We show that every point in the plane which can be constructed by a compass and a ruler, given a setS of points, can be constructed using a compass alone so that the following restriction is met. LetO andK be two arbitrarily chosen distinct points ofS. Then every point is obtained as a proper intersection of two circles that are either completely symmetrical with respect to the lineOK or have both their centers on this line.
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AVRON, A.:Theorems on strong constructibility with a compass alone. Journal of Geometry, vol. 30 (1987), pp. 28–35.
MASCHERONI, L.:La Geometria del Compasso, Pavia V (1797).
MOHR, G.:Euclides Danicus, Amsterdam (1672).
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Avron, A. On strict strong constructibility with a compass alone. J Geom 38, 12–15 (1990). https://doi.org/10.1007/BF01222890
- Distinct Point
- Proper Intersection
- Strong Constructibility