Facilitator: Aubrey Rhoden and Kim Moore
Agenda: Stochasticity and Coin Flipping
Let’s Do an Experiment!
A Close Look at the Results
What is the largest number of heads you had in a row?
What is the largest number of tails you had in a row?
What is the probability of getting 2 heads in a row?
What is the probability of getting 3 heads in a row?
What is the probability of getting 4 heads in a row?
What is the probability of getting a string of 7 heads or 7 tails if you flip a coin 100 times?
Facilitator: Dr. Frank Sottile
Agenda: Hyperbolic Soccer Ball
Template for Center of Ball Template for Side of Ball
What are the properties of parallel lines in hyperbolic geometry?
What are the properties of triangles in hyperbolic geometry?
Facilitators: Dr. Philip Yaskin
Agenda: Polygon Differencing
Put 4 integers on the corners of a square. At the midpoint of each side put the positive difference of the numbers at the corners. Connect the midpoints to form a new square. Repeat this process until it terminates. What do you notice? Do you think this happens no matter what numbers you put on the 4 corners? Repeat this process with a triangle. Now what do you think about your conjecture about the square? Repeat this process for an N-gon (a polygon with N sides). For which N’s does the process behave like a square? For which does it behave like the triangle? Prove your conjectures.