Madison Math Circle Abstracts 2023-2024

Abstract 10/2

Uri Andrews

Title: How many paradoxes are there?

"This statement is false". That's the so-called liar's paradox. (Think through why that statement cannot be either true or false). A paradox is a statement or collection of statements that cannot be meaningfully assigned truth values. Aristotle thought that all paradoxes were essentially the same as the liar's paradox. In 1985, Yablo found a different paradox (though there is some disagreement here). A brand new paper claimed to show that there are only 2 paradoxes (Yablo and the liar's paradox). I'll talk about all these topics and also a brand new paradox. Are there more than 2 paradoxes after all?

Abstract 10/16

Diego Rojas La Luz

Title: How to Not Die While Eating a Poisoned Chocolate Bar

We are going to talk about Chomp, a game where you take turns eating chocolate and you try not to die from poisoning! This is one of those very easy-to-state combinatoric games which happens to be very hard to fully analyze. We'll see that we can say some rather surprising things regarding winning strategies, so stay tuned for that. Who wants to play?

Abstract 10/30

Oh Hoon Kwon

Title: Your (Life) Turning Points: Chasing Angles for Proofs

We're bringing a fresh approach to Euclidean geometry by incorporating physical movements involving a pencil to illustrate proofs related to angle concepts. This inventive method acts as a potential link between inductive, exploratory techniques and deductive proofs. It provides students with a new perspective on Euclidean geometry, particularly in the context of angle concepts, making it an enjoyable and captivating way to engage with the subject.

Abstract 11/13

Aleksandra Cecylia Sobieska

Title: Trapezoid Numbers

Perfect squares are numbers that can be represented as a square arrangement of dots, like 1, 4, 9, 16, and so on. This Math Circle, we will investigate a similar question: what numbers can be represented as a trapezoidal arrangement of dots?