The discussion at mathpuzzle.com has mostly been about the longest snakes that can fit inside a square of side 2:
What are the longest 30o snakes you can find in some small squares? How about 22.5o snakes? What about the longest snakes that fit inside rectangles? circles?
Here are the longest known 30o snakes inside small squares:
Here are the longest known 22.5o snakes inside small squares:
Here are the longest known 18o snakes inside small squares:
Here are the longest known 45o snake loops inside small squares:
Here are the longest known 30o snake loops inside small squares:
Here are the longest 45o snakes inside some small rectangles:
Here are the longest 30o snakes inside some equilateral triangles:
Here are the longest 30o snakes inside some circles:
Trevor Green and Jeremy Galvagni worked on an efficient snake in rectangles of width 1 and d small. The basic idea is shown below:
Serhiy Grabarchuk found the longest 30o snakes inside regular polygons:
Serhiy Grabarchuk also found the longest 30o snake on the surface of a unit cube. The red lines are on the front faces, and the blue lines are on the back faces.
In November 2006, Al Zimmerman held a contest to find the largest possible 360/N degree snakes inside a circle of diameter D, for small N and D. Below is a table showing the best results.
If you can extend any of these results, please e-mail me. Click here to go back to Math Magic. Last updated 8/23/08.