Explore the mathematics behind shoe lacing in this 29-minute video that delves into a quest to determine the optimal methods for lacing shoes. Learn about mathematical lacings, the definition of "best" in this context, and discover the shortest lacing techniques, including crisscross and bowtie patterns. Understand how to prove the efficiency of these methods using the traveling salesman problem. Investigate the longest lacing techniques, such as devil and angel lacings, and consider their real-world applications. Examine the concept of lacing strength and ponder the validity of proofs conceived in dreams. Gain insights into this accessible yet intriguing mathematical topic, complete with visual demonstrations and references to further reading materials on shoelace mathematics and knot theory.
Overview
Syllabus
Intro.
What's a mathematical lacing?.
What does "best" mean?.
What is the shortest lacing? Crisscross and bowtie lacings..
How to prove that the shortest are the shortest? Travelling salesman problem.
What are the longest lacings? Devil and angel lacings..
What about real lacings?.
What are the strongest lacings?.
Can proofs hatched in dreams be true?.
Taught by
Mathologer
