I came across the following problem from an Italian high school exam on the British Aperiodical website presented by Adam Atkinson:

“There have been various stories in the Italian press and discussion on a Physics teaching mailing list I’m accidentally on about a question in the maths exam for science high schools in Italy last week. The question asks students to confirm that a given formula is the shape of the surface needed for a comfortable ride on a bike with square wheels.

What do people think? Would this be a surprising question at A-level in the UK or in the final year of high school in the US or elsewhere?”

I had seen videos of riding a square-wheeled bicycle over a corrugated surface before, but I had never inquired about the nature of the surface. So I thought it would be a good time to see if I could prove the surface (cross-section) shown would do the job. See Square Wheels.

(Update 9/14/2023)  Square Bridge That Rolls!

This is an incredible application of the rolling square wheels idea described on Matt Parker’s Stand-up Maths Youtube website.  It also demonstrates the difference between engineering and pure math.  The engineers had to solve some challenging problems to adapt the theoretical math to a practical application.  And such solutions are always required under tight time constrictions.  Engineering certainly is a noble profession.