# Cat Curl

## by Kim Holman

Have you ever wondered why cats curl up when they’re cold? Or why the circle is Such A Big Deal in geometry?

Well, I’ll be honest here, this geometry nerd thinks the circle is one of the Best. Shapes. Ever. I’m not sure if it is The Best, but we’ll rank it up there with hexagons and triangles.

But why?

What’s been known, even in the days of ancient Babylon and Greece, is that the circle is the shape with the largest area when the perimeter is fixed. Not even my beloved hexagons and triangles can compete with this beautiful, amazing shape: the circle.

In Virgil’s Aeneid there is a story about Queen Dido who was fleeing from Tyre and her brother Pygmalion, and her clever use of this property to outline a maximal area for the city of Carthage, present day Tunisia, she would soon find.

The circle has some really amazing properties. That is what my research is all about! In particular, I’m exploring what’s called the isoperimetric property of the circle by studying objects with the same perimeter and comparing their area.

What does that have to do with here and now? Anything we do that involves maximal area and minimal material needs to be a circle. A cylindrical column supporting a bridge uses less concrete than a square column. That saves money! The circle shows up in buttons, cakes, pizza, steering wheels – things we use frequently and some even daily.

My cat, Pascal, curls up when he’s cold. We all know that cats are basically liquid and can take on any shape. When cold, he needs to condense his body into the optimal shape for heat retention. In other words, he is contorting into a circular shape to minimize his surface area, hence minimizing heat loss. His volume is fixed, so the thing he can change is his shape.

The research I am doing focuses on the explanations of the isoperimetric property as well as creating a booklet of problems to solve suitable for advanced high school and college students. My goal is to become a mathematics professor and spread my love of geometry to the students I encounter. This is a tangible way to give back to the mathematical education community, to strengthen students’ knowledge and comprehension of geometry.

I told you that the ancients knew that the circle was The Best, but they couldn’t prove it. You know how we mathematicians love our proofs. It wasn’t until the 1840s when a man named Steiner published the first proof that the circle is, in fact, the best when it comes to fixed perimeter and maximal area. My research looks at Steiner’s proof and his methods as well as a subsequent proof by Garvin that uses different methods, and I’m working on other ways to prove the same thing. Who knows? Maybe Holman will become more famous than Steiner!

**Disclaimer:*** The views and opinions in this work are those of the author and do not necessarily reflect the views of Auburn University.*