The Pythagoras and cousins module, as you might guess, delves into the Pythagorean Theorem (the sum of the squares of the lengths of the legs of a right triangle is equal to the square of the length of its hypotenuse) and related topics. Some of the topics include various proofs and generalizations of the Theorem - did you know that the book The Pythagorean Proposition contains 366 proofs of the Theorem? - and properties of Pythagorean triangles (right triangle with integer-valued legs and hypotenuse). We'll also derive an algorithm for producing every Pythagorean triple (an ordered triple of positive integers, (a,b,c), so that a² + b² = c²) and use this algorithm to solve a variety of problems. Some of the questions we'll ask:

• What happens in triangles that don't contain a right angle?
• Does the Pythagorean Theorem generalize to higher dimensions?
• Is it true that every Pythagorean triple contains a multiple of 3? of 4? of 5? of . . . ?
• Which 17th century mathematician is one of Pythagoras' cousins?

For further information, contact CwM at cwm@edc.org
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