Wobbly tables and the intermediate value theorem

Tomorrow I’ll be introducing the intermediate value theorem (IVT) to my calculus class.  Recall the statement of the IVT: if is a continuous function on the interval and is between and , then there exists a value such that .  In other words, achieves all of the intermediate values between  and . This is a very underappreciated theorem…

Topological claymation

For my first post, I thought I’d post a couple of short videos that I made earlier this year.  The inspiration was the following sequence of pictures I put in my book illustrating what I call the “double torus clothesline trick.” It seemed like everyone I showed it to had trouble following the sequence of…