Spring, 2015

January 29th: Strange Number Combinations

This circle will feature a seemingly haphazard system of jumbling the numbers of a list. As time goes on, though, patterns emerge, and opacity becomes clarity. 

February 12th: Liars Bingo

This circle will feature a type of bingo card, and a clever trick to catch someone lying to you. 

February 26th: Serious Sudoku

Sudoku puzzles are wildly popular, with thousands of books published with hundreds of puzzles each. How many of these puzzles are repeats? Are we ever going to run out of different puzzles? How many are there? The answer is harder than you would think. 

March 12th: Tilings

Can you use a certain shape tile to cover an infinite floor? How about a floor that has a specific shape? We will investigate what different shapes tiles can cover floors of various sizes and shapes. 

March 26th: Pascal's Triangle

Known long before Pascal, the eponymous triangle shows up in unbelievable strange places in mathematics. We will investigate some of the patterns hidden in Pascal's triangle. 

April 9th: Fold and Cut

Given a triangle on a piece of paper, is it possible to fold the paper in such a way that you can cut the triangle out with only one straight cut? We will experiment with various types of triangles and other polygons to see what we can accomplish. 

April 23rd: Paradoxes Cancelled

This statement is a lie. If the town barber shaves every man who doesn't shave himself, who shaves the barber? These and many other paradoxes and seeming-paradoxes will be covered.Fall, 2014

Fall, 2014

Oct 27th: Random Fibonacci Sequences

The Fibonacci sequence is generated by taking the numbers 1 and 1, then adding them together to get 2, then adding 1 and 2 to get 3, adding 2 and 3 to get 5, and repeating. The result is 1, 1, 2, 3, 5, 8, 13.... The sequence is very well behaved, and extensively studied. In this math circle, we will examine what happens if we introduce a random factor into the sequence that has us subtract instead of add from time to time. 

Nov 3rd: Parking Sequences

A Parking Sequence is a sequence of numbers chosen by "drivers" who want to park in a strange sort of parking lot that is dangerously close to a cliff. It should also be mentioned that the cars have no reverse gear and the parking lot is too narrow to turn around. The drivers are also so stubborn that refuse to park in very many parking spots. What happens when we let them loose in the parking lot? 

Nov 10th: Cellular Automata

Certain seashells display impressive patterns that appear to be digital. Many of the fascinating designs are actually very simple applications of a mathematical rule. We can reproduce these patterns using what we call cellular automata. 

Nov 17th: Ramsey Theory

How many people do you need in a room to guarantee that there are at least 3 people wearing the same color shirt, or three people who are all wearing different colored shirts? This is an example of a simple type of question that falls under the umbrella of Ramsey theory. We will explore this question and many like it to try to find patterns and applications to real world scenarios. 

Nov 24th: Ouroboros

An ouroboro is most easily described in art as a snake that is eating itself. They have been depicted throughout the ages as simple circles or very complicated and beautiful knots. In this circle, we will learn a very easy method for drawing arbitrarily complicated ouroboros and many other similiar objects. No artistic talent is needed! 

Dec 1st: Games with Othello Pieces

The simple Othello game piece is a disc that is white on one side, and black on the other. From this simple object, we can play countless games other than Othello. One game in particlar will be taught, and we will think our way to a strategy that will always favor one player or the other. 

Dec 8th: Euclidean Algorithm

In our final circle of the semester, we will visit the Euclidean algorithm. This algorithm is used to find the greatest common divisor between two numbers, as well as some other information about two numbers. We will learn what the algorithm is, and we will find a deep connection with the Fibonacci sequence hidden in the algorithm!