Softcover ISBN:  9781470443986 
Product Code:  CLRM/55 
List Price:  $59.00 
MAA Member Price:  $44.25 
AMS Member Price:  $44.25 
eBook ISBN:  9781470448462 
Product Code:  CLRM/55.E 
List Price:  $55.00 
MAA Member Price:  $41.25 
AMS Member Price:  $41.25 
Softcover ISBN:  9781470443986 
eBook: ISBN:  9781470448462 
Product Code:  CLRM/55.B 
List Price:  $114.00 $86.50 
MAA Member Price:  $85.50 $64.88 
AMS Member Price:  $85.50 $64.88 
Softcover ISBN:  9781470443986 
Product Code:  CLRM/55 
List Price:  $59.00 
MAA Member Price:  $44.25 
AMS Member Price:  $44.25 
eBook ISBN:  9781470448462 
Product Code:  CLRM/55.E 
List Price:  $55.00 
MAA Member Price:  $41.25 
AMS Member Price:  $41.25 
Softcover ISBN:  9781470443986 
eBook ISBN:  9781470448462 
Product Code:  CLRM/55.B 
List Price:  $114.00 $86.50 
MAA Member Price:  $85.50 $64.88 
AMS Member Price:  $85.50 $64.88 

Book DetailsClassroom Resource MaterialsVolume: 55; 2018; 153 ppMSC: Primary 11
Nuggets of Number Theory will attract fans of visual thinking, number theory, and surprising connections. This book contains hundreds of visual explanations of results from elementary number theory. Figurate numbers and Pythagorean triples feature prominently, of course, but there are also proofs of Fermat's Little and Wilson's Theorems. Fibonacci and perfect numbers, Pell's equation, and continued fractions all find visual representation in this charming collection. It will be a rich source of visual inspiration for anyone teaching, or learning, number theory and will provide endless pleasure to those interested in looking at number theory with new eyes. Author Roger Nelsen is a longtime contributor of “Proofs Without Words” in the MAA's Mathematics Magazine and College Mathematics Journal. This is his twelfth book with MAA Press.
ReadershipUndergraduate students, high school students, and teachers interested in number theory and visualization.

Table of Contents

Chapters

Chapter 1. Figurate numbers

Chapter 2. Congruence

Chapter 3. Diophantine equations

Chapter 4, Pythagorean triples

Chapter 5. Irrational numbers

Chapter 6. Fibonacci and Lucas numbers

Chapter 7. Perfect numbers

Solutions to the exercises


Additional Material

Reviews

The starting point for this book was the author's observation that many number theory texts contain few figures. He wrote an article for Math Horizons in 2008 that showed ways to use figures (the article was reprinted in the book "Biscuits of Number Theory"), and eventually expanded it to the present book. The book starts out with figurate numbers (squares, triangular numbers, etc.) that have an obvious picture, but quickly moves to other areas that we usually don't think of visually. This is not a complete introduction to number theory, but it does cover a good sampling, with something about congruences, Diophantine equations, irrational numbers, perfect numbers, and Fibonacci numbers.
Allen Stenger, MAA Reviews


RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Additional Material
 Reviews
 Requests
Nuggets of Number Theory will attract fans of visual thinking, number theory, and surprising connections. This book contains hundreds of visual explanations of results from elementary number theory. Figurate numbers and Pythagorean triples feature prominently, of course, but there are also proofs of Fermat's Little and Wilson's Theorems. Fibonacci and perfect numbers, Pell's equation, and continued fractions all find visual representation in this charming collection. It will be a rich source of visual inspiration for anyone teaching, or learning, number theory and will provide endless pleasure to those interested in looking at number theory with new eyes. Author Roger Nelsen is a longtime contributor of “Proofs Without Words” in the MAA's Mathematics Magazine and College Mathematics Journal. This is his twelfth book with MAA Press.
Undergraduate students, high school students, and teachers interested in number theory and visualization.

Chapters

Chapter 1. Figurate numbers

Chapter 2. Congruence

Chapter 3. Diophantine equations

Chapter 4, Pythagorean triples

Chapter 5. Irrational numbers

Chapter 6. Fibonacci and Lucas numbers

Chapter 7. Perfect numbers

Solutions to the exercises

The starting point for this book was the author's observation that many number theory texts contain few figures. He wrote an article for Math Horizons in 2008 that showed ways to use figures (the article was reprinted in the book "Biscuits of Number Theory"), and eventually expanded it to the present book. The book starts out with figurate numbers (squares, triangular numbers, etc.) that have an obvious picture, but quickly moves to other areas that we usually don't think of visually. This is not a complete introduction to number theory, but it does cover a good sampling, with something about congruences, Diophantine equations, irrational numbers, perfect numbers, and Fibonacci numbers.
Allen Stenger, MAA Reviews