Euclidean vs. Hyperbolic Formulas

angles:

tan beta = b/a        tan beta = tanh(b)/tanh(a)

circle circumference:

2*pi*r        2*pi*sinh(r)

circle area:

pi*r^2        2*pi(cosh(r)-1)

hemisphere area:

2*pi*r^2        2*pi*sinh^2(r)

spherical cap area:

2*pi*r(1-cos(phi))        2*pi*sinh(r)(1-cos(phi))