cover -- copyright page -- title page -- Contents -- Preface -- Imaginative Words -- Lemniscate -- Centillion -- Golden Ratio -- Borromean Rings -- Sieve of Eratosthenes -- Transversal of Primes -- Waterfall of Primes -- Squares, Triangular Numbers, and Cubes -- Determinant -- Complex Plane -- Intriguing Images -- Square Pyramidal Square Number -- Binary Trees -- Bulging Hyperspheres -- Projective Plane -- Two-Colored Graph -- Hypercube -- Full Adder -- Sierpi0ntoto 0"13nski's Triangle -- Squaring Map -- Riemann Sphere -- Captivating Formulas -- Arithmetical Wonders -- Heron's Formula and Heronian Triangles -- Sine, Cosine, and Exponential Function Expansions -- Tangent and Secant Function Expansions -- Series for Pi -- Product for Pi -- Fibonacci Numbers and Pi -- Volume of a Ball -- Euler's Integral Formula -- Euler's Polyhedral Formula -- The Smallest Taxicab Number -- Infinity and Infinity Squared -- Complex Functions -- The Zeta Function and Bernoulli Numbers -- The Riemann Zeta Function -- The Jacobi Identity -- Entropy -- Rook Paths -- Delightful Theorems -- A Square inside Every Triangle -- Morley's Theorem -- The Euler Line -- Monge's Theorem -- Power Means -- Regular Heptagon -- Isometries of the Plane -- Symmetries of Regular Convex Polyhedra -- Polynomial Symmetries -- Kings and Serfs -- The Erd0ototo 0"7Dos--Szekeres Theorem -- Minkowski's Theorem -- Lagrange's Theorem -- Van der Waerden's Theorem -- Latin Squares and Projective Planes -- The Lemniscate Revisited -- Pleasing Proofs -- The Pythagorean Theorem -- The Erd0ototo 0"7Dos--Mordell Inequality -- Triangles with Given Area and Perimeter -- A Property of the Directrix of a Parabola -- A Classic Integral -- Integer Partitions -- Integer Triangles -- Triangle Destruction -- Squares in Arithmetic Progression -- Random Hemispheres -- Odd Binomial Coefficients.

Frobenius' Postage Stamp Problem -- Perrin's Sequence -- On the Number of Partial Orders -- Perfect Error-Correcting Codes -- Binomial Coefficient Magic -- A Group of Operations -- Elegant Solutions -- A Tetrahedron and Four Spheres -- Alphabet Cubes -- A Triangle in an Ellipse -- About the Roots of a Cubic -- Distance on Planet X -- A Tilted Circle -- The Millionth Fibonacci Number -- The End of a Conjecture -- A Zero-Sum Game -- An Expected Maximum -- Walks on a Graph -- Rotations of a Grid -- Stamp Rolls -- Making a Million -- Coloring a Projective Plane -- Creative Problems -- Two-Dimensional Gobbling Algorithm -- Nonattacking Queens Game -- Lucas Numbers Mod m -- Exact Colorings of Graphs -- Queen Paths -- Transversal Achievement Game -- Binary Matrix Game -- Harmonious Foundations -- Sets -- Relations -- Functions -- Groups -- Fields -- Vector Spaces -- Eye-Opening Explorations -- Problems -- Solutions -- Bibliography -- Index -- About the Author.