Numbers: Their Tales, Types, and Treasures.
Chapter 1: Numbers and Counting
1.5.COLLECTIONS OF OBJECTS, ELEMENTS IN A SET
1.6.THE BIJECTION PRINCIPLE AND THE COMPARISON OF SETS
1.8.CARDINAL AND ORDINAL NUMBERS
1.10.COUNTING BY THE ORDINAL PRINCIPLE
1.12.THE NUMERAL SYSTEM IN WRITING
Chapter 2: Numbers and Psychology
2.1.CORE KNOWLEDGE OF THE WORLD
2.2.OUR BUILT-IN OBJECT-TRACKING SYSTEM
2.3.THE APPROXIMATE-NUMBER SYSTEM
2.4.GOING BEYOND THE CORE SYSTEMS
2.6.LOGICAL FOUNDATIONS FIRST?
2.9.IDIOSYNCRASIES OF LANGUAGES
Chapter 3: Numbers in History
3.1.NUMBERS IN BABYLON—THE FIRST PLACE-VALUE SYSTEM IN HISTORY
3.2.NUMBERS IN EGYPT—THE FIRST DECIMAL SYSTEM IN HISTORY
3.5.THE CHINESE PLACE-VALUE NOTATION
3.7.SYMBOLIC NUMBER NOTATION AND THE ABACUS IN INDIA
3.8.THE SLOW RECEPTION OF THE HINDU-ARABIC SYSTEM IN EUROPE
Chapter 4: Discovering Properties of Numbers
4.2.PYTHAGOREAN PHILOSOPHY OF NUMBERS
4.4.RECTANGULAR AND SQUARE NUMBERS
4.6.TRIANGULAR AND RECTANGULAR
Chapter 5: Counting for Poets
5.1.VERSE METRIC—THE ROLE OF RHYTHM
5.3.THE PROBLEM OF COUNTING METRIC PATTERNS
5.4.SOLVING PINGALA'S FIRST COUNTING PROBLEM IN SPECIAL CASES
5.5.A GENERAL SOLUTION TO PINGALA'S FIRST PROBLEM
5.6.DISCOVERING COMMON TRAITS OF COUNTING PROBLEMS
5.7.THE ART OF COUNTING SYLLABLES
5.9.SOLVING PINGALA'S THIRD PROBLEM
5.10.THE PASCAL TRIANGLE AND PINGALA'S PROBLEMS
5.11.LOTTERY GAMES AND OTHER AMUSEMENTS
Chapter 6: Number Explorations
6.1.THE FIBONACCI NUMBERS IN EUROPE
6.3.MORE ABOUT THE PASCAL TRIANGLE
Chapter 7: Placement of Numbers
7.2.GENERAL PROPERTIES OF MAGIC SQUARES
7.3.HOW TO CONSTRUCT A DOUBLY-EVEN MAGIC SQUARE
7.4.CONSTRUCTION OF A MAGIC SQUARE OF ORDER 3
7.5.CONSTRUCTING ODD-ORDER MAGIC SQUARES
7.6.CREATING SINGLY-EVEN MAGIC SQUARES
Chapter 8: Special Numbers
Chapter 9: Number Relationships
9.1.BEAUTIFUL NUMBER RELATIONSHIPS
9.3.OTHER TYPES OF AMICABILITY
9.4.PYTHAGOREAN TRIPLES AND THEIR PROPERTIES
9.5.FIBONACCI'S METHOD FOR FINDING PYTHAGOREAN TRIPLES
9.6.STIFEL'S METHOD FOR GENERATING PRIMITIVE PYTHAGOREAN TRIPLES
9.7.EUCLID'S METHOD FOR FINDING PYTHAGOREAN TRIPLES
9.8.EXPLORING PYTHAGOREAN TRIPLES
9.9.CONSECUTIVE MEMBERS OF A PYTHAGOREAN TRIPLE
9.10.SOME OTHER PYTHAGOREAN CURIOSITIES
Chapter 10: Numbers and Proportions
10.3.EUCLID'S ALGORITHM AND CONTINUED FRACTIONS
10.4.CREATING RECTANGLES FROM SQUARES
10.9.FAMOUS NUMBERS IN THE GREAT PYRAMID
10.11.THE HISTORICAL EXPLANATION
Chapter 11: Numbers and Philosophy
11.1.NUMBERS—INVENTED OR DISCOVERED?
11.2.THE PLATONIC POINT OF VIEW
11.4.PHILOSOPHY OF MATHEMATICS
11.5.THE LOGICIST DEFINITION OF A CARDINAL NUMBER
11.6.A FORMALIST'S DEFINITION OF NUMBER
11.7.THE STRUCTURALIST'S POINT OF VIEW
11.8.THE UNREASONABLE EFFECTIVENESS OF MATHEMATICS
11.10.LIMITS OF THE MODEL OF NATURAL NUMBERS
11.11.THE PROBLEM WITH REALLY HUGE NUMBERS
Appendix: Tables
A.1. TABLE OF FIBONACCI NUMBERS
A.2. TABLE OF THE FIRST PRIME NUMBERS UNDER 10,000
A.3. TABLE OF ALL KNOWN MERSENNE PRIMES
A.4. TABLE OF ALL KNOWN PERFECT NUMBERS
A.5. TABLE OF KAPREKAR NUMBERS
A.6. TABLE OF ARMSTRONG NUMBERS
A.7. TABLE OF AMICABLE NUMBERS
A.8. PYTHAGOREAN TRIPLES WITH A PAIR OF PALINDROMIC NUMBERS