My Project
Coprimes - Upload a doc Read this doc on Scribd: Coprimes
*UPDATE: you may have to download this for it to look right. It is a problem with scribd, not with the pdf.
Ok, so let me talk about this project. This is my final project for my Linear Algebra/Multivariable Calc class, but it uses no math more advanced than a college Calc 2 or a high school Calc BC course. My teacher, Mr. Weis, asked me what the probability was that two randomly selected numbers would be relatively prime. My guess after doing some arithmetic was 2/3, which turns out to not quite be the case.
The capital Pi is similar to a sigma, except it represents a product rather than a sum. I am talking about infinite products, as can be shown. Most of the math was done originally by Euler. In reality, there is no good way to justify being able to take an infinite polynomial and make it the product of it’s factors, as you would with a finite one, but the other way I know to prove it involves Fourier transforms, which would be extremely messy. I prefer that people are able to follow this than that it is the most taut proof in the world; after all, this is the internet, and you all have lives (except you, in the yellow shirt).
