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Hilbert’s Error?

Alexander Shen 1 
1 ESCAPE - Systèmes complexes, automates et pavages
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : Geometric constructions have been a topic of interest among mathematicians for centuries. The Euclidean tradition uses two instruments: a straightedge (ruler) and a compass. However, limited constructions have also been studied. The Mohr–Mascheroni theorem says that every construction using both instruments can be replaced by a construction of the same object that uses only a compass. (Obviously, a line cannot be drawn with a compass; we construct two distinct points on that line instead.) Another result, the Poncelet–Steiner theorem, says that in a construction using straightedge and compass, a single application of a compass suffices: if a circle with its center is given, then every straightedge–compass construction can be performed with only a straightedge. Today, such results are considered to belong to recreational mathematics, and they can be found in many books, such as [6], for example.
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Alexander Shen. Hilbert’s Error?. Mathematical Intelligencer, Springer Verlag, 2018, 40 (4), pp.6-11. ⟨10.1007/s00283-018-9792-8⟩. ⟨lirmm-01982335⟩



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