Hyperbolic volume

The hyperbolic volume of the figure-eight knot is 2.0298832.

In the mathematical field of knot theory, the hyperbolic volume of a hyperbolic link is the volume of the link's complement with respect to its complete hyperbolic metric. The volume is necessarily a finite real number, and is a topological invariant of the link.[1] As a link invariant, it was first studied by William Thurston in connection with his geometrization conjecture.[2]

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