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A massive thank you to Prof. Alex Kontorovich for all his help with this video.

A huge thank you to Prof. Geraint Lewis and Dr. Ashmeet Singh for helping us understand the applications of NonEuclidean geometry in astronomy/cosmology.

Lastly, a big thank you to Dr. Henry Segerman and Dr. Rémi Coulon for helping us visualize what it’s like to be inside hyperbolic space and helping us understand hyperbolic geometry.

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Images:
Euclid via Science Museum Group https://ve42.co/Euclid

Geodesy survey via ams https://ve42.co/Geodesy

John Wheeler via NAS Online https://ve42.co/Wheeler

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References:
Dunham, W. (1991). Journey through Genius: Great Theorems of Mathematics. John Wiley & Sons.

Bonola, R. (1955). NonEuclidean geometry: A critical and historical study of its development. Courier Corporation.

Library of Congress. (n.d.). The Library of Congress. https://ve42.co/LibofCongress

Euclid’s Elements, Wikipedia https://ve42.co/Elements

The History of NonEuclidean Geometry, Extra History via YouTube https://ve42.co/ExtraHistory

We (could) live on a 4D Pringle Physics for the Birds via YouTube https://ve42.co/4DPringle

Parallel Postulate, Wikipedia https://ve42.co/Parallel

Prékopa, A., & Molnár, E. (Eds.). (2006). Noneuclidean geometries: János Bolyai memorial volume (Vol. 581). Springer Science & Business Media.

St Andrews, University of. (n.d.). Bolyai. MacTutor History of Mathematics. https://ve42.co/Bolyai

Bolyai, J. (1896). The Science Absolute of Space.. (Vol. 3). The Neomon.

Gauss, Wikipedia https://ve42.co/Gauss

Singh, U. (2022). GaussBolyaiLobachevsky: The dawn of noneuclidean geometry. Medium. https://ve42.co/CPNonEuclidean

Landvermessung, D. Z. (1929). Abhandlungen ueber Gauss' wissenschaftliche Taetigkeit auf den Gebieten der Geodaesie, Physik und Astronomie Bd. 11, Abt. https://ve42.co/Landvermessung

Nikolai Lobachevsky, Wikipedia https://ve42.co/Lobachevsky

Lobachevskiĭ, N. I. (1891). Geometrical researches on the theory of parallels. University of Texas.

A Problem with the Parallel Postulate, Numberphile via YouTube https://ve42.co/NumberphileParallel

Riemann, B. (2016). On the hypotheses which lie at the bases of geometry. Birkhäuser. https://ve42.co/Riemann

Einstein, A. (1905). On the electrodynamics of moving bodies. Annalen der physik, 17(10), 891921. https://ve42.co/Einstein1905'>https://ve42.co/Einstein1905

ESA/Hubble. (n.d.). Hubblecast 90: The final frontier of the Frontier Fields. ESA/Hubble. https://ve42.co/Einstein1905'>https://ve42.co/Einstein1905

Agazie, G., et al. (2023). The NANOGrav 15 yr data set: Constraints on supermassive black hole binaries from the gravitationalwave background. https://ve42.co/NANOGrav

Secrets of the Cosmic Microwave Background, PBS Spacetime via YouTube https://ve42.co/PBSCMB

Wood, C. (2020). How Ancient Light Reveals the Universe's Contents. Quanta Magazine. https://ve42.co/AncientLight

Collaboration (2014). Planck 2013 results. XVI. Cosmological parameters. A&A, 571, A16. https://ve42.co/Planck2013

WMAP Science Team, NASA. (2014). Matter in the Universe. WMAP, NASA. https://ve42.co/WMAP2014

What Is The Shape of Space, minutephysics via YouTube https://ve42.co/SpaceShape

Shape of the universe, Wikipedia https://ve42.co/UniverseShape

Crocheting Hyperbolic Planes: Daina Taimina by Ted, via YouTube https://ve42.co/Hyperbolic

Hyperbolic Crochet model https://ve42.co/Crochet

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Directed by Casper Mebius
Written by Casper Mebius, Petr Lebedev, Emily Zhang, Derek Muller, and Alex Kontorovich
Edited by Jack Saxon
Animated by Fabio Albertelli, Ivy Tello, and Mike Radjabov
Illustrations by Jakub Misiek and Celia Bode
Filmed by Derek Muller
Produced by Casper Mebius, Derek Muller, and Han Evans

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