Classification of First-order Flexible Regular Bicycle Polygons
نویسندگان
چکیده
A bicycle (n, k)-gon is an equilateral n-gon whose k-diagonals are equal. S. Tabachnikov 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(krπ/n) = tan(kπ/n) tan(rπ/n). In the present paper, we solve this trigonometric diophantine equation. In particular, we describe the family of first order flexible regular bicycle polygons.
منابع مشابه
On the rigidity of regular bicycle (n, k)-gons
Bicycle (n, k)-gons are equilateral n-gons whose k-diagonals are equal. In this paper, the order of infinitesimal flexibility of the regular n-gon within the family of bicycle (n, k)-gons is studied. An equation characterizing first order flexible regular bicycle (n, k)-gons were computed by S. Tabachnikov in [7]. This equation was solved by R. Connelly and the author in [3]. S. Tabachnikov has...
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