My Numbers, My Friends: Popular Lectures on Number Theory

ISBN-13: 9780387989112 / Angielski / Miękka / 2000 / 376 str.

Paulo Ribenboim

Opis

Dear Friends of Numbers: This little book is for you. It should o?er an exquisite int- lectual enjoyment, which only relatively few fortunate people can experience. May these essays stimulate your curiosity and lead you to books and articles where these matters are discussed at a more technical level. I warn you, however, that the problems treated, in spite of - ing easy to state, are for the most part very di?cult. Many are still unsolved. You will see how mathematicians have attacked these problems. Brains at work But do not blame me for sleepless nights (I have mine already). Several of the essays grew out of lectures given over the course of years on my customary errances. Other chapters could, but probably never will, become full-sized books. The diversity of topics shows the many guises numbers take to ? tantalize and to demand a mobility of spirit from you, my reader, who is already anxious to leave this preface. Now go to page 1 (or 127?). Paulo Ribenboim ? Tantalus, of Greek mythology, was punished by continual disappointment whenhetriedtoeatordrinkwhatwasplacedwithinhisreach. 1 The Fibonacci Numbers and the Arctic Ocean Introduction There is indeed not much relation between the Fibonacci numbers and the Arctic Ocean, but I thought that this title would excite your curiosity for my lecture. You will be disappointed if you wished to hear about the Arctic Ocean, as my topic will be the sequence of Fibonacci numbers and similar sequences.

Recenzje

"The exposition is relaxed, with plenty of numerical examples, conjectures and other asides. Technicalities are largely avoided, so that a beginning graduate student could read and enjoy this without preparation." (D.R.Heath-Brown, zbMATH 0947.11001, 2022)

From the reviews:

MATHEMATICAL REVIEWS

"...the author is extremely knowledgeable in his subjects and the reader can profit from the wealth of material contained in this book. Therefore this book is a welcome reference for anyone interested both in trivia and in serious background material about popular topics in elementary number theory."

Spis treści

The Fibonacci Numbers and the Arctic Ocean.- Representation of Real Numbers by Means of Fibonacci Numbers.- Prime Number Records.- Selling Primes.- Euler’s Famous Prime Generating Polynomial and the Class Number of Imaginary Quadratic Fields.- Gauss and the Class Number Problem.- Consecutive Powers.- 1093.- Powerless Facing Powers.- What Kind of Number Is $$ \sqrt 2 ^{\sqrt 2 } $$ ?.- Galimatias Arithmeticae.

O autorze

Paulo Ribenboim ist emeritierter Professor der kanadischen Queen's University, Fellow der Royal Society of Canada und Träger des George Pólya-Preises der Mathematical Association of America. Er ist Autor von 13 Büchern und über 150 Forschungsartikeln.