Back
 AM  Vol.4 No.10 , October 2013
Rational Equiangular Polygons
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.
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

 
 
Top