## Playing With And Classifying Pythagorean Triples |

**Paul Friedman**

Union College

April 15, 2014

5:00 pm

Bailey Hall 207

Refreshments will be served in Bailey Hall 204 at 4:45pm

The relationship between the length, z, of the hypotenuse of a right triangle to the lengths, x and y, of the legs of the triangle provides one of the most famous equations in math: $x^2+y^2=z^2$. Integral solutions to this equation are called Pythagorean Triples. We all know some Pythagorean Triples, the most well known being 3-4-5. Of course, multiples of this triple, like 6-8-10 and 9-12-15 are also triples. But how many other "Primitive” Pythagorean Triples (PPTs), that is, solutions, like 3-4-5, that are not multiples of other solutions, do you know? Perhaps you know a few, like 5-12-13 and 8-15-17, and even 7-24-25. How many more PPTs are there? Can you find some? Can you find them all?! In this talk, we will first have some fun exploring patterns in the PPTs. For example, notice that in the sample PPTs above, exactly one leg-length is even. After this we will work (hopefully still having fun) to classify, all solutions to $x^2+y^2=z^2$.

For additional information, send e-mail to math@union.edu or call (518) 388-6246.

Union College Math Department Home PageComments to: math@union.edu Created automatically on: Fri Jan 19 04:43:43 EST 2018 |