Thales’ Theorem and Lockhart’s Lament...

The Yorkshire Branch of the Mathematical Association recently hosted a talk by David Acheson entitled Proof, Pizza and Guitar. (By the way I’ll be giving a talk on card cheating for the YBMA on Wednesday 8th February at 7.30pm in School of Mathematics. All welcome but a small charge of a pound may be made.) During David’s talk he gave a proof of Thales’ Theorem. This is a theorem that states the following. For any point in a semi-circle, the angle formed by the lines from that point to the two edge points of the base is right-angled. This is a good theorem in that, to me at least, it does not seem intuitively obvious (what, it’s always a right angle? Really?) and yet it is easy to convince yourself it’s true by doing some examples. Thales (c624BC – c547BC) is often considered to be the first scientist because he was the first person (we know of) who looked for non-supernatural reasons for phenomena. Rather than believing lightning or earthquakes were caused by gods he considered more natural explanations. However, his solution to the latter involved the way that the land floated on the sea, i.e., he was totally wrong but here it is the concept of avoiding invoking the gods that counts. In the case of mathematics he is credited with a number of theorems and the main point is that, allegedly, he provided proof. He is also credited with measuring the pyramids in Egypt. His method is interesting because it does not involve a brute force use of measuring instruments, i.e., get out measuring rods and send people up the pyramids with them. His proof is more elegant than that. He measured the height of a slave and when the sun was...