As we near the end of another Mathematics Unit, students will be diving back into our exploration of Euclid’s Elements. While searching for the best angle at which to enter into this difficult but important text (see video for more on that), we’ve recently adopted an unexpected role in our approach: skeptics.
Let’s face it; no one is particularly interested in learning how to regurgitate a proof from memory or wrestle with a text that some consider to be infallible. At least, not until their own experience as devil’s advocate has led them to see that the proofs and therefore the text are quite useful, brilliant, and hard to argue against. Thus, our study of Euclid has taken this turn.
Euclid, for example, states that the base angles of an isosceles angle are equal; can you draw a case where they aren’t? If not, why? What problems do you run into? Now read his proof. Do you understand it? Where can you poke it, where can you ask why? Does Euclid have an answer to your prodding, or have you found a slip or error in his logic?
Our students are bright and are asking great questions. As of writing this, we’ve found Euclid to be a bit vague (in just a few cases) when it comes toon stating supporting information. But we’ve also found that propositions are built on previous propositions, built on previous propositions, built on…back and back and back, with some common notions or definitions sprinkled in. In other words, we can only fault Euclid on his decision to not restate all that he’s already proved.
So the search continues, and let me assure you; if there’s a hole in his argument somewhere, these students will find it.