Isoperimetric Triangular Enclosure with a Fixed Angle
نویسندگان
چکیده
Given a set S of n > 2 points in the plane (in general position), we show how to compute in O(n) time, a triangle T with maximum (or minimum) area enclosing S among all enclosing triangles with fixed perimeter P and one fixed angle ω. We show that a similar approach can be used to compute a triangle T with maximum (or minimum) perimeter enclosing S among all enclosing triangles with fixed area A and one fixed angle ω.
منابع مشابه
MHD Natural Convection and Entropy Generation of Variable Properties Nanofluid in a Triangular Enclosure
Natural convection heat transfer has many applications in different fields of industry; such as cooling industries, electronic transformer devices and ventilation equipment; due to simple process, economic advantage, low noise and renewed retrieval. Recently, heat transfer of nanofluids have been considered because of higher thermal conductivity coefficient compared with those of ordinary fluid...
متن کاملAn Isoperimetric Theorem in Plane Geometry
An isoperimetric theorem in plane geometry Alan Siegel1 COURANT INSTITUTE OF MATHEMATICAL SCIENCES NEW YORK UNIVERSITY New York Abstract Let be a simple polygon. Let the vertices of be mapped, according to a counterclockwise traversal of the boundary, into a strictly increasing sequence of real numbers in . Let a ray be drawn from each vertex so that the angle formed by the ray and a horizontal...
متن کاملConvection in a Tilted Square Enclosure with Various Boundary Conditions and Having Heat Generating Solid Body at its Center
In this study free convection flow and heat transfer of a fluid inside a tilted square enclosure having heat conducting and generating solid body positioned in the center of the enclosure with various thermal boundary conditions has been investigated numerically. The governing equations are transformed into non-dimensional form and the resulting partial differential equations are solved by Fini...
متن کاملNumerical investigation of natural convection phenomena in uniformly heated trapezoidal Cylinder inside an elliptical Enclosure
A numerical study of the natural convection of the laminar heat transfers in the stationary state was developed in a horizontal ring and compared between a heated trapezoidal internal cylinder and a cold elliptical outer cylinder. This annular space is traversed by a Newtonian and incompressible fluid. The Prandtl number is set to 0.7 (air case) for different Rayleigh numbers. The system of equ...
متن کاملThread-wire surfaces: Near-wire minimizers and topological finiteness
Alt’s thread problem asks for least-area surfaces bounding a fixed “wire” curve and a movable “thread” curve of length L. We conjecture that if the wire has finitely many maxima of curvature, then its Alt minimizers have finitely many surface components. We show that this conjecture reduces to controlling near-wire minimizers, and thus begin a three paper series to understand them. In this pape...
متن کامل