Poncelet–Steiner theorem

In Euclidean geometry, the Poncelet–Steiner theorem is a result about compass and straightedge constructions with certain restrictions. This result states that whatever can be constructed by straightedge and compass together can be constructed by straightedge alone, provided that a single circle and its centre are given.

This shows that, while a compass can make constructions easier, it is no longer needed once the first circle has been drawn. All constructions thereafter can be performed using only the straightedge, although the arcs of circles themselves cannot be drawn without the compass. This means the compass may be used for aesthetic purposes, but it is not required for the construction itself.

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