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Area of a hyperbolic disc

In curvature minus one, a hyperbolic disc of radius

R

has area

A (R) = 4 π sinh^{2} (R /2) = 2 π (cosh R - 1) .

In the Poincare disc this follows by integrating

4 r (1 - r^{2})^{- 2} d r d θ

up to Euclidean radius

tanh (R /2)

.

Table of contents 59 1
- Radial chain of equal hyperbolic discs Area of a hyperbolic disc 30

 Ancestors (6)

 Incoming links (1)

Solution