@article {MATHEDUC.05804998,
author = {Percy, Andrew and Carr, Alistair},
title = {Leaning on Socrates to derive the Pythagorean theorem.},
year = {2010},
journal = {The Australian Mathematics Teacher},
volume = {66},
number = {2},
issn = {0045-0685},
pages = {8-12},
publisher = {Australian Association of Mathematics Teachers (AAMT), Adelaide, SA},
abstract = {Summary: The one theorem just about every student remembers from school is the theorem about the side lengths of a right angled triangle which Euclid attributed to Pythagoras when writing Proposition 47 of "The Elements". Usually first met in middle school, the student will be continually exposed throughout their mathematical education to the formula $b^2 + c^2 = a^2$, where "a" is the length of the hypotenuse. It is so important in school mathematics and in mathematical thinking that the student deserves to be able to derive the Pythagorean theorem with an appropriate degree of rigour. The aim of the authors, in this article, is to provide a repertoire of derivations that range from the visual and geometrical to the algebraic and, in doing so, expose the interconnectedness of many parts of the school curriculum. They begin by "allowing students to explore concrete examples". The simple case for a right isosceles triangle is easily seen to be true by construction. The construction can then generalised to any right-angled triangle. The student performs "dissections and recombinations of shapes", requiring no algebra or non-geometric manipulation. (Contains 6 figures and 1 footnote.) (ERIC)},
msc2010 = {G43xx (G44xx E53xx E54xx)},
identifier = {2010f.00732},
}