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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?

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    $\begingroup$ en.wikipedia.org/wiki/Heptagon#Construction $\endgroup$ – carmichael561 Jan 19 '17 at 21:25
  • $\begingroup$ Relevant wikipedia page. $\endgroup$ – Arthur Jan 19 '17 at 21:25
  • $\begingroup$ Pentagon: 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). $\endgroup$ – Jack D'Aurizio Jan 19 '17 at 21:26
  • $\begingroup$ @JackD'Aurizio Apparently, a regular heptagon is constructible using a marked straightedge. $\endgroup$ – Arthur Jan 19 '17 at 21:26
  • $\begingroup$ @Arthur: or a trisectrix of Hippias, sure. $\endgroup$ – Jack D'Aurizio Jan 19 '17 at 21:28
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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.

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