Poncelet-Steiner theorem

In geometry, the Poncelet-Steiner theorem on compass and straightedge construction states that whatever can be constructed by straightedge and compass together can be constructed by straightedge alone, if given a single circle and its centre. This result is the best possible: a straightedge alone, without a circle given, cannot construct square roots.

The result was conjectured by Jean Victor Poncelet in 1822, and proven by Jakob Steiner in 1833.

See also: Mohr-Mascheroni theorem.

External link

* Jacob Steiner's theorem at cut-the-knot (It is impossible to find the center of a given circle with the straightedge alone)