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.
Share and Cite:
Munteanu, M. and Munteanu, L. (2013) Rational Equiangular Polygons.
Applied Mathematics,
4, 1460-1465. doi:
10.4236/am.2013.410197.
Conflicts of Interest
The authors declare no conflicts of interest.
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
|