Suppose you have a room, and you need to guard it using ceiling mounted cameras. Assume the cameras can see in 360 degrees. If the room is very simple, such as a square shape, you can get away with just one. But if the room is more complicated, say with nooks and crannies, you may need many cameras. How can you find how many? Continue reading Taking in the whole room
A graph is a collection of dots (called vertices) joined by curve segments (called edges). It doesn’t matter how you name the vertices and it doesn’t matter where you put them in your drawing. Two graphs are called isomorphic if you can rearrange the way one of them is drawn to make it look like the other. So for example you might convince yourself that a pentagon and pentagram are isomorphic to each other.
Imagine three friends play a game. Mia beats Alex, Alex beats Siki, and Siki beats Mia. Which one of the three, if any, should we consider to be overall winner? In this session, we consider the idea of a tournament, which is a series of one-on-one win-or-lose games in which every player plays everyone else one time. Continue reading Tournament Winners
For this last session of the Fall 2014 meetings, we explored a type of number puzzle involving labeling undirected graphs.
Map-making has some interesting connections to math. For example, it’s tough to draw a round earth on flat paper. Other problems can come up when one tries to highlight regions in a map using color. Our big question for this session is:
How can you color a map with only a few colors?
Continue reading Coloring Maps