Share This Article:

Construction of Regular Heptagon by Rhombic Bicompasses and Ruler

Abstract Full-Text HTML Download Download as PDF (Size:3601KB) PP. 2370-2380
DOI: 10.4236/am.2014.515229    2,687 Downloads   3,158 Views   Citations
Author(s)    Leave a comment


We discuss a new possible construction of the regular heptagon by rhombic bicompasses explained in the text as a new geometric mean of constructions in the spirit of classical constructions in connection with an unmarked ruler (straightedge). It avoids the disadvantages of the neusis construction which requires the trisection of an angle and which is not possible in classical way by compasses and ruler. The rhombic bicompasses allow to draw at once two circles around two fixed points in such correlated way that the position of one of the rotating points (arms) on one circle determines the position of the points on the other circle. This means that the positions of all points (arms) on both circles are determined in unique way.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Wünsche, A. (2014) Construction of Regular Heptagon by Rhombic Bicompasses and Ruler. Applied Mathematics, 5, 2370-2380. doi: 10.4236/am.2014.515229.


[1] Courant, R. and Robbins, H. (1996) What Is Mathematics? Oxford University Press, Oxford.
[2] Stewart, I. (2004) Galois Theory. 3rd Edition, Chapman & Hall/CRC, Boca Raton.
[3] Convay, J.H. and Guy, R.K. (1996) The Book of Numbers. Springer, New York.
[4] Edwards, H. (1984) Galois Theory. Springer, New York.
[5] Postnikov, M.M. (1963) Teorija Galoa (in Russian), Fizmatgiz, Moskva. (English translation: Postnikov, M.M. (2004) Foundations of Galois Theory. Dover Publications, New York).
[6] Shkolnik, A.G. (1961) The Problem of Circle Division (in Russian). Uchpedgiz, Moscow.
[7] Bold, B. (1969) Famous Problems of Geometry and How to Solve Them. Dover, New York.
[8] Weisstein, E.W. (2013) Heptagon, from MathWorld—A Wolfram Web Resource.
[9] van der Waerden, B.L. (1964) Algebra, 1. Teil. 6th Edition, Springer, Berlin.
[10] Klein, F. (1884) Vorlesungen über das Ikosaeder und die Auflösung der Gleichungen vom fünften Grade. Leipzig.

comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.