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Any nontrivial, closed, simple, smooth spherical curve dividing the surface of a sphere into two parts of equal areas has at least four inflection points.

The surface area of a spherical segment. Call the radius of the sphere R, the upper and lower radii b and a, respectively, and the height of the spherical segment h. The zone ...

The polar sine is a function of a vertex angle of an n-dimensional parallelotope or simplex. If the content of the parallelotope is P and the lengths of the n edges of the ...

There are (at least) two mathematical constants associated with Theodorus. The first Theodorus's constant is the elementary algebraic number sqrt(3), i.e., the square root of ...

A catacaustic is a curve that is the envelope of rays emanating from a specified point (or a point at infinite distance producing parallel rays) for a given mirror shape. The ...

Johnson solid J_7.

The geometry of Finsler space.

The geodesics on a general cylinder generated by lines parallel to a line l with which the tangent makes a constant angle.

A type of point at infinity in which parallel lines in the hyperbolic plane intersect at infinity in one direction, while diverging from one another in the other.

The principal normal indicatrix of a closed space curve with nonvanishing curvature bisects the area of the unit sphere if it is embedded.