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If you’re looking for a molecular modeling kit, try Snatoms – a kit I invented where the atoms snap together magnetically – https://ve42.co/SnatomsV
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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 Non-Euclidean 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). Non-Euclidean 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 Non-Euclidean 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). Non-euclidean 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). Gauss-Bolyai-Lobachevsky: The dawn of non-euclidean 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), 891-921. - https://ve42.co/Einstein1905
ESA/Hubble. (n.d.). Hubblecast 90: The final frontier of the Frontier Fields. ESA/Hubble. - https://ve42.co/Einstein1905
Agazie, G., et al. (2023). The NANOGrav 15 yr data set: Constraints on supermassive black hole binaries from the gravitational-wave 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
Additional video/photos supplied by Getty Images, Pond5, and by courtesy of: NASA, NASA's Goddard Space Flight Center, NASA Goddard Flight Lab/ CI Lab, NASA’s WMAP science teams, ESO, and ESA/Hubble.
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