Everything we were taught in geometry falls apart if our universe is curved. This video is a friendly introduction to nonEuclidean geometry and how cosmologists used the Cosmic Microwave Background to calculate the curvature of our universe.

See Part Two of the shape of the universe duology here:    • So, space isn't a 4D Pringle... Maybe...  

This video is a submission to the second Summer of Math Exposition #some2. Hope you enjoy it!

Thank you to Caleb Birtwistle for captioning!

If you want to try out some of the code used in the video, check out this notebook on Geodesics on a Pringle: https://drive.google.com/file/d/1p2dv...

Become a Patreon member:   / physicsforthebirds  

0:00 Origami cranes, intro
3:04 Axioms of Euclidean geometry
5:24 Hyperbolic geometry
7:59 Curvature of our universe with the CMB
11:44 Conclusion

Alperin, Hayes, Lang, "Folding the Hyperbolic Crane": https://www.langorigami.com/wpconten...
Euclid, Elements: https://archive.org/details/euclid_he...
Playfair's Axiom: https://archive.org/details/elementsg...
Bolyai, The Science Absolute of Space: https://jscholarship.library.jhu.edu/...
Liddle, An Introduction to Modern Cosmology: http://alpha.sinp.msu.ru/~panov/LibBo...
Olive, Peacock, "BigBang Cosmology": https://pdg.lbl.gov/2018/reviews/rpp2...
Planck 2018 results: https://arxiv.org/pdf/1807.06209.pdf

Image Credit NASA / WMAP Science Team.