ohwelliguessnot

What is the best gift you've either given or received? And what is the coolest thing on your resume?

First of all thanks so much for taking the time to do this. Fractals are beautiful and so are you!

I'll try to keep this short and clear. I'm currently a math undergrad. A year or so back I was working on calculating the function that would allow a square to revolve smoothly (a bike with square wheels, for instance). Once I had that figured out a few professors I was working with encouraged me to try to generalize the function for other figures. Triangles, hexagons, five pointed stars and so on. At this point I didn't know how to do all of the math by myself so they pointed me in the right direction with materials and theory already done by others. Then they approached me with a new "twist" on the problem (at least, it seemed to be new as we couldn't find any material on it). This is where I get to my question.

Do you think a function could be calculated that would complement a fractal in the way I suggested? Or in other words, could a fractal ever "roll smoothly?"

Thank you for your time!

That's what confuses me. I have trouble imagining what the opposite/complement of a fractal would look like. It's why I have so much trouble answering my question. I suppose these matching pairs could exist in theory, as indicated by Professor Frame's response... but not all shapes have them. (an equilateral triangle, for instance, will never roll perfectly smoothly). I think there is more of an answer out there than just a theoretical speculation.