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File: ThalesTheorem One of the CircleTheorems. I've just been watching "Art Attack", a program with some amazing work by Neil Buchanan, which encourages children to produce pictures, models, and art in all forms. Not generally my thing, really, but some of his work is brilliant. And then he did something that *really* caught my attention. He described a method to find the centre of a circle. [[[> images/ThalesTheorem.gif ]]] Take a circle drawn on a sheet of paper. Take another piece of paper, and position one corner on the circle you have. Mark the circle where the paper crosses it, then join those marks. The line you get will cut the circle exactly in half. Do it again, and you have two lines that cross in the exact centre of the circle. There's a cute animation here: * http://www.mathopenref.com/constcirclecenter2.html Fantastic. This is was proved by Thales ("Ta - less") of Miletus around 2600 years ago. He said that the diameter of a circle always subtends a right angle from anywhere on the circumference. And now I've seen it in action on television. Maths really is everywhere. Even (especially?!) in art.