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Constructions using a compass and twice-notched straightedge. (English) Zbl 1026.51014
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.

##### MSC:
 51M15 Geometric constructions
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