Nice Numbers
In this intriguing book, John Barnes takes us on a journey through aspects of numbers much as he took us on a geometrical journey in Gems of Geometry. Similarly originating from a series of lectures for adult students at Reading and Oxford University, thi
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Nice Numbers
Nice Numbers
John Barnes
Nice Numbers
John Barnes Caversham England
ISBN 978-3-319-46830-3 DOI 10.1007/978-3-319-46831-0
ISBN 978-3-319-46831-0
(eBook)
Library of Congress Control Number: 2016957844 © Springer International Publishing Switzerland 2016 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This book is published under the trade name Birkhäuser The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland (www.birkhauser-science.com)
To Bobby, Janet, Helen, Christopher and Jonathan
Preface This book is based on lectures given originally at Reading University and more recently at Oxford as part of the Continuing Education program of Oxford University in England. In a sense it is a sequel to Gems of Geometry (now in its second edition) and which is also based on lectures given at Reading and Oxford. Having given the geometry lectures a few times, it was suggested that I should develop another course based on aspects of numbers. I was extremely busy at the time updating my book on the Ada programming language so settled on a short course of just five lectures entitled Nice and Noughty (sic) Numbers. However, as the time approached I was still too busy and so the course was kindly given by Aruna Hardy. The next year, the pressure of life abated and I was able to gave a full ten lecture course. I have since given the course a number of times at both Reading and Oxford and the notes eventually matured into this book. The lectures divide into two kinds: some address the theme of simple number theoretic topics such as prime numbers and cryptography, whereas others address the theme of daily needs and pleasures such as keeping track of time and enjoying music. There are ten basic lectures. The first lecture is entitled Measures. Measuring and counting various things are fundamental human activities. In earlier times one might have been interested i
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