Infinite Paths with No Small Angles
نویسنده
چکیده
It is shown here that given a discrete (and infinite) set of points in the plane, it is possible to arrange them on a polygonal path so that every angle on the polygonal path is at least 9. This has been known to hold for finite sets (with 20). The main result holds for discrete sets in higher dimensions as well, with a smaller bound on the angle. §
منابع مشابه
Investigation and Simulation of the Effects of Dispersion and Transmittance angles on the Solar Cells Quantum Efficiency
In this paper the effects of transmittance, dispersion angle and diffusion length on the quantum efficiency of solar cells (QESC) have been simulated and investigated. Optical path technic is used for simulation. The results show that base thickness, diffusion length, dispersion angle, number of optical confinement path and transmission angles have an extremely effects on the QESC. Simulation r...
متن کاملThe choice of arboreal escape paths and its consequences for the locomotor behaviour of four species of Anolis lizards
The direction and speed of escape locomotion can affect the ability of an animal to evade a predator, and variation in habitat structure often affects speed. Consequently, the escape paths chosen by animals may affect their performance and subsequent survival. Arboreal locomotion is well suited for gaining insight into the choice of escape routes because of the discrete paths formed by branches...
متن کاملCompact compatible topologies for graphs with small cycles
A topology τ on the vertices of a comparability graph G is said to be compatible with G if each subgraph H of G is graph-connected if and only if it is a connected subspace of (G,τ). In two previous papers we considered the problem of finding compatible topologies for a given comparability graph and we proved that the nonexistence of infinite paths was a necessary and sufficient condition for t...
متن کاملQuasi-fuchsian Manifolds with Particles
We consider 3-dimensional hyperbolic cone-manifolds which are “convex cocompact” in a natural sense, with cone singularities along infinite lines. Such singularities are sometimes used by physicists as models for massive spinless point particles. We prove an infinitesimal rigidity statement when the angles around the singular lines are less than π: any infinitesimal deformation changes either t...
متن کاملA Wavelet-based Approach for Ball Grid Array (BGA) Substrate Conduct Paths Inspection
The aim of this paper is to locate the boundary defects such as open, short, mousebite, and spur on Ball Grid Array (BGA) substrate conduct paths using machine vision. The 2-D boundaries of BGA substrate conduct paths are initially represented by the 1-D tangent angles. The tangent angles are evaluated from the covariance matrix eigenvector over a region of support on a boundary segment. Bounda...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009