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This is a book which will serve as a source both of recreation and instruction. It is not in any way intended to be used as a textbook, yet it will provide invaluable supporting reading to students and others who wish to Know something more of the background to the bare processes demonstrated in textbooks. Numbers are the concern of everybody in everyday affairs and it is for this reason that the book is designed for the general public as well as for the professional and amateur mathematicians. It sets out to show in a simple form the ways in which numbers or groups of numbers are related to each other; how they may be expressed in terms of each other; and the general nature of number behaviour in varying circumstances. The greater part of this work is concerned with the fundamental and less abstruse aspects of number theory and assumes little more than an elementary knowledge of mathematics. At the same time it contains much of stimulating interest to the trained mathematician. A great deal of information has been collated and brought together into one volume for the first time. In particular, the chapters on Digital Roots and Recurring Decimals represent the first attempt to deal with the subject matter on any reasonable scale, and there is a suggested new method for testing primality which, while itself complicated, may point the way for further developments. In addition to the strictly scientific contents, some lighter relief is provided by chapters on Magic Squares, Number peculiarities, pseudo-telepathy and mathematical recreations, and the whole is a work which should awaken a lively interest in the average reader and delight those who like to dabble in numbers.

This is a book which will serve as a source both of recreation and instruction. It is not in any way intended to be used as a textbook, yet it will provide invaluable supporting reading to students and others who wish to Know something more of the background to the bare processes demonstrated in textbooks. Numbers are the concern of everybody in everyday affairs and it is for this reason that the book is designed for the general public as well as for the professional and amateur mathematicians. It sets out to show in a simple form the ways in which numbers or groups of numbers are related to each other; how they may be expressed in terms of each other; and the general nature of number behaviour in varying circumstances. The greater part of this work is concerned with the fundamental and less abstruse aspects of number theory and assumes little more than an elementary knowledge of mathematics. At the same time it contains much of stimulating interest to the trained mathematician. A great deal of information has been collated and brought together into one volume for the first time. In particular, the chapters on Digital Roots and Recurring Decimals represent the first attempt to deal with the subject matter on any reasonable scale, and there is a suggested new method for testing primality which, while itself complicated, may point the way for further developments. In addition to the strictly scientific contents, some lighter relief is provided by chapters on Magic Squares, Number peculiarities, pseudo-telepathy and mathematical recreations, and the whole is a work which should awaken a lively interest in the average reader and delight those who like to dabble in numbers.

This is a book which will serve as a source both of recreation and instruction. It is not in any way intended to be used as a textbook, yet it will provide invaluable supporting reading to students and others who wish to Know something more of the background to the bare processes demonstrated in textbooks. Numbers are the concern of everybody in everyday affairs and it is for this reason that the book is designed for the general public as well as for the professional and amateur mathematicians. It sets out to show in a simple form the ways in which numbers or groups of numbers are related to each other; how they may be expressed in terms of each other; and the general nature of number behaviour in varying circumstances. The greater part of this work is concerned with the fundamental and less abstruse aspects of number theory and assumes little more than an elementary knowledge of mathematics. At the same time it contains much of stimulating interest to the trained mathematician. A great deal of information has been collated and brought together into one volume for the first time. In particular, the chapters on Digital Roots and Recurring Decimals represent the first attempt to deal with the subject matter on any reasonable scale, and there is a suggested new method for testing primality which, while itself complicated, may point the way for further developments. In addition to the strictly scientific contents, some lighter relief is provided by chapters on Magic Squares, Number peculiarities, pseudo-telepathy and mathematical recreations, and the whole is a work which should awaken a lively interest in the average reader and delight those who like to dabble in numbers.