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.