We live on a 4-dimensional Pringle (Non-Euclidean Geometry and the shape of the Universe)
Everything we were taught in geometry falls apart if our universe is curved. This video is a friendly introduction to non-Euclidean geometry and how cosmologists used the Cosmic Microwave Background to calculate the curvature of our universe.
This video is a submission to the second Summer of Math Exposition #some2. Hope you enjoy it!
If you want to try out some of the code used in the video, check out this notebook on Geodesics on a Pringle:
Alperin, Hayes, Lang, “Folding the Hyperbolic Crane“:
Euclid, Elements:
Playfair’s Axiom:
Bolyai, The Science Absolute of Space:
Liddle, An Introduction to Modern Cosmology: ~panov/LibBooks/CS/
Olive, Peacock, “Big-Bang Cosmology“:
Planck 2018 results:
Image Credit NASA / WMAP Science Team.
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