Pigeonhole Principle
I chose to discuss the Pigeonhole Principle. The concept is also known as the Dirichlet's Box Principle, which states if there are more pigeons(n), then there are pigeon holes(m); there will always be one spot with at least two pigeons inside. If n+1 or more objects are placed into n boxes, then there is at least one box containing two or more of the objects. As I began my research, I quickly understood the many variations of where the pigeons can be. If there were five pigeons and only four holes, it's possible all five could be in one hole, leaving three empty No matter where they land, the fundamental concept of this principle remains the same. Common sense and logic make it impossible for there not to be a pair in at least one of the holes.
As shown in the photo above, the idea is very straightforward and doesn't seem to be crucial in mathematics, but after my research, I see how this "simple" principle can be applied to a vast range of problems.
The variety of different examples which utilize this principle are countless. I know there are twenty-six letters in the alphabet. Therefore if I wrote twenty-seven different English words, each starting with a different letter, I know there will be at least two words that begin with the
Since there are only three hundred sixty-six possible birthdays, there will always be at least two people in the group that share a birthday.
I found a fun video filled with several interesting examples and explanations. After viewing it more than several times I feel confident in my understanding of the PHP. https://youtu.be/20YlivzViOo
"The Pigeonhole Principle." CircleOfMath, 30 Apr. 2016, circleofmath.wordpress.com/2016/04/30/the-pigeonhole-principle/.
"There Are n Cars and n+1 Pigeons. At Least One Car Gets Pooped on Twice. By the PigeonHole Principle." Quickmeme, www.quickmeme.com/meme/3rktv0.
Ttor68, Mr., director. Basic PigeonHole Principle Problems. YouTube, YouTube, 17 June 2012. www.youtube.com/watch?v=20YlivzViOo