Here is a 3-paragraph summary of the blog post for mathopen.com:
This post revisits a fun geometry puzzle originally shared in 2016 called "An Asteroid Walk." The setup involves seven astronauts who all start from the same location on a small spherical asteroid. Each astronaut follows the same walking algorithm: travel a set distance forward, turn 90 degrees left, and repeat the process, though each astronaut walks in a different initial direction.
The puzzle explores what happens to the astronauts as they follow this repeated algorithm on the curved surface of a sphere rather than a flat plane. On a flat surface, this kind of movement would produce a predictable square path, but the curvature of the asteroid changes everything. The geometry of a sphere causes the paths to behave in surprising and counterintuitive ways compared to standard Euclidean expectations.
The post ultimately delivers the answer to this clever mathematical brainteaser, walking readers through the reasoning behind the solution. It is a great example of how switching from flat geometry to spherical geometry can completely transform a seemingly simple problem into something much richer and more complex. The puzzle is accessible and engaging, making it a wonderful entry point for anyone curious about the mathematics of curved surfaces.