131
TIL Colorado isn’t a rectangle and actually has 697 sides, mostly due to poor measurement tools
(www.atlasobscura.com)
this post was submitted on 06 Aug 2024
131 points (97.8% liked)
Today I Learned (TIL)
6549 readers
28 users here now
You learn something new every day; what did you learn today?
/c/til is a community for any true knowledge that you would like to share, regardless of topic or of source.
Share your knowledge and experience!
Rules
- Information must be true
- Follow site rules
- No, you don't have to have literally learned the fact today
- Posts must be about something you learned
founded 2 years ago
MODERATORS
you are viewing a single comment's thread
view the rest of the comments
view the rest of the comments
Good point. Four equal angles, then, although they will each have to be greater than 90 degrees.
I don't think that would work for just 4 lines? I think you have to have arcs, not straight lines
It's possible to have an equiangular quadrilateral, i.e. whose sides are geodesics (the analogue of "straight line" on a sphere). The Gauss-Bonnet theorem implies their total interior angle is greater than 2pi, so four right angles can't work.
Here's an interactive demo of quadrilaterals on the sphere: https://geogebra.org/m/q83rUj8r
Notice that each side is a segment of a great circle, i.e. a circle that divides the sphere in half. That's what it means for a path to be a geodesic on the sphere.