## Chapter37Ramsey's Main Coure – A Comic

###### Project by: Marina Gloanec, Gabriel Leung, Alex McCourt, Caitlin McMahon, and Melanie Oldham.

$\textbf{Summary:}$ Our comic strip is focused around Ramsey's Theory. We played on the 'pigeon hole' theme of Ramsey's theory as well as the name Ramsey by including a chef cooking pigeons for a dinner party.

In terms of Ramsey's theory, the comic includes an explanation and proof of $R(3,4)=9$ as well as $w(3,2)=9$ for the arithmetic progression.

Here is the story line:

• Host plans a dinner party for nine and hires a chef.

• Chef plans to cook pigeons for the dinner party.

• Chef realizes there are only eight pots, but nine pigeons (one for each guest).

• Here, we explain the pigeon hole principle briefly, with host and chef conversing.

• A guest calls and asks how many people are coming, and wonders if he will know anyone.

• The Ramsey number $R(3,4)=9$ is explained.

• Guests are asked by the host to wear either red or blue, and the van der Waerden number $w(3,2)=9$ is explained.

Watch “Ramsey's Main Course” through the link below. The background music on the theme of van der Waerden's Theorem is composed and performed by Leifshane Estrada, Vanessa Gottfriedson, and Matthew Tong.

Enjoy!