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The involute of the deltoid x = 1/3[2cost-cos(2t)] (1) y = 1/3[2sint-sin(2t)] (2) is a hypocycloid involute for n=3 x_i = 1/9[2cost-cos(2t)] (3) y_i = 1/9[2sint+sin(2t)], (4) ...

A generalization of the helicoid to the parametric equations x(u,v) = avcosu (1) y(u,v) = bvsinu (2) z(u,v) = cu. (3) In this parametrization, the surface has first ...

A set of curves whose equations are of the same form but which have different values assigned to one or more parameters in the equations. Families of curves arise, for ...

Given a differential p-form q in the exterior algebra ^ ^pV^*, its envelope is the smallest subspace W such that q is in the subspace ^ ^pW^* subset ^ ^pV^*. Alternatively, W ...

A ruled surface is called a generalized cone if it can be parameterized by x(u,v)=p+vy(u), where p is a fixed point which can be regarded as the vertex of the cone. A ...

A hexecontahedron is a 60-faced polyhedron. Examples include the deltoidal hexecontahedron, rhombic hexecontahedron, and triakis icosahedron. Counting the faces produced by ...

A general concept in category theory involving the globalization of topological or differential structures. The term derives from the Greek omicronlambdaomicronsigma (holos) ...

The surface with parametric equations x = (sinhvcos(tauu))/(1+coshucoshv) (1) y = (sinhvsin(tauu))/(1+coshucoshv) (2) z = (coshvsinh(u))/(1+coshucoshv), (3) where tau is the ...

A function for which the integral can be computed is said to be integrable.

Given a function of the form y=Ax^B, (1) least squares fitting gives the coefficients as b = ...