Dr. Price's Favorite Theorem: Rational Tangles

Thursday, February 15, 2018

Picture of a rational tangle

Dr. Price’s favorite theorem is John H. Conway’s basic theorem about the correspondence of rational tangles to the extended rational numbers. You are probably familiar with rational numbers: all the numbers that can be written as a ratio of two whole numbers. The “extended” bit just means we throw infinity into the pot as well. Rational tangles are knot-like objects that you can form by twisting pieces of string or rope in different ways. This video shows a group of students making some rational tangles. The theorem is that each rational tangle can be paired uniquely with a rational number (or infinity), and likewise each rational number gets a rational tangle. So these complicated tangles can be boiled down to relatively familiar numbers.



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