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The Gömböc (meaning "sphere-like" in Hungarian) is the name given to a class of convex solids which possess a unique stable and a unique unstable point of equilibrium. ...

The spherical curve taken by a ship which travels from the south pole to the north pole of a sphere while keeping a fixed (but not right) angle with respect to the meridians. ...

A subset S subset R^n is said to be pseudo-convex at a point x in S if the associated pseudo-tangent cone P_S(x) to S at x contains S-{x}, i.e., if S-{x} subset P_S(x). Any ...

An affine variety V is an algebraic variety contained in affine space. For example, {(x,y,z):x^2+y^2-z^2=0} (1) is the cone, and {(x,y,z):x^2+y^2-z^2=0,ax+by+cz=0} (2) is a ...

A conical wedge is an ungula obtained by cutting a solid cone with a plane placed at an angle oblique to its base. For the special conical wedge obtained from a cone of ...

A developable surface, also called a flat surface (Gray et al. 2006, p. 437), is a ruled surface having Gaussian curvature K=0 everywhere. Developable surfaces therefore ...

The Steinmetz solid is the solid common to two (or three) right circular cylinders of equal radii intersecting at right angles is called the Steinmetz solid. Two cylinders ...

A cyclide is a pair of focal conics which are the envelopes of two one-parameter families of spheres, sometimes also called a cyclid. The cyclide is a quartic surface, and ...

If a function phi is harmonic in a sphere, then the value of phi at the center of the sphere is the arithmetic mean of its value on the surface.

The placement of n points on a sphere so as to minimize the maximum distance of any point on the sphere from the closest one of the n points.