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| But First, a Word from our Sponsors | |
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| Welcome! | |
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| Surfing the Book | |
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| Fun and Games: An Introduction to Rigorous Thought | |
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| Silly Stories Each with a Moral | |
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| Conundrums that Evoke Techniques of Effective Thinking | |
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| Nudges | |
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| Leading Questions and Hints for Resolving the Stories | |
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| The Punch Lines | |
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| Solutions and Further Commentary | |
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| From Play to Power | |
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| Discovering Strategies of Thought for Life | |
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| Number Contemplation | |
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| Counting | |
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| How the Pigeonhole Principle Leads to Precision Through Estimation | |
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| Numberical Patterns in Nature | |
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| Discovering the Beauty of the Fibonacci Numbers | |
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| Prime Cuts of Numbers | |
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| How the Primes Numbers are the Building Blocks of All Natural Numbers | |
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| Crazy Clocks and Checking Out Bars | |
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| Cyclical Clock Arithmetic and Bar Codes | |
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| Public Secret Codes adn How to Become a Spy | |
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| Encrypting Information Using Modula Arithmetic and Primes | |
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| The Irrational Side of Numbers | |
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| Are There Numbers Beyond Fractions? | |
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| Get Real | |
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| The Point of Decimals and Pinpointing Numbers on the Real Line | |
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| Infinity | |
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| Beyond Numbers | |
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| What Does Infinity Mean? | |
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| Comparing the Infinite | |
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| Pairing Up Collections via a One-to-One Corerspondence | |
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| The Missing Member | |
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| Georg Cantor Answers: Are Some Infinities Larger Than Others? | |
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| Geometric Gems | |
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| Pythagoras and His Hypotenuse | |
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| How a Puzzle Leads to the Proof of one of the Gems of Mathematics | |
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| A View of an Art Gallery | |
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| Using Computational Geometry to Place Security Cameras in Musuems | |
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| The Sexiest Rectangle | |
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| Finding Aesthetics in Life, Art, and Math Through the Golden Rectangle | |
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| Soothing Symmetry and Spinning Pinwheels | |
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| Can a Floor be Tiled without any Repeating Pattern? | |
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| The Platonic Solids Turn Amorous | |
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| Discovering the Symmetry and Interconnections Among the Platonic Solds | |
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| The Shape of Reality? | |
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| How Straight Lines Can Bend in Non-Euclidean Geometries | |
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| The Fouther Dimension | |
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| Can You See It? | |
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| Contortions of Space | |
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| Rubger Sheet Geometry | |
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| Discovering the Topological Idea of Equivalence by Distortion | |
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| The Band That Wouldn't Stop Playing | |
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| Experimenting with the Mobius Band and Klein Bottle | |
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| Feeling Edgy? | |
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| Exploring Relationships Among Vertices, Edges, and Faces | |
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| Knots and Links | |
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| Untangling Ropes and Rings | |
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| Fixed Points, Hot Loops, and Rainy Days | |
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| How the Certainty of Fixed Points Implies Certain Weather Phenomena | |
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| Chaos and Fractals | |
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| Images | |
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| Viewing a Gallery of Fractals | |
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| The Dynamics of Change | |
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| Can Change be Modeled by Repeated Applications of Simple Processes? | |
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| The Infinitely Detailed Beuty of Fractals | |
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| How to Create Workds of Ifinite Intricacy THrough Repeated PRocesses | |
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| The Mysterious Art of Imaginary Fractals | |
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| Creating Juila and Mandelbrot Sets by Stepping Out in the Complex Plane | |
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| Predetermined Chase | |
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| How Repeated SImple Processes Result in Utter Chaos | |
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| Between Dimnsions | |
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| Can the Dimensions of Fractals Fall Through the Cracks? | |
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| Taming Uncertainty | |
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| Chance Surprises | |
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| Some Scenarioos Involving Chance that Confound our Intuition | |
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