The hyperbolic volume of the knot complement of a hyperbolic knot is a knot
invariant. Adams (1994) lists the hyperbolic volumes for knots
and links.
The knot complement of the figure
eight knot has hyperbolic volume
(OEIS A091518; Borwein and Bailey 2003, p. 89), where 
is Clausen's integral. No closed forms are known
for most (if not all) others.
See also
Hyperbolic Knot
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References
Adams, C. C. "Table of Knots, Links, and Knot and Link Invariants." Appendix in The
Knot Book: An Elementary Introduction to the Mathematical Theory of Knots.
New York: W. H. Freeman, pp. 279-290, 1994.Adams, C.;
Hildebrand, M.; and Weeks, J. "Hyperbolic Invariants of Knots and Links."
Trans. Amer. Math. Soc. 326, 1-56, 1991.Borwein, J. and
Bailey, D. Mathematics
by Experiment: Plausible Reasoning in the 21st Century. Wellesley, MA: A
K Peters, p. 89, 2003.Sloane, N. J. A. Sequence A091518
in "The On-Line Encyclopedia of Integer Sequences."Referenced
on Wolfram|Alpha
Hyperbolic Volume
Cite this as:
Weisstein, Eric W. "Hyperbolic Volume."
From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/HyperbolicVolume.html
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