Is it possible to construct a regular heptagon (a figure with seven sides) with just compass and straightedge? If so, could you please give me directions for how to do this?
Is it possible to construct a regular heptagon with just compass and straightedge?
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geometry
polygons
geometric-construction
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1https://en.wikipedia.org/wiki/Heptagon#Construction – 2017-01-19
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0[Relevant wikipedia page](https://en.wikipedia.org/wiki/Constructible_polygon). – 2017-01-19
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0Pentagon: constructible. Heptagon: not constructible (but half the side length for an inscribed equilateral triangle is a good approximation for the side length of the inscribed heptagon). – 2017-01-19
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0@JackD'Aurizio Apparently, a regular heptagon is constructible using a _marked_ straightedge. – 2017-01-19
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0@Arthur: or a trisectrix of Hippias, sure. – 2017-01-19
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0Why do people provide "simple" answers as comments instead of proper answers? It seems like a form of "modesty", but it makes a lot of things harder (among other things, it shows the question among the unanswered ones). – 2017-01-19
1 Answers
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No, it's not possible; in fact, the regular heptagon is the regular polygon with the least number of sides that is impossible to construct with compass and straightedge alone. It is, however, possible to construct it using a neusis ruler. A related question has been asked (and answered) here.