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:
“I was at work that morning. Someone came riding like mad
Over the bridge and up the road—Farmer Rouf’s little lad.
Bareback he rode; he had no hat; he hardly stopped to say,
“Morgan’s men are coming, Frau, they’re galloping on this way.”
—Constance Fenimore Woolson (1840–1894)
“He is the greatest artist who has embodied, in the sum of his works, the greatest number of the greatest ideas.”
—John Ruskin (1819–1900)