Share This Article:

Rational Equiangular Polygons

Abstract Full-Text HTML XML Download Download as PDF (Size:264KB) PP. 1460-1465
DOI: 10.4236/am.2013.410197    5,398 Downloads   6,683 Views  

ABSTRACT

The main purpose of this note is to investigate equiangular polygons with rational edges. When the number of edges is the power of a prime, we determine simple, necessary and sufficient conditions for the existence of such polygons. As special cases of our investigations, we settle two conjectures involving arithmetic polygons.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Munteanu, M. and Munteanu, L. (2013) Rational Equiangular Polygons. Applied Mathematics, 4, 1460-1465. doi: 10.4236/am.2013.410197.

References

[1] D. Ball, “Equiangular Polygons,” The Mathematical Gazette, Vol. 86, No. 507, 2002, pp. 396-407. http://dx.doi.org/10.2307/3621131
[2] P. R. Scott, “Equiangular Lattice Polygons and Semiregular Lattice Polyhedra,” College Mathematics Journal, Vol. 18, No. 4, 1987, pp. 300-306. http://dx.doi.org/10.2307/2686799
[3] R. Honsberger, “Mathematical Diamonds,” The Mathematical Association of America, Washington DC, 2003.
[4] R. Dawson, “Arithmetic Polygons,” American Mathematical Monthly, Vol. 119, No. 8, 2012, pp. 695-698. http://dx.doi.org/10.4169/amer.math.monthly.119.08.695
[5] P. Samuel, “Algebraic Theory of Numbers,” Kershaw, 1972.
[6] M. A. Bean, “Binary Forms, Hypergeometric Functions and the Schwarz-Christoffel Mapping Formula,” Transactions of the American Mathematical Society, Vol. 347, No. 12, 1995, pp. 4959-4983.
http://dx.doi.org/10.1090/S0002-9947-1995-1307999-2

  
comments powered by Disqus

Copyright © 2019 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.