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Dido's problem : the lattice version
Author
Lim, Gek Huey
Supervisor
Awyong, Poh Wah
Abstract
In this thesis, we solve a lattice version of the classical isoperimetric problem, otherwise called Dido's problem. The problem is to find the shape of the figure with the largest area and the value of the area, given that the figure must enclose only one lattice point and is symmetric about it.
This problem was solved by Arkinstall and Scott (1979) and Croft (1979) simultaneously. We reconstruct the proofs by Arkinstall and Scott (1979) in this thesis.
In Chapter 1, the notations and definitions that will be used in the subsequent sections and chapters will be given. In Chapter 2, we describe a method and a result that will be used in solving the problem. Chapter 3 contains the solution to the problem and a corollary to the main result. The corollary in fact confirms a conjecture by Scott (1974). Finally in Chapter 4, we consider the extensions and generalisations for the area-perimeter problem.
This problem was solved by Arkinstall and Scott (1979) and Croft (1979) simultaneously. We reconstruct the proofs by Arkinstall and Scott (1979) in this thesis.
In Chapter 1, the notations and definitions that will be used in the subsequent sections and chapters will be given. In Chapter 2, we describe a method and a result that will be used in solving the problem. Chapter 3 contains the solution to the problem and a corollary to the main result. The corollary in fact confirms a conjecture by Scott (1974). Finally in Chapter 4, we consider the extensions and generalisations for the area-perimeter problem.
Date Issued
1999
Call Number
QA171.5 Lim
Date Submitted
1999