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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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