4th Saturday Math Meetups: Mathematical Illustration

Earlier in the year, the group looked at Mathematical Iluustration by Bill Cassleman, which is a free online text that covers mathematics through Postscript programing. What makes the book standout is how it uses Postscript as a way to teach college level coordinate geometry and covers concepts like mathematical projection on a globe and perspective in later chapters. In the first meeting, the group covered the first chapter and a bit of the second since the chapters are presented as pairs, with one chapter covering concepts in Computer Science and the next chapter going over the same concepts in more rigourus mathematical way.

Since the last time the group covered this book, there has been other discussions based on history of mathematics and geometry due to the "Induction and Analogy in Mathematics" series. For those not familiar, the series this year has been covering proof of the isoperimetric theorem which involves analyzing the area of shape with respect to it's perimeter, while also looking at historical attempts that look at the theorem. Inspired by this as well as the problems in the first chapter of Mathematical Illustrations that ask us to write a program that prints a few of the proofs from "The Elements", this month we'll be looking at both Isaac Newton's and Gottfried Leibniz's work and proof of the fundamental theorem of calculus. That is, differentiating a function is roughly the inverse of integrating a function.

For this event, we'll be looking at Gottfried Leibniz's 1684 paper "A New Method for Maximum and Minimum" and Lemma 1 through 4 in Isaac Newton's Philosophiæ Naturalis Principia Mathematica*.* Participant's are encouraged to work through these problems either through a programming language they are comfortable in, or some sort of coordinate geometry