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Lee (1944) defines an authalic map projection to be one in which at any point the scales in two orthogonal directions are inversely proportional.

A method for mapping three-dimensional figures onto the plane.

The azimuthal angle is an angle measured from the x-axis in the xy-plane in spherical coordinates, denoted theta in this work.

An azimuthal projection which is neither equal-area nor conformal. Let phi_1 and lambda_0 be the latitude and longitude of the center of the projection, then the ...

The Balthasart projection is a cylindrical equal-area projection that uses a standard parallel of phi_s=50 degrees.

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 ...

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.