Comment on 3blue1brown video on Otto Toeplitz conjecture, “inscribed square problem”

https://www.youtube.com/watch?v=IQqtsm-bBRU

This open problem taught me what topology is – Otto Toeplitz conjecture, “inscribed square problem”

If you color the edges and regions of your blue shapes with red, it would be easier than pointing to an all blue (transparent) shape and saying “look at this part here”. My hunch is you are asking the wrong questions and should be looking at finite sets of constraint equations. Even infinite sets of constraint equations.

I can see some applications in the real world in engineering, plasma physics, lasers, and gravitational detection and imaging, finance, budgeting, energy conservation, optimal controls, fast sorting. Your tools and methods might be more important to share, than how “you” play with them. This particular problem, it is probably easier to solve with infinite tables, not geometric shapes you have to look at and hold in mind. Or ALGEBRA. The 3d curve equivalent might be a cube? Start with the square and generate all paths, and their surfaces? Thanks for your videos. This was a very pleasant break, the smooth generation of surfaces is nice. But tables are more useful. N columns, N dimensions, just make it continuous or very fine grained. Richard Collins,The Internet Foundation