Come una frase nel più antico testo matematico svela universi nascosti

A huge 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. Finally, a huge thank you to Dr. Henry Segerman and Dr. Rémi Coulon for helping us visualize what it means to be inside hyperbolic space and for helping us understand hyperbolic geometry. Euclid via Science Museum Group - https://ve42.co/Euclid Geodetic Survey via ams - https://ve42.co/Geodesy John Wheeler via NAS Online - https://ve42.co/Wheeler 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 Euclidean 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 absolute science 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 That Underlie 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 Frontier Fields. ESA/Hubble. - https://ve42.co/Einstein1905 Agazie, G., et al. (2023). The 15-Year NANOGrav Dataset: Constraints on Binary Supermassive Black Holes 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 Contents of the Universe. 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 Knitting hyperbolic planes: Daina Taimina by Ted, via YouTube - https://ve42.co/Hyperbolic Hyperbolic crochet pattern - https://ve42.co/Crochet 👉 This channel is created in collaboration with    / @veritasium   and localized in your language by https://www.linguana.com 0:00 - The Enigma of Euclid's Elements 0:52 - The Birth of Mathematical Proof 2:32 - The Postulates and the Parallel Problem 5:14 - The Failure of Proofs 6:57 - Bolyai's Revolution and Geometry Hyperbolic Geometry 10:26 AM - Gauss, Lobachevsky, and Non-Euclidean Geometry 1:30 PM - Riemann, Relativity, and Curved Geometry 7:50 PM - Geometry in the Universe and Modern Confirmations