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Nonconcurrent triangles with parallel sides are always homothetic. Homothetic triangles are always perspective triangles. Their perspector is called their homothetic center.

The inversion of a horn torus. If the inversion center lies on the torus, then the horn cyclide degenerates to a parabolic horn cyclide.

Let a_1, a_2, ..., a_n be scalars not all equal to 0. Then the set S consisting of all vectors X=[x_1; x_2; |; x_n] in R^n such that a_1x_1+a_2x_2+...+a_nx_n=c for c a ...

The circle with respect to which an inverse curve is computed or relative to which inverse points are computed. In three dimensions, inverse points can be computed relative ...

The isogonal transform of a geometric object is the object obtained by collectively taking the isogonal conjugates of all its points.

The isotomic transform of a geometric object is the object obtained by collectively taking the isotomic conjugates of all its points.

Finding the densest not necessarily periodic sphere packing.

An a×b rectangle can be packed with 1×n strips iff n|a or n|b.

A sphere is rigid.

The polyhedron resulting from letting each sphere in a sphere packing expand uniformly until it touches its neighbors on flat faces.