منابع مشابه
Protecting regular polygons
The minimum number of mutually non-overlapping congruent copies of a convex body K so that they can touch K and prevent any other congruent copy of K from touching K without overlapping each other is called the protecting number of K. In this paper we prove that the 1 2 Arnfried Kemnitz, LL aszll o Szabb o, Zoltt an Ujvv ary-Menyhh art protecting number of any regular polygon is three or four, ...
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In this paper, we study the symplectic volume of the moduli space of polygons by using Witten’s formula. We propose to use this volume as a measure for the flexibility of a polygon with fixed side-lengths. The main result of our is that among all the polygons with fixed perimeter in S or E the regular one is the most flexible and that among all the spherical polygons the regular one with side-l...
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This is an exposition of some results on classification of spherical polygons with prescribed interior angles and prescribed images of vertices under a conformal map onto the unit disk. MSC 2010: 30C20, 34M03.
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It is calculated the number of symmetric r-colorings of vertices of a regular n-gon and the number of equivalence classes of symmetric r-colorings [1, 2]. A coloring is symmetric if it is invariant in respect to some mirror symmetry with an axis crossing center of polygon and one of its vertices. Colorings are equivalent if we can get one from another by rotating about the polygon center.
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The full asymptotic expansion of the trace of the heat semi–group, tr(e−∆Ωt),where −∆Ω is the Dirichlet Laplace-Beltrami operator acting on L2(Ω) for geodesic spherical polygons Ω ⊂ S2, is derived in half–powers of t, and the coefficients determined explicitly. Let Ω be a non-empty open connected set in S = {x ∈ R : |x| = 1} with a piecewise geodesic boundary ∂Ω and interior angles γ1, · · · , ...
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 2019
ISSN: 0161-1712,1687-0425
DOI: 10.1155/2019/7148538