)/(c^2)=(x^2+y^2)/(a^2).

A tensor t is said to satisfy the double contraction relation when t_(ij)^m^_t_(ij)^n=delta_(mn). (1) This equation is satisfied by t^^^0 = (2z^^z^^-x^^x^^-y^^y^^)/(sqrt(6)) ...

The double sphere is the degenerate quartic surface (x^2+y^2+z^2-r^2)^2=0 obtained by squaring the left-hand side of the equation of a usual sphere x^2+y^2+z^2-r^2=0.

The Droussent cubic is the triangle cubic with trilinear equation sum_(cyclic)(b^4+c^4-a^4-b^2c^2)aalpha(b^2beta^2-c^2gamma^2)=0. It passes through Kimberling centers X_n for ...

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 ...