Construction of Regular Heptagon by Rhombic Bicompasses and Ruler
Abstract: 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.
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.
References

[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.
http://dx.doi.org/10.1007/978-1-4612-4072-3

[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.
http://mathworld.wolfram.com/Heptagon.html

[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.

Top