Can You Squeeze the Sheets?

Published on January 6, 2025

The Problem

Two identical sheets have equally spaced ridges on one side. When the sheets are squeezed together with the ridges facing each other, what spacing maximizes the empty volume between them?

Problem

Which value of L (the spacing between ridges) maximizes the empty space between the sheets?

My Approach to Finding the Maximum

To find the greatest value, we created a simulation and ran it for each value of L

Solution

This led to us seeing the solution for 2.83. This was confirmed by hand, using math (as intended)

I have made the code used for this available here in case others would like to view it