How Simple Math Can Cover Even the Most Complex Holes — Quanta Magazine

My latest column for Quanta Magazine starts with a simple question: If you had a cover a hole that was at most 1 inch wide, what kind of patch would you need?

This problem is related to Lebesgue’s universal covering problem: The goal is to find the smallest such patch that could cover any hole of diameter one. After 100 years mathematicians still don’t have a full answer, but some techniques from high school geometry are getting us closer.

By starting with known covers, we can chop off pieces we can prove we don’t need, and make our covers smaller and smaller.

Read the full article for more, which is freely available in Quanta Magazine.