Enrichment Paper #2 - Covany Gardner Math 108 Enrichment Paper#2 For my second enrichment paper I chose to do it on the Dirichlet box or more commonly

# Enrichment Paper #2 - Covany Gardner Math 108 Enrichment...

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Covany Gardner Math 108 Enrichment Paper #2 For my second enrichment paper, I chose to do it on the Dirichlet box, or more commonly called the Pigeonhole Principle. It pretty much states “suppose we have four pigeons but only three pigeon holes. No matter how we assign a hole to each pigeon, at least two pigeons have to share the same hole.” Other examples of that would be that in a certain city, there are at least two people that have the same amount of hairs on their heads. Or there is at least two people who wake up at the same exact time. This is not probability or likelihood; they are not happening by chance. If you have a group of 13 people, at least two of them have birthdays in the same month. Using the quote, the pigeons are the 13 people, and the pigeon holes are the 12 months. Now think of having 7 pigeons but only 3 pigeonholes, at least three pigeons have to share pigeonholes. Andrew Wiles at Princeton University used the pigeonhole principle in his proof of Fermat’s last theorem. The Pigeonhole Principle is used as an analytical