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:
“Like a bridge over troubled water
I will lay me down.”
—Paul Simon (b. 1949)
“It seems to me that there must be an ecological limit to the number of paper pushers the earth can sustain, and that human civilization will collapse when the number of, say, tax lawyers exceeds the world’s total population of farmers, weavers, fisherpersons, and pediatric nurses.”
—Barbara Ehrenreich (b. 1941)