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From Pentagon to Heptagon: A Discovery on the Generation of the Regular Heptagon from the Equilateral Triangle and Pentagon

Abstract.

Geometer Marcus the Marinite presents a construction for the heptagon that is within an incredibly small percent deviation from the ideal. The relationship between the incircle and excircle of the regular pentagon is the key to this construction, and their ratio is 2 : ϕ. In other words, the golden section plays the critical role in the establishment of this extremely closeto-ideal heptagon construction.

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Correspondence to Mark A. Reynolds.

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Reynolds, M.A. From Pentagon to Heptagon: A Discovery on the Generation of the Regular Heptagon from the Equilateral Triangle and Pentagon. Nexus Netw J 3, 139–146 (2001). https://doi.org/10.1007/s00004-001-0028-3

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  • DOI: https://doi.org/10.1007/s00004-001-0028-3

Keywords.

  • Mark Reynolds
  • vesica piscis
  • architecture and mathematics
  • constructing regular polygons with compass and straightedge
  • plane geometry
  • golden secion
  • regular heptagon