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Poncelet-Steiner Theorem

All Euclidean Geometric Constructions can be carried out with a Straightedge alone if, in addition, one is given the Radius of a single Circle and its center. The theorem was suggested by Poncelet in 1822 and proved by Steiner in 1833. A construction using Straightedge alone is called a Steiner Construction.

See also Geometric Construction, Steiner Construction


Dörrie, H. ``Steiner's Straight-Edge Problem.'' §34 in 100 Great Problems of Elementary Mathematics: Their History and Solutions. New York: Dover, pp. 165-170, 1965.

Steiner, J. Geometric Constructions with a Ruler, Given a Fixed Circle with Its Center. New York: Scripta Mathematica, 1950.

© 1996-9 Eric W. Weisstein