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:
“It launch’d forth filament, filament, filament, out of itself,
Ever unreeling them, ever tirelessly speeding them.
And you O my soul where you stand,
Surrounded, detached, in measureless oceans of space,
Ceaselessly musing, venturing, throwing, seeking the spheres to connect them,
Till the bridge you will need be form’d, till the ductile anchor hold,
Till the gossamer thread you fling catch somewhere, O, my soul.”
—Walt Whitman (1819–1892)
“If the head is lost, all that perishes is the individual; if the balls are lost, all of human nature perishes.”
—François Rabelais (1494–1553)