Jonathan Lubin, Professor Emeritus from Brown University, will present the Dan E. Christie Mathematics Lecture on Tuesday, October 23, at 7:30 pm in Searles Science Building, Room 315. The title of his talk is "The Pythagorean Theorem Seen From A More Modern Viewpoint."
Professor Lubin provided the following abstract of his talk:
The Pythagorean Theorem is one of the triumphs of Greek mathematics from around the time of Euclid. They thought of it purely geometrically, speaking of the areas of squares built on the three sides of a right triangle, but we have the advantage of algebra, and express the Theorem in the equation a^{2}+b^{2}=c^{2}, where the three letters represent the lengths of the two legs and the hypotenuse of any right triangle. The most interesting examples of a^{2}+b^{2}=c^{2} are where a,b,c are whole numbers-then a,b,c form a Pythagorean triple. The standard example that comes up again and again in geometric examples is a=3, b=4, c=5, and there are a few others thrown at high-school students. But in fact there are infinitely many essentially different Pythagorean triples.
The Hellenistic-period mathematician Diophantos gave a formula for finding them all, expressed in the cumbersome non-algebraic language of the time, and there is some evidence that the Babylonians about two millennia earlier had pretty much the same information. More modern methods, now taught in all our high schools, allow a clear and understandable method not only to find Diophantos' formulas, but to see why they hold.