Poncelet-Steiner theorem

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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.

[edit] See also

• Mohr-Mascheroni theorem

[edit] 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)