1. Introduction 7
2. How to Use This Book 8

Geometry: Learn About Shapes 11

• Prisms and pyramids and Platonic solids, oh my!
  • Lab 1: Prisms 12
  • Lab 2: Pyramids 14
  • Lab 3: Antiprisms 16
  • Lab 4: Platonic Solids 18
  • Lab 5: Perfect Circles 24
  • Lab 6: Try a Triangle 26
  • Lab 7: Exact Ellipses 28
  • Lab 8: Draw Giant Circles and Ellipses 30

Topology: Mind-Bending Shapes 35

• Learn about squeezable, squishable shapes and surfaces
  • Lab 9: Compare and Classify Shapes 36
  • Lab 10: Möbius Strips 38
  • Lab 11: Möbius Surprise 42

Color Maps Like a Mathematician 45

• Using the fewest number of colors possible, fill in a map so adjacent shapes are different
  • Lab 12: Map Coloring Basics 46
  • Lab 13: Efficient Map Coloring 50
  • Lab 14: Squiggle Maps 54

Stitching Curves 57

• Learn to create curves using only straight lines
  • Lab 15: Drawing Parabolas 58
  • Lab 16: Stitching Stars 62
  • Lab 17: Creative Curves 64

Fantastic Fractals 67

• A fractal is a shape that is similar to itself no matter how far you zoom in on one particular part
  • Lab 18: Draw a Sierpinski Triangle 68
  • Lab 19: Build a Sierpinski Triangle 70
  • Lab 20: Draw a Koch Snowflake 74
  • Lab 21: Draw a Square Fractal Snowflake 78
  • Lab 22: Explore the Koch Snowflake’s Perimeter 80

Terrific Tangrams 83

• Solve ancient Chinese puzzles by making different shapes from the same seven pieces
  • Lab 23: Tangram Basics 84
  • Lab 24: Teaser Tangrams 86
  • Lab 25: Tougher Tangrams 88

Toothpick Puzzles 91

• Create and solve brainteasers using patterns of toothpicks
  • Lab 26: Starter Toothpick Puzzles 92
  • Lab 27: Toothpick Puzzles: The Next Level 94
  • Lab 28: Challenging Toothpick Puzzles 96

The Game of Nim 99

• Learn the game of Nim and develop a strategy to win every time
  • Lab 29: Learn to Play Nim 100
  • Lab 30: Win Nim: The Copycat Strategy 104
  • Lab 31: Copycat Nim as Player 1 106
  • Lab 32: Win Nim: 1 + 2 = 3 Strategy 108