Results 1 to 10 of about 159,907 (343)
Outer billiard outside regular polygons [PDF]
Journal of the London Mathematical Society, 2011. Number 83 volume
2, 301-323, 2009 We consider outer billiard outside regular convex polygons. We deal with the case of regular polygons with $\{3,4,5,6,10\}$ sides, and we describe the symbolic dynamics of the map and compute the complexity of the language.
Nicolas Bédaride, Julien Cassaigne
arxiv +10 more sources
Formation of a 3D Particle Array Actuated by Ultrasonic Traveling Waves in a Regular Polygon Resonator [PDF]
Micromachines, 2022 Acoustic radiation forces have been extensively studied regarding static particles, cell patterning, and dynamic transportation. Compared with standing wave manipulation, traveling wave manipulation can be more easily modulated in real time and has no ...
Fei Wan +7 more
doaj +2 more sources
An inequality for regular near polygons [PDF]
European Journal of Combinatorics, 2003 Let $G$ denote a near-polygon distance-regular graph with diameter $d\geq 3$, valency $k$ and intersection numbers $a_1>0$, $c_2>1$. Let $ _1$ denote the second largest eigenvalue for the adjacency matrix of $G$. We show $ _1$ is at most $(k-a_1-c_2)/(c_2-1)$. We show the following are equivalent: (i) Equality is attained above; (ii) $G$ is $Q$-
Paul Terwilliger, Chih-wen Weng
openalex +4 more sources
Distance Distributions in Regular Polygons [PDF]
IEEE Transactions on Vehicular Technology, 2013 This paper derives the exact cumulative density function of the distance between a randomly located node and any arbitrary reference point inside a regular $\el$-sided polygon.
Salman Durrani +3 more
core +6 more sources
Buckling loads of columns of regular polygon cross-section with constant volume and clamped ends
Electronic Journal of Structural Engineering, 2002 A numerical method is developed for calculating the buckling loads of tapered columns of regular polygon cross-section with constant volume and both clamped ends. The linear, parabolic and sinusoidal tapers are considered in numerical examples. From the
Byoung Koo Lee, Sang Jin Oh, Guangfan Li
doaj +3 more sources
Ergodicity of polygonal slap maps [PDF]
, 2013 Polygonal slap maps are piecewise affine expanding maps of the interval obtained by projecting the sides of a polygon along their normals onto the perimeter of the polygon.
Del Magno, Gianluigi +3 more
core +4 more sources
Some contributions to Regular Polygons [PDF]
arXiv, 2016 The aim of this work is to use Napoleon's Theorem in different regular polygons, and decide whether we can prove Napoleon's Theorem is only limited with triangles or it could be done in other regular polygons that can create regular polygons.
ÖNCEL, Deniz, KİRİŞÇİ, Murat
arxiv +4 more sources
Examples, Counterexamples, and Enumeration Results for Foldings and Unfoldings between Polygons and Polytopes [PDF]
arXiv, 2000 We investigate how to make the surface of a convex polyhedron (a polytope) by folding up a polygon and gluing its perimeter shut, and the reverse process of cutting open a polytope and unfolding it to a polygon.
Demaine, Erik D. +3 more
core +4 more sources
Regular Polygonal Complexes in Space, I [PDF]
Transactions of the American Mathematical Society, 2009 A polygonal complex in euclidean 3-space is a discrete polyhedron-like structure with finite or infinite polygons as faces and finite graphs as vertex-figures, such that a fixed number r of faces surround each edge. It is said to be regular if its symmetry group is transitive on the flags.
Daniel Pellicer, Egon Schulte
openalex +7 more sources
Regular ternary polygonal forms [PDF]
The Ramanujan Journal, 2019 Inspired by Dickson's classification of regular ternary quadratic forms, we prove that there are no primitive regular $m$-gonal forms when $m$ is sufficiently large. In order to do so, we construct sequences of primes that are inert in a certain quadratic field and show that they satisfy a certain inequality bounding the next prime by the product of ...
Zilong He, Ben Kane
openalex +5 more sources