跳至主要内容

Construction of Regular Heptagon by Rhombic Bicompasses and Ruler

Read full paper at:
http://www.scirp.org/journal/PaperInformation.aspx?PaperID=48887#.VDcwLlfHRK0

Author(s)   
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. 
 

[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.                     eww141010lx
标签：

评论

发表评论

此博客中的热门博文

Does Immigration Promote the Investment of the Monopolistic Firm?

In the present paper, we examine the effect of increasing uncertainty of immigrants’ growth on the optimal timing of investment of a firm that has a monopolistic power over the labor market. It is revealed that when the uncertainty of immigrants’ growth is more than a threshold level, increasing uncertainty of immigrants’ growth accelerates the optimal timing of firms’ investment and enhances the economic growth, even if the uncertainty of immigrants’ growth is formulated by the geometric Brownian motion, which is in sharp contrast to the standard result that an increase in the uncertainty postpones the optimal timing. With an increase in the immigrants over the past ten years, workforces in the host countries have been growing significantly to the extent that the immigrants represent 70% of the increase in the workforce in Europe, and 47% in the United States as OECD indicates. In the present paper, we attempted to investigate the effect of increased uncertainty caused by the growi...
发表评论
阅读全文

Education Policy Implementation: A Mechanism for Enhancing Primary Education Development in Zanzibar

Education is one of the fundamental rights of individuals; therefore, the government of a country needs to develop and strengthen educational policy and quality as well as to ensure that everyone has equal access to basic education. The improvement of access and quality of education in the world is becoming as an essential factor in development, whereas the basic education (primary school), is acknowledged as a foundation of the higher educational development for every country. To fulfill this goal, governments introduce several policies and procedures; however, it requires some reforms and participation from the politician, policymakers, and other stakeholders to re-examine educational policy so that it can lead to multiplication and betterment of the reforms. Educational reforms actually focus on accountability. A positive educational development and reform is very challenging and needs more effort and strategy on how to use and utilize the resources effectively as such it can achie...
发表评论
阅读全文