| Abstract: |
| A cylinder will roll down an inclined plane in a straight line. A cone will
wiggle along a circle on that plane and then will stop rolling.
We ask the inverse question: For which curves drawn on the inclined plane
$R^2$ can one chisel a shape that will roll downhill following precisely
this prescribed curve and its translationally repeated copies?
This is a nice, and easy to understand problem, but the solution is quite
interesting.
(After a Nature paper,
Solid-body trajectoids shaped to roll along desired pathways, August
2023, and Notices AMS, Vol 71, 2024) |
|