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The insphere of a solid is a sphere that is tangent to all faces of the solid. An insphere does not always exist, but when it does, its radius r is called the inradius and ...

A regular patch is a patch x:U->R^n for which the Jacobian J(x)(u,v) has rank 2 for all (u,v) in U. A patch is said to be regular at a point (u_0,v_0) in U provided that its ...

The vertical perspective projection is a map projection that corresponds to the appearance of a globe when directly viewed from some distance away with the z-axis of the ...

The Voronov-Neopryatnaya-Dergachev graphs are two graphs on 372 and 972 vertices which have unit-distance embeddings with all vertices on a sphere and chromatic number 5. The ...

The homotopy groups generalize the fundamental group to maps from higher dimensional spheres, instead of from the circle. The nth homotopy group of a topological space X is ...

A tiling consisting of a rhombus such that 17 rhombuses fit around a point and a second tile in the shape of six rhombuses stuck together. These two tiles can fill the plane ...

A generalization of calculus of variations which draws the relationship between the stationary points of a smooth real-valued function on a manifold and the global topology ...

Points, also called polar reciprocals, which are transformed into each other through inversion about a given inversion circle C (or inversion sphere). The points P and P^' ...

As defined by Gray (1997, p. 201), Viviani's curve, sometimes also called Viviani's window, is the space curve giving the intersection of the cylinder of radius a and center ...

A geodesic is a locally length-minimizing curve. Equivalently, it is a path that a particle which is not accelerating would follow. In the plane, the geodesics are straight ...