Explorations in Math

"Exploration is the act of searching or traveling a terrain for the purpose of discovery."

No matter how much math you learn there is always more to find. Mathematicians love to explore the wilderness establishing new frontiers. The process of discovery continues even today.

The papers on this page are explorations I lead with gifted primary and middle school students. I hope you will enjoy these explorations too.

The column on the right lists concepts that it will be helpful to know before you head into each adventure.

Spaceship above earth

Polar Bear Math
(PDF icon printable version)
How does a Polar Bear tell where he's going when he's at the north pole and every direction is south? Basic graphing, angle measure
PDF icon Introduction to Complex Numbers What is \(\sqrt{-1}\) and what is it good for? Basic algebra, basic graphing
PDF icon From Simple Math--Chaos Two computers give completely different answers. Which one's lying? Basic algebra
PDF icon Introduction to Algebra with Modular Arithmetic The Affine Cipher is a secret code based on algebra. Here's how to use it and how to break it if your enemies are using it. Intermediate algebra
PDF icon Complex Prime Numbers What happens when you mix Complex Numbers and Prime Numbers? Among other things, 2 is no longer prime! Intermediate algebra, basic number theory (prime factoring)
PDF icon Amazing Connections Worksheet
PDF icon Amazing Connections Solutions
What do trigonometry, exponentiation, and complex numbers have to do with each other? Discover the most beautiful formula in math:
Advanced algebra, basic trigonometry, polar graphing

These are currently available only as PDF files. I'm working on converting them to HTML presentations.