When I was in high school, my math teacher asked the class a question which I still think about quite often. Can you show that, at any time, there are two different points on the Equator that have the same temperature? I thought: is this even math class? Am I in the right room? Perhaps I’d walked into a science class by accident. But no, this was indeed a math class! In this issue, I want to explain how you can solve this problem using calculus: namely, an important fact called the Intermediate Value Theorem. But before that, we need to remember an important concept from high-school calculus: that of a continuous function. continuous functions Let’s look at these two functions here. The left function is continuous. You can draw it without lifting your pencil off the paper. The right is not continuous. To draw it, you’ll have to lift your pencil off the paper at the discontinuity. remember this picture! Imagine you have a dotted green line on top of the graph. Now imagine moving it up and down.