Figure-eight knot (mathematics)
In knot theory, a figure-8 knot is the unique knot with a crossing number of four, the smallest possible except for the unknot and trefoil knot. The name is given because joining the ends of a string with a normal figure-8 knot tied in it, in the most natural way, gives a model of the mathematical knot.
A simple representation of the figure-8 knot is as the set of all points (x,y,z) where
x = (2 + cos(2t)) cos(3t)
y = (2 + cos(2t)) sin(3t)
z = sin (4t)
for some real value of t. The knot is alternating, rational with an associated value
of 5/2, and is achiral. It is also the hyperbolic knot whose complement has the largest possible volume, 2.02988...
Referenced By
Figure-of-eight knot | Flemish knot | List of geometric topology topics | List of mathematical topics (D-F) | List of mathematical topics (F-Z)
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