Circles, Spheres and Balls
In hyperbolic geometry the circumference of a circle of radius r is greater than 2πr. It is in fact equal to
The area of the enclosed disk is
The surface area of a sphere is
The volume of the enclosed ball is
For the measure of an n-1 sphere in n dimensional space the corresponding expression is
where the full n dimensional solid angle is
using for the Gamma function.
The measure of the enclosed n ball is:
Read more about this topic: Hyperbolic Geometry
Famous quotes containing the words spheres and/or balls:
“The world has already learned that woman has other virtues than meekness, patience, humility and endurance. She possesses courage above all fear, and a will that knows no obstacles; and when these are called forth by some great emergency, false modesty is trampled in the dust, and spheres are scattered to the winds.”
—A. Holley, U.S. women’s magazine contributor. The Lily, p. 38 (May 1852)
“look the spangles
that sleep all the year in a dark box
dreaming of being taken out and allowed to shine,
the balls the chains red and gold the fluffy threads,
put up your little arms
and i’ll give them all to you to hold”
—E.E. (Edward Estlin)