Outer billiards outisde regular polygons: a hand case

2022 ◽  
Vol 86 (3) ◽  
Author(s):  
Philip Dmitrievich Rukhovich
Keyword(s):  
Regular Polygons ◽  
Outer Billiards

scholarly journals Outer billiards with contraction: regular polygons

2017 ◽  
Vol 33 (4) ◽  
pp. 565-580
Author(s):  
In-Jee Jeong
Keyword(s):  
Regular Polygons ◽  
Outer Billiards

Dense Periodic Packings of Regular Polygons

1995 ◽  
Vol 5 (12) ◽  
pp. 1539-1550 ◽  
Author(s):  
Y. Limon Duparcmeur ◽  
A. Gervois ◽  
J. P. Troadec
Keyword(s):  
Regular Polygons

Random Close Packings of Regular Polygons

1997 ◽  
Vol 7 (10) ◽  
pp. 1181-1189 ◽  
Author(s):  
Y. Limon Duparcmeur ◽  
J. P. Troadec ◽  
A. Gervois
Keyword(s):  
Regular Polygons

New Theorems for Moments of Inertia

1993 ◽  
Vol 21 (4) ◽  
pp. 355-366 ◽  
Author(s):  
David L. Wallach
Keyword(s):  
Regular Polygon ◽  
Moment Of Inertia ◽  
Regular Polygons ◽  
Centre Of Mass ◽  
Moments Of Inertia ◽  
The Moment

The moment of inertia of a plane lamina about any axis not in this plane can be easily calculated if the moments of inertia about two mutually perpendicular axes in the plane are known. Then one can conclude that the moments of inertia of regular polygons and polyhedra have symmetry about a line or point, respectively, about their centres of mass. Furthermore, the moment of inertia about the apex of a right pyramid with a regular polygon base is dependent only on the angle the axis makes with the altitude. From this last statement, the calculation of the centre of mass moments of inertia of polyhedra becomes very easy.

94.34 Regular polygons with integer coordinates

2010 ◽  
Vol 94 (531) ◽  
pp. 495-498 ◽  
Author(s):  
Jeremy D. King
Keyword(s):  
Regular Polygons

scholarly journals RIBBONLENGTH OF TORUS KNOTS

2008 ◽  
Vol 17 (01) ◽  
pp. 13-23 ◽  
Author(s):  
BROOKE KENNEDY ◽  
THOMAS W. MATTMAN ◽  
ROBERTO RAYA ◽  
DAN TATING
Keyword(s):  
Crossing Number ◽  
Regular Polygons ◽  
Torus Knots ◽  
Torus Knot

Using Kauffman's model of flat knotted ribbons, we demonstrate how all regular polygons of at least seven sides can be realized by ribbon constructions of torus knots. We calculate length to width ratios for these constructions thereby bounding the Ribbonlength of the knots. In particular, we give evidence that the closed (respectively, truncation) Ribbonlength of a (q + 1,q) torus knot is (2q + 1) cot (π/(2q + 1)) (respectively, 2q cot (π/(2q + 1))). Using these calculations, we provide the bounds c1 ≤ 2/π and c2 ≥ 5/3 cot π/5 for the constants c1 and c2 that relate Ribbonlength R(K) and crossing number C(K) in a conjecture of Kusner: c1 C(K) ≤ R(K) ≤ c2 C(K).

scholarly journals Dihedral F-Tilings of the Sphere by Equilateral and Scalene Triangles - II

10.37236/815 ◽  
2008 ◽  
Vol 15 (1) ◽  
Author(s):  
A. M. d'Azevedo Breda ◽  
Patrícia S. Ribeiro ◽  
Altino F. Santos
Keyword(s):  
Equilateral Triangle ◽  
Isosceles Triangle ◽  
Subsequent Paper ◽  
Euclidean Sphere ◽  
Regular Polygons ◽  
Combinatorial Description ◽  
Equilateral Triangles

The study of dihedral f-tilings of the Euclidean sphere $S^2$ by triangles and $r$-sided regular polygons was initiated in 2004 where the case $r=4$ was considered [5]. In a subsequent paper [1], the study of all spherical f-tilings by triangles and $r$-sided regular polygons, for any $r\ge 5$, was described. Later on, in [3], the classification of all f-tilings of $S^2$ whose prototiles are an equilateral triangle and an isosceles triangle is obtained. The algebraic and combinatorial description of spherical f-tilings by equilateral triangles and scalene triangles of angles $\beta$, $\gamma$ and $\delta$ $(\beta>\gamma>\delta)$ whose edge adjacency is performed by the side opposite to $\beta$ was done in [4]. In this paper we extend these results considering the edge adjacency performed by the side opposite to $\delta$.

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