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.
Share and Cite:
Wünsche, A. (2014) Construction of Regular Heptagon by Rhombic Bicompasses and Ruler.
Applied Mathematics,
5, 2370-2380. doi:
10.4236/am.2014.515229.
Conflicts of Interest
The authors declare no conflicts of interest.
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.
|