• Art and Sculpture Book
  • Calculus Book
  • Dance Book
  • Games and Puzzles Book
  • Geometry Book
  • Knot Theory Book
  • Music Book
  • Number Theory Book
  • Patterns Book
  • Infinite Book
  • Truth, Reasoning, Certainty, and Proof Book


Discovering the Art of Patterns lets you, the explorer, investigate how mathematics uses the concepts and ideas of patterns to give meaning for mathematical structures. Using patterns you will explore the mathematics behind the naming of large numbers such as a millinillitrillion, famous Islamic Art, and spirographs. While investigating the connections between patterns and problem solving techniques, you will encounter a precocious elementary student who surprised his teacher with his ability to solve a busywork problem in a snap of insight, some combinatorics and discrete calculus as well as interesting families of numbers.

Additional Version Notes

Chapters on Pick's theorem, Patterns and Language in the Creation of Powerful Number Systems, Patterns Linear and Arithmetic, and Circles, Stars, Gears and Unity are solid and ready for external beta-testing. Reviewers & Beta Testers Wanted »

Compass Rose

We present the following case study as a way of illustrating the power of inquiry-based learning to transform how we think about what we know and how we know. It challenges us to reconsider the nature of teaching and learning in mathematics. Julian Fleron describes how he and his students explore triangle patterns.
What we know changes several times in the story of Rascals’ triangle. And each time the matter of what we know is inextricably intertwined with how we know it.