Madison Math Circle Abstracts 2020-2021
|February 1, 2021 at 5-6pm||Connor Simpson||Pick's theorem
Pick's theorem relates the area of a polygon whose vertices lie on points of an evenly spaced grid to the number of grid points inside it. We'll do a sequence of examples to discover this theorem, outline a proof, and consider 3-dimensional analogues.
|March 1, 2021 at 5-6pm||Colin Crowley||Fractals and Imaginary numbers
We'll explore some famous mathematical pictures such as the Mandelbrot set and Julius sets, which are examples of what are called fractals. In a quest to understand where these astonishing pictures come from, we will dip our toes into the world of imaginary numbers. While they are vastly complicated and beautiful, these come from simple equations.
|April 5, 2021 at 5-6pm||Aleksandra (Ola) Sobieska||Flipping Pancakes
A waiter delivering pancakes must sort disorganized stacks of pancakes before delivering them to guests, but can only use a spatula to do so. How many flips are necessary? Can we come up with a method that will get him a perfect stack of pancakes every time?
|May 3, 2021 at 5-6pm||Trevor Leslie||We'll give a gentle introduction to the concept of an infinite series of numbers, with a focus on geometric series. As an application, we'll discuss how to find the area of a fractal---the Koch snowflake.|