Affiliation:
1. 1 Cornell University Ithaca Department of Mathematics Malott Hall, Room 433 NY 14853 USA
2. 2 Eötvös University Institute of Mathematics Pázmány Péter sétány 1/C H-1117 Budapest Hungary
Abstract
A bicycle (
n
,
k
)-gon is an equilateral
n
-gon whose
k
-diagonals are equal. S. Tabach-nikov proved that a regular
n
-gon is first-order flexible as a bicycle (
n
,
k
)-gon if and only if there is an integer 2 ≦
r
≦
n
-2 such that tan (π/
n
) tan (
kr
π/
n
) = tan (
k
π/
n
) tan (
r
π/
n
). In the present paper, we solve this trigonometric diophantine equation. In particular, we describe the family of first order flexible regular bicycle polygons.
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