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; if the centre of the circle is not given, it cannot be constructed by a straightedge alone. Also, the entire circle is not required; usually just a small arc will suffice.

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

See also

• Mohr–Mascheroni theorem

External links

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