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The circle through the cusp of the arbelos and the tangent points of the first Pappus circle, which is congruent to the two Archimedes' circles. If AB=r and AC=1, then the ...

The triangle center with triangle center function alpha=A.

A face-centered cubic sphere packing obtained by placing layers of spheres one on top of another. Because there are two distinct ways to place each layer on top of the ...

A construction for the rhombic dodecahedron.

Let f:M->N be a geodesic mapping. If either M or N has constant curvature, then both surfaces have constant curvature (Ambartzumian 1982, p. 26; Kreyszig 1991).

Two curves which, at any point, have a common principal normal vector are called Bertrand curves. The product of the torsions of Bertrand curves is a constant.

The biaugmented pentagonal prism is Johnson solid J_(53), which is formed from double augmentation of two nonadjacent lateral faces of the equilateral pentagonal prism by an ...

Johnson solid J_(50).

Johnson solid J_(67).

Given two bicentric points P=p:q:r and U=u:v:w, their bicentric sum is defined by p+u:q+v:r:w.