MAGIC SQUARES WITH ADDITIONAL PROPERTIES
By
Author
Presented To
Department of Mathematics
ABSTRACT
My final year project entitled ’Magic Squares with Additional Prop-
erties’ aims to research on one of the branches of mathematics which is
magic squares. Since magic squares have existed for a long time, there
are many interesting properties on magic squares that are found and yet to
be found. We shall learn about the history and origin of magic squares.
In addition, a magic square also has its uses that we can make use of.
By referring to some published materials, we can learn more about it and
therefore understand its properties better. For a magic square, the sum
of the row entries, column entries and entries of the main diagonals has
to be the same and therefore this constant sum is known as the magic
sum. With this property itself, it makes this magic square seems unique
and distinguished. And also in order to understand some other proper-
ties, the method of construction of magic squares must be known first.
With different methods to construct these magic squares of different order,
these properties can be identified throughout the way. These methods are
known and its construction are detailed and clear for someone with least
mathematical background to understand them. Not only that, there are
fairly many types of magic squares which are interesting enough to catch
anyone’s attention. Such special characteristics comprising of symmetric
properties to having broken diagonals in a square definitely made magic
squares a distinctive part of mathematics. Lastly, we will try to modify a
method of construction to produce magic squares as well.
TABLE OF CONTENTS
TITLE i
DECLARATION OF ORIGINALITY ii
ACKNOWLEDGEMENTS vii
ABSTRACT viii
LIST OF FIGURES x
CHAPTER 1 Introduction 1
1-1 Background of Magic Squares . . . . . . . . . . . . . . . 1
1-2 Application of Magic Squares . . . . . . . . . . . . . . . 2
CHAPTER 2 Objectives and Planning 4
2-1 Project Scopes . . . . . . . . . . . . . . . . . . . . . . . 4
2-2 Planning . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2-2-1 Action plan for Project I . . . . . . . . . . . . . . 5
2-2-2 Action plan for Project II . . . . . . . . .
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