In the mathematical field of knot theory, the bridge number is an invariant of a knot. It is defined as the minimal number of bridges required in all the possible bridge representations of a knot. In bridge representation, a knot lies entirely in the plane apart for a finite number of bridges whose projections onto the plane are straight lines.
Equivalently the bridge number is the minimal number of local maxima of the projection of the knot onto a vector, where we minimize over all projections and over all conformations of the knot.
It can be shown that every n-bridge knot can be decomposed into two trivial n-tangles and hence 2-bridge knots are rational knots.
Famous quotes containing the words bridge and/or number:
“In bridge clubs and in councils of state, the passions are the same.”
—Mason Cooley (b. 1927)
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—Graham Greene (1904–1991)