The fourth day of class went bery well. The students' first challenge was to connect two homes to the electric company, the phone company, and the gas company. To make it more difficult the students then had to connect three homes and each utility company. This excercise was intended to introduce the students to graph theory.

Next, the students had to contruct a figure using an Euler Path. Then using the Euler Circuit figure once and decide whether it was a path or not. The students then explored spreadsheets by contructing a spreadsheet on excel with the vertices and sides of the letters of the alphabet.

After break Jon asked the students to color in figures so that no two regions that share a side have the same color. He then challenged the students to draw figures or maps that would require five colors. Many students formed elaborate figures, but failed to meet the challenge. Then they looked at fractals and the Mendelbroth Set. The students learned that fractals are made through mathematical equations and have infinite iterations. They were also given an example of a recursive function. By using the computer to slowly zoom in on the figures they saw the self similarity properties it had. To help the students understand the concept of fractals he used the analogy of a coast. No matter how detailed you try to give detail.