In 1797 Lorenzo Mascheroni proved that any construction carried out with a straightedge and compass can be carried out with only a compass. Later it came to light that this theorem had already been proved by Georg Mohr in 1672. After explaining in Sect. 13.1 what is meant by performing a construction with only a compass, the proof is presented in stages starting with four auxiliary constructions: reflection of a point (Sect. 13.2), construction of a circle with a given radius (Sect. 13.3), addition and subtraction of line segments (Sect. 13.4) and construction of a line segment as a ratio of segments (Sect. 13.5). Section 13.6 shows how to find the intersection of two lines and Sect. 13.7 shows how to find the intersection of a line and a circle.
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Ben-Ari, M. (2022). A Compass Is Sufficient. In: Mathematical Surprises. Springer, Cham. https://doi.org/10.1007/978-3-031-13566-8_13
Publisher Name: Springer, Cham
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