An innate curiosity and the need to search for patterns is the superpower of human beings. It leads babies to become linguists and learn languages on their own and it helps them make sense of the world. While many of us have always asked the question ”Why?” from an early age, too many teachers have not always been thrilled with the question. In this course, I would like for us to explore and answer some basic mathematical questions which have arisen in human history. Each session, we will talk about simple yet powerful ideas which were developed centuries or even millennia ago. The goal of each session will be to understand the ”Why” of a topic as well as to learn about the applications in a non-technical fashion. Many of the activities will be hands on and will be illustrated with pictures. I hope that everyone will leave the course with an awareness of the mathematics which surrounds us as well as a glimpse of the beauty which mathematicians feel for their subject.

The topics will include the Pythagorean theorem, circles, conic sections, the Euclidean algorithm, logarithms and slide rules, and Egyptian arithmetic and will be presented in six sessions of 90 minutes each.

The emphasis will be on understanding the ideas and appreciating many of the cool applications of the ideas. For example, the Pythagorean theorem has several beautiful proofs which were discovered independently by many cultures. We will see why the area of a circle of radius r is p r2 is true without using complicated mathematics. We will see how the ideas of conic sections leads to whispering galleries, tools for destroying kidney stones, GPS, and satellite dishes. The Euclidean algorithm is notable for making possible the encryption of data sent over computers. The invention of logarithms in the 1600’s is based on a simple idea and led to slide rules which many of us used into college. We will learn how to multiply and divide like an Egyptian scribe and learn how to take take roots like a Babylonian mathematician and see how their approaches were not fully appreciated until modern times.

I shall often use the free program Geogebra to illustrate some of the fun one can have with mathematics. Those interested may download the program for themselves, but it is not required to have to participate.