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New Recreations with Magic Squares

William H. Benson

New Recreations with Magic Squares - William H. Benson
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Flaptekst

William H. Benson is a leading researcher on magic squares, well-known in recreational math circles, and Oswald Jacoby is a well-known writer on games in books and newspapers. Together they have compiled what is probably the best book ever done on magic squares. Covering the fundamental aspects of the subject and offering much new material and many new methods, this book presents a wide range of material that will challenge the resourcefulness of interested laymen, puzzlers, and mathematicians.

The book is divided into four parts. Part I presents the simplest possible methods for constructing magic squares of various orders and types, including doubly-even-order, odd-order, and singly-even-order magic squares. Part II develops methods for constructing squares that are magic as well as possessing additional properties that can be predicted in advance. Here, the authors offer the first cyclical method for constructing magic squares that is applicable to both odd-order and even-order squares. Other topics covered include bimagic and trimagic squares, and irregular and noncyclical pandiagonal magic squares.

Part III enumerates the generation of magic squares that are possible for third-order, fourth-order, and fifth-order pandiagonal magic squares, plus pandiagonal magic squares of the nth order — n a prime number. Part IV gives mathematical proofs of the various methods. An appendix contains all 880 fourth-order magic squares in tabular form.

Practically all of the contents of this book can be easily understood by anyone with high-school algebra. Persons with no previous experience with magic squares will find this book, and this field, thoroughly enjoyable, while ardent magic-square enthusiasts will discover much interesting and entirely original material.

Specificaties

ISBN9780486232362
TaalEngels
Aantal pagina's198
UitgeverijDover Publications
Publicatiedatum1976

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