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Nexus Network Journal

, Volume 3, Issue 2, pp 139–146 | Cite as

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

  • Mark A. ReynoldsEmail author
The Geometer’s Angle

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.

Keywords.

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

Copyright information

© Birkhäuser Verlag, Basel 2001

Authors and Affiliations

  1. 1.Mill ValleyUSA

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