The Collapsing Compass
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|There has been considerable interest during the past 2300 years in comparing different models of geometric computation in terms of their computing power. One of the most well-known results is the proof in 1672 due to Mohr that all constructions that can be executed with straight-edge and compass can be carried out with compass alone. The earliest such proof of the equivalence of models of computation is due to Euclid in his second proposition of Book I of the Elements in which he establishes that the collapsing compass is equivalent in power to the modern compass... download Toussaint's article, "A new look at Euclid's second proposition," The Mathematical Intelligencer, vol. 15, No. 3, 1993, pp. 12-23, in zipped postscript format, in English or Spanish.|
|Math Topics:||Computational Geometry, Constructions|
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