John Conway created the Rational Tangles dance as a way to make progress on unsolved questions in Knot Theory. Four dancers hold two ropes. As they Do-si-do and Turn 'em Round, the ropes become intricately tangled. However, no matter how complicated the tangle gets, it is possible to completely describe the configuration using a fraction. In fact, we can actually untangle the ropes without seeing them simply by performing simple computations with fractions.
We will take a deep dive into the proof behind why the tangle dance works. Along the way, we will explore concepts from knot theory, continued fraction expansions, linear fractional transformations and the modular group, and much more.
In addition to exploring Rational Tangles, we will also tackle some Math Wrangle problems together. Students will learn a wide range of proof techniques and will become more comfortable wielding algebra. Participants should have long attention spans and be interested in learning deep mathematics.
Math Circles are free and open to all students in Pre-K through 12th grade who love math and want a challenge. Math Circles are an opportunity to discuss mathematical ideas with like-minded peers. Our pedagogy is based on the approach used in by Bob and Ellen Kaplan in the Boston Math Circle.
Faculty and students from Notre Dame partner with Riverbend Community Math Center to offer Math Circles for four different age ranges. All Math Circles will meet on Mondays from 5 to 6 p.m. in Pasquerilla Center (the ROTC building) at Notre Dame from September 14th through December 7th. We will not meet October 19th due to Notre Dame Fall Break, and families will meet in Jordan Hall of Science for our end of semester poster session on December 7th.
Typical Ages: 4–5 year olds
Named for Joan Birman (1927–)
Typical Ages: 1st – 2nd grade students
Named for Evariste Galois (1811–1832)
Typical Ages: 3rd – 5th grade students
Named for Sophie Germain (1776–1831)
Typical Ages: 6th – 12th grade students
Named for Andrew Wiles (1953–)
