
Joy of Mathematics
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Content
- Cover
- Title Page
- Copyright Page
- CONTENTS
- INTRODUCTION
- CHAPTER 1: ARITHMETIC NOVELTIES
- When Is a Number Divisible by 3 or 9?
- When Is a Number Divisible by 11?
- Divisibility by Prime Numbers
- Squaring Numbers Quickly
- Squares and Sums
- Using Squares to Multiply Arbitrary Numbers
- An Alternative Method for Extracting a Square Root
- Sensible Number Comparisons
- Euclidean Algorithm to Find the GCD
- Sums of Positive Integers
- Sums of Odd Positive Integers
- The Realm of Nonterminating Decimals
- Atoms in the Universe of Numbers
- Fun with Number Relationships
- Friendly Numbers
- Palindromic Numbers
- Prime Numbers
- Infinite Primes
- The Neglected Triangular Numbers
- Perfect Numbers
- Making Mistaken Generalizations
- The Fibonacci Numbers
- CHAPTER 2: ALGEBRAIC EXPLANATIONS OF ACCEPTED CONCEPTS
- Simple Algebra Helps Logical Reasoning
- Division by Zero
- Irrationality of the Square Root of 2
- Bisection Method to Approximate Square Roots
- Continued Fractions of Square Roots
- Fermat's Method of Factoring
- Comparing Means
- Diophantine Equations
- Falling Squares
- Descartes's Rule of Signs
- Horner's Method to Evaluate Polynomials
- Generating Pythagorean Triples
- The Frobenius Problem
- CHAPTER 3: GEOMETRIC CURIOSITIES
- Parallelograms and Triangles
- Using a Grid to Calculate Areas
- The Center of a Quadrilateral
- Beyond the Formula for the Area of a Triangle
- Heronian Triangles
- A New Formula for the Area of Isosceles Triangles
- Pick's Theorem
- When Intersecting Lines Meet a Circle
- Origins of Trigonometry
- Sines of Small Angles
- An Unconventional View of the Sine
- Surprising Proofs of the Pythagorean Theorem
- Beyond the Pythagorean Theorem-Part I
- Beyond the Pythagorean Theorem-Part II
- Beyond the Pythagorean Theorem-Part III
- The Pythagorean Theorem Extended to Three Dimensions
- Polyhedra: Sides, Faces, and Vertices
- Lunes and the Right Triangle
- Concurrency
- Similarity and the Golden Ratio
- A Relation between Points and Circles
- Constructions with Compasses Alone
- The Sphere and the Cylinder
- Regular Polygons and Stars
- Platonic Solids and Star Polyhedra
- CHAPTER 4: PROBABILITY APPLIED TO EVERYDAY EXPERIENCES
- How the Theory of Probability Began
- Benford's Law
- The Birthday Phenomenon
- The Monty Hall Problem
- Bertrand's Box
- The False Positive Paradox
- Pascal's Triangle
- Random Walks
- The Poker Wild-Card Paradox
- CHAPTER 5: COMMON SENSE FROM A MATHEMATICAL PERSPECTIVE
- The Origins of Some Mathematics Symbols
- The Counterintuitive
- A Surprising Solution
- Don't "Wine" over This Problem-A Problem-Solving Approach
- Organized Thinking
- Successive Percentages
- Rule of 72
- A Mathematical Conjecture
- Unexpected Patterns
- An Infinity Conundrum
- The Concept of Infinity
- Counting the Uncountable
- Mathematics on a Bicycle
- The Parabola: A Remarkable Curve
- ACKNOWLEDGMENTS
- APPENDIX
- NOTES
- INDEX
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