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Zbl 1026.51014
Baragar, Arthur
Constructions using a compass and twice-notched straightedge. (English)
[J] Am. Math. Mon. 109, No.2, 151-164 (2002). ISSN 0002-9890

The author studies geometric constructions by compass and twice-notched straightedge in comparison with constructions solvable by using conic sections. He shows that using the twice-notched straightedge is at least as powerful as a conic section drawing tool, concluding that a regular 23-gon or 29-gon cannot be constructed by compass and twice-notched straightedge. Based on these results he shows that one can construct several points whose $x$-coordinates are roots of a quintic that is not solvable by radicals. Finally some questions are posed, e.g. the problem whether a regular 11-gon can be constructed using compass and twice-notched straightedge.
[Horst Martini (Chemnitz)]

MSC 2000:: *51M15 Geometric constructions

Keywords: ruler and compass constructions; straightedge and compass; trisection of angle; quintic; Galois theory; twice-notched straightedge; conic section

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