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Curated by: Physics for the Birds (26 videos)
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. See Part Two of the shape of the universe duology here: https://youtu.be/qeLkEHmPbYI 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/1p2dvarjbPJem-EEFuX3w1oIRCjqDh-in/view?usp=sharing Become a Patreon member: https://www.patreon.com/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/wp-content/uploads/2015/09/hyperbolic-crane.pdf Euclid, Elements: https://archive.org/details/euclid_heath_2nd_ed/1_euclid_heath_2nd_ed/page/n167/mode/2up?view=theater Playfair's Axiom: https://archive.org/details/elementsgeometr05playgoog/page/n34/mode/2up?view=theater Bolyai, The Science Absolute of Space: https://jscholarship.library.jhu.edu/bitstream/handle/1774.2/34236/31151000225759.pdf?sequence=76&isAllowed=y Liddle, An Introduction to Modern Cosmology: http://alpha.sinp.msu.ru/~panov/LibBooks/CS/liddle_a_an_introduction_to_modern_cosmology.pdf Olive, Peacock, "Big-Bang Cosmology": https://pdg.lbl.gov/2018/reviews/rpp2018-rev-bbang-cosmology.pdf Planck 2018 results: https://arxiv.org/pdf/1807.06209.pdf Image Credit NASA / WMAP Science Team.