Although it is impossible to construct a regular heptagon and a regular nonagon using a compass and unmarked straightedge, it is possible to construct them with a compass and marked straightedge using the neusis technique. We give a geometric proof of Johnson’s neusis construction of the regular heptagon, which he had proven using trigonometry. We do so using so-called central triangles and zig-zag paths in the polygons. We then give efficient neusis constructions of the regular heptagon and the regular nonagon.

Lawson, Dan, and David Richeson. Zig-Zag Paths and Neusis Constructions of a Heptagon and a Nonagon. The College Mathematics Journal (Article published online October 13, 2023). https://www.tandfonline.com/doi/full/10.1080/07468342.2023.2261347?src=

David Richeson is a professor of Mathematics at Dickinson College.

For more information on the published version, visit Taylor and Francis's Website. https://www.tandfonline.com/doi/full/10.1080/07468342.2023.2261347?src=

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