HKUST Library Institutional Repository Banner

HKUST Institutional Repository >
Mathematics >
MATH Master Theses  >

Please use this identifier to cite or link to this item:
Title: Local approaches to the isoperimetric problem for octahedra
Authors: Dai, Shouxin
Issue Date: 2001
Abstract: In this thesis, we study the isoperimetric problem for octahedra. By Lindelof-Minkowski's theorem, we can reduce our problem to the study of circumscribing octahedra of a sphere. Using a volume formula by Hsiang for tangent polyhedron, we obtain a gradient formula and a formula of quadratic form for the volume function of octahedra. By applying these two formulae in mathematica, we obtain a local minimum of the volume function with precision of 10[supersprite -8]. In Chapter 1, we introduce the isoperimetric problem, including a short history, the solved and unsolved problems. Then we discuss how to reduce our problem to the cases of circumscribing polyhedra. Finally we introduce the concept of spherical configuration. In Chapter 2, we introduce a clean-cut volume formula for tangent polyhedra, and some of its applications. In Chapter 3, we derive a gradient formula and a formula for quadratic form of the volume function. Then we describe a concise method for determinating a local minimum of the volume function. In Chapter 4, we give discussions and future works.
Description: Thesis (M.Phil.)--Hong Kong University of Science and Technology, 2001
vii, 47 leaves : ill. ; 30 cm
HKUST Call Number: Thesis MATH 2001 Dai
Appears in Collections:MATH Master Theses

Files in This Item:

File Description SizeFormat

All items in this Repository are protected by copyright, with all rights reserved.