quod erat demonstrandum
Saturday 23 February 2013
There is a great little book entitled QED - Beauty in Mathematical Proof that I keep on my desk at school - not as a resource for juicy example questions to use in class lectures, but as something to share with individual students when they ask me a question which reveals a genuine interest in how mathematics works. I've also used as a resource for discussions about the nature of mathematical proof in TOK classes. I've also used it in pre-IB classes to offer students a nice insight into some classic examples of an elegant proof in mathematics, with emphasis on 'elegant'. I've even used it to assist students writing an extended essay in mathematics - when they've given me the impression that they do not fully understand what a proof in mathematics entails. And, of course, I hold it up in class the first time that I write the acronymn Q.E.D. at the end of finishing a brief proof - or, more likely, after answering a "show that" question which commonly appear on IB mathematics exams.
The simple act of writing Q.E.D. at the end of some work in a classroom lesson gives a teacher an opportunity to give a mini-lesson about the nature of proof mixed with a little history of mathematics. Any discussion has to start (hopefully initiated by a student asking what Q.E.D. stands for) with giving a translation of the phrase "quod erat demonstrandum". The most accepted translation into English is "that which was to be demonstrated (or proved)".