Fall 2019 MTCA Workshop #2

Post date: Oct 23, 2019 5:37:21 PM

Altha Rodin

Department of Mathematics

The University of Texas at Austin

Coloring the Plane

We will consider the use of colors not only as a problem-solving tool but also as a source of interesting mathematical questions. After trying out a few different types of problems and puzzles for which coloring is a useful technique, we will consider a few problems in which the goal is to find a particular type of coloring. We will finish with a look at an open problem in mathematics, namely the problem of determining the chromatic number of the plane. This problem is easy to state: what is the fewest number of colors needed to color the plane in such a way that no two points that are exactly one unit apart are the same color? In the graphs below, each edge is one unit long. Seven colors were used to ensure that two adjacent vertices are different colors in the graph on the left. Is there a coloring that uses fewer than seven colors? What is the smallest number of colors that are needed? What does your answer tell you about the chromatic number of the plane?

We will meet at 6-8 pm in PMA (RLM) 12.166.

We validate campus parking, provide dinner, and participants earn CPE hours for this workshop.

Please register by October 22 as dinner is provided for participants.

https://forms.gle/Wqe7anKKHfCE8Uor5

Free parking is provided in the Speedway Garage (SWG). Enter the garage on Speedway, between Dean Keaton and 27th street. Pull a ticket when you enter the garage. We will give participants cards to exit.