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: 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.
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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)