Cover -- Copyright -- Title Page -- Dedication -- Contents -- Introduction -- Newsletters and Commentaries -- 1. Arctangents -- 2. Benford's Law -- 3. Braids -- 4. CLIP Theory -- 5. Dots and Dashes -- 6. Factor Trees -- 7. Folding Fractions and Conics -- 8. Folding Patterns and Dragons -- 9. Folding and Pouring -- 10. Fractions -- 11. Integer Triangles -- 12. Lattice Polygons -- 13. Layered Tilings -- 14. The Middle of a Triangle -- 15. Partitions -- 16. Personalized Polynomials -- 17. Playing with Pi -- 18. Pythagoras's Theorem -- 19. On Reflection -- 20. Repunits and Primes -- 21. The Stern-Brocot Tree -- 22. Tessellations -- 23. Theon's Ladder and Squangular Numbers -- 24. Tilings and Theorems -- 25. The Tower of Hanoi -- 26. Weird Multiplication -- Appendices -- I: Numbers that are the Sum of Two Squares -- II: Pick's Theorem -- III: The Möbius Function -- IV: The Borsuk-Ulam Theorem -- V: The Galilean Ratios -- VI: A Candy-Sharing Game -- VII: Bending Buffon's Needle -- VIII: On Separating Dots -- Indexes -- Index of Topics -- Classic Theorems Proved -- About the Author.