PM  >> Vol. 7 No. 4 (July 2017)

    勾股定理离散性质的推广和应用—Pythagorean方程和特殊的M角数
    An Extension of Pythagorean Equation with Its Application—Pythagorean Equation and Special M-Gonal Numbers

  • 全文下载: PDF(538KB) HTML   XML   PP.255-261   DOI: 10.12677/PM.2017.74033  
  • 下载量: 152  浏览量: 208  

作者:  

郭铭浩:上海交通大学生物医学工程学院,上海;
郭志成:北方设计研究院,河北 石家庄

关键词:
Pythagorean方程M角数拓扑椭圆Pythagorean Equation M-Gonal Number Topological Ovals

摘要:

采用Pythagorean方程的解决方法,我们得到了一对M角数之差仍然为M角数的连接形式。使用给出的这些明显可计算的普通表达式,我们在两种数组之间建立了一种非凡的连接。从而使得两种数组的平面射影可以成为“局部”拓扑,并且在Desarguesian型拓扑实数射影平面上,自然而然的可以共享许多拓扑椭圆的性质。

Based on the solution of Pythagorean Equation, we obtain a relationship that the difference be-tween two M-Gonal numbers is still an M-Gonal number. With this explicit computable expression, we establish a remarkable connection between two pairs of numbers. The projected planes of two pairs of numbers generate partial topological structure. In real Desarguesian projective plane, this structure shares many existing properties of topological ellipsoid naturally.

文章引用:
郭铭浩, 郭志成. 勾股定理离散性质的推广和应用—Pythagorean方程和特殊的M角数[J]. 理论数学, 2017, 7(4): 255-261. https://doi.org/10.12677/PM.2017.74033

参考文献

[1] Dickson, E.L. (2010) History of the Theory of Numbers. Diophantine Analysis, Vol. 2.
[2] Gopalan, M.A., Somanath, M. and Vanitha, N. (2007) M-Gonal Number – 1 = A Perfect Square. Acta Ciencia Indica Mathematics, Vol XXXIII M, 479-480.
[3] Bhanumathy, T.S. (1995) Ancient Indian Mathematics. New Age Publishers Ltd, New Delhi.
[4] Gopalan, M.A., Somanath, M. and Vanitha, N. (2009) On pairs of M-Gonal Numbers with Unit Difference. Reflections des ERA-JMS, 4, 365-376.
[5] Gopalan, M.A., Geetha, K. and Somanath, M. (2014) M-Gonal Number, ±2 = A Perfect Square. International Journal of Innovative Technology and Research, 2, 1618-1620.
[6] Gopalan, M.A. and Geetha, V. (2015) M-Gonal Number ±3 = A Perfect Square. International Journal of Mathematics Trends and Technology, 17, 32-35.
[7] Gopalan, M.A. and Devibala, S. (2006) Equality of Triangular Numbers with Special M-Gonal Numbers. Bulletin of Allahabad Mathematical Society, 21, 25-29.
[8] Armstrong, M.A. (1983) Basic Topology. Undergraduate Texts in Mathematics, 137-155.
https://doi.org/10.1007/978-1-4757-1793-8
[9] Polster, B., Rosehr, N. and Steinke, G.F. (1997) On the Existence of Topological Ovals in Flat Projective Planes. Archiv der Mathematik, 68, 418-429.
https://doi.org/10.1007/s000130050074