What is the best way to lace your shoes? Dream proof.

TL;DR

A mathematician goes on a quest to determine the best ways to lace shoes, discovering that the crisscross and zigzag lacings are the shortest and strongest options.

Transcript

Welcome to another Mathologer video today's video is about one of my own mathematical adventures my quest to pin down the mathematically best ways to lace shoes yes you heard right the guy who only ever wears Birkenstocks and went on a mathematical shoelace expedition. this goes back to the time when my own kids were little. teaching them to tie th... Read More

Key Insights

• 💖 Teaching his children to tie shoelaces sparked the Mathologer's interest in exploring the mathematical aspects of lacing shoes.
• 💪 The crisscross lacing is the shortest and most popular lacing, and it is also the strongest for most shoes.
• 😒 The Mathologer uses the concept of exploded lacings to prove that the crisscross lacing is the shortest overall.
• 🍰 The Traveling Salesman problem, which involves finding the shortest route between multiple cities, has connections to the shortest shoelace lacing.
• 🦕 The Mathologer's exploration extends to lacings with odd and even numbers of eyelet pairs, resulting in different variations of the bowtie lacing.
• 👞 Real shoes often have similar shortest lacings to ideal mathematical shoes, making the findings applicable to everyday footwear.

Questions & Answers

Q: How did the Mathologer become interested in studying the mathematical aspects of lacing shoes?

The Mathologer's interest in lacing shoes began when he was teaching his children to tie their shoelaces and noticed the mathematical elements involved.

Q: What are some examples of different lacings that the Mathologer explores?

The Mathologer explores lacings such as crisscross, zigzag, and various unique lacings found in shoe shops.

Q: What is the shortest tight lacing for a shoe with an odd number of eyelet pairs?

The shortest tight lacing for a shoe with an odd number of eyelet pairs is the crisscross lacing.

Q: How does the Mathologer prove that the crisscross lacing is the shortest?

The Mathologer uses a concept called "exploded lacings" and shows that the exploded crisscross lacing is the shortest among all possible exploded lacings.

Q: What is the "Traveling Salesman problem" and how does it relate to shoelace mathematics?

The Traveling Salesman problem involves finding the shortest round trip that visits multiple cities. The Mathologer shows that the solutions to this problem do not have intersections, which helps in proving the shortest shoelace lacing.

Q: Are the shortest lacings for ideal mathematical shoes the same for most real shoes?

Yes, the crisscross lacing is usually the shortest for most real shoes, as it is for ideal mathematical shoes.

Q: What are some of the other interesting findings of the Mathologer's shoelace exploration?

The Mathologer also explores the longest lacings among different classes and identifies lacings with the highest strength for different types of shoes.

Q: Where can one find more information and resources about shoelaces and different lacings?

The Mathologer recommends visiting Ian's shoelace site, which offers a wealth of information on shoelaces, including different lacings and ways to tie them.

Summary & Key Takeaways

• The Mathologer embarks on a mathematical investigation into the best ways to lace shoes, sparked by teaching his children to tie their shoelaces.

• He explores various mathematical aspects of lacing and tying shoes, publishing an article and a book on the subject.

• The Mathologer discovers that the crisscross lacing is the shortest and strongest option for most shoes.