---
tag: G44YY10VC4
kind: concept
name: Bridge number
msc: [57K10]
specializes: [GZQ5ZE3X6G]
sources:
  - url: https://en.wikipedia.org/wiki/Bridge_number
same_as:
  wikidata: Q4966409
  wikipedia: Bridge number
---

## Summary

The bridge number of a [[knot|QYEAZTYGPT]] is the least number of local maxima of the height on the knot.
The least is taken over all positions of the knot in space.
It is a [[knot invariant|GZQ5ZE3X6G]] introduced by Horst Schubert.
Knots with bridge number $2$, the two-bridge knots, form a well-understood family that is classified completely.

## Explanations

### L1 human

Lay a knotted rope in space and look at its height above the floor.
The rope goes up and down; count the hilltops.
The bridge number is the smallest number of hilltops you can get by moving the rope around without cutting it.
A plain circle has one hilltop, and nothing smaller is possible.
The [[trefoil knot|VYTYSVHN4A]] needs two hilltops, so its bridge number is $2$.