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The Average Distance betreen Two Points of a Convex Set

Author: GuanXiuJuan
Tutor: RenDeZuo
School: Wuhan University of Science and Technology
Course: Applied Mathematics
Keywords: Generalized support function Maximum chord length The average distance Semicircle domain Isosceles trapezoid domain
CLC: O186.5
Type: Master's thesis
Year: 2010
Downloads: 27
Quote: 0
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Abstract


In this paper, the concept of generalized support function , semicircle domain and isosceles trapezoid domain both symmetry is not very satisfactory convex domain between two points the average distance between the previous literature within two points of the Convex the general formula of the average distance , but did not give details of the derivation process after there have been many concrete results , but only for some of the more simple , good symmetry convex domain ( such as a square , equilateral triangle , rectangle , circle) the average distance between the the semicircle domains and the two points of an isosceles trapezoid domain studied in this paper is relatively more difficult , which is reflected in the regional classification , generalized support function and maximum chord length function method and the chord power integrals calculated . and discussion on the domain of an isosceles trapezoid , for there is no symmetry generally trapezoidal also applies to the average distance between the two points of the convex domain is a very important issue in integral geometry , geometry problems an important role in the average distance between two points of a convex domain has wide application background . generalized support functions and convex domain chord power integrals and maximum chord length function of the average distance between the two points of a convex domain , and arriving at the the average distance between two points of a convex domain general formula : ( ? ) (where F is the area of the convex set K ) where ( ? ) and use this formula calculated the average distance between the the semicircle domains and the isosceles trapezoid within two points .

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CLC: > Mathematical sciences and chemical > Mathematics > Geometry, topology > Differential geometry,integral geometry > Integral geometry
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