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How One Line in the Oldest Math Text Hinted at Hidden Universes
Discover strange new universes that turn up at the core of Einstein’s General Relativity. Head to https://brilliant.org/veritasium to start your free 30-day trial, and the first 200 people get 20% off an annual premium subscription.
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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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