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??????? ??????? ?????? ??????? , tessellations
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  • ??????? ?. ?????
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  • ????? ?????
  • ??? ??. ???????
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??? ????
?????? ??????  
  • Moore?Penrose pseudoinverse
  • ??????? ??????, Twistor theory
  • ????? ???????, Spin network
  • Abstract index notation
  • Black hole bomb
  • ?????-???? ????????, Geometry of spacetime
  • Cosmic censorship hypothesis
  • Weyl curvature hypothesis
  • Contributors to general relativity
  • Penrose interpretation of quantum mechanics
  • Diosi?Penrose model
  • Newman?Penrose formalism
  • Penrose diagram
  • Penrose inequality
  • Penrose process
  • Penrose tiling
  • Penrose stairs
  • Penrose graphical notation
  • Penrose transform
  • Terrell rotation
  • Penrose-Terrell effect
  • pp-wave spacetime
  • Schrodinger?Newton equations
  • Orch-OR/Penrose?Lucas argument
  • Free-orbit experiment with laser interferometry X-rays, FELIX experiment
  • Trapped surface
  • Andromeda paradox
  • Conformal cyclic cosmology
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  • ????? ???? (????)
  • ??????? ?????????????? ???? ??????? ???? (????)
  • ????? ?'?????? ????, (????)
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  • ????? ???? ??? ??????? (Lectureship) (????)
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  • ???? ???? ???? ???????, (?????????)
  • ????? ?????????????? ???, (????)
  • ?? ?????? ???, (????)
  • ?????? ???, (????)
  • ?'???? ???, (????)
  • ???????? ????, (????)
  • ?????? ???????? ?'??? ???? (????)

??? ?'??? ????'? ( ?????? : Sir Roger Penrose ; ????: ? ????? ????) ???? ?????? ????? ??????? ?????????, ???????, ???????? ???????? ??? ?????? ???????? ?'??? ???? ?????? ? ????? ???????? ??????????????? ???? ?? ??????? ?? ??????????? ? ????????? ????? ???? ????? ????? ????? ???????? ????, ???????????? ???? ????? (UCL) ??? ????????? ?????? ??? ????? ????????? ?????

????'?? ????? ??????????? ??? ?????? ????????????? ? ??????? ?????? ????????? ????? ??????? ?????? ???? ??? ??? ??? ???? ?????? ??? ?????? ???? ????? ???? ??????? ???? ??? ?????? ??? ?????? ????? ????? ?????? ???????? ???? ??? ??? ???? ?????? ????'?-???? ??????????? ?????? ? ???? ?????? ???????? ??????? ???? ? ??? ??????????? ??? ??????? ???? ??? ?????? ?????? ???????? ?'??? ???? ??? ?????? ????? ???? ?????? ???????? ??? ??- ?????????? ? ??? ?????????????? ?????? ??????? ??? ?????? ??????????? (for the discovery that black hole formation is a robust prediction of the general theory of relativity) ? ?????? ???? ???? ??? ?????? ???????? ?'??? ????????? ?????? ??? ?????????? ????? ?????? ??? ???? [1] [2]

?????????? ???? [ ???????? ??? ]

??????? ?'????????? ????????? ??? ?'??? ????'? ????????? (?????) ??? ?????? ???????? ??? ???????????? ???'??? ????'?? ?????? ?????? ????-????? (????? ????) ???? ????????????? ???? ??????????? ??. ???? ????'? ??? ????????? ???????? ?????? ????'???? ?????? ????? ???? ????-????? ???? ???????????? ??? ????????? ????? ??? ?'????? ???? ??????'?? [3] [4] ???? ??????'? ?????? ????? ???????? ?? ????? ???? ???????? ?????? ??????????? ??? ?????? ??????? [5] [3] ?????? ?????? ???? ??????????? ?'????? ????'?? ????? ??? ?????? ????????? ?? ?????? ????? ???? ?????? ????'?? [6] [7] ????'?? ????????? ?????? ????????? ?????? ????'?, ???????????? ????? ????? ??? ??? ???? ?????????????? ????? ????'?? [8] [9]

?'??? ????'?? ???????????? ???? ????? ??? ???????????? ???? ????? ? ??????????? ??????; ?'???? ?????? ???? ???????? ????? ??????? ?????? ?????? ???????? ???? [8]

?????? [ ???????? ??? ]

???? ??? ????? ?????? ??????????? ??? ???? ?????? ????'?? ?.???. ????? ??????? ????????? ??????? (generalised matrix inverse) ???????????? ???? ????? ????-????'? ??????? (Moore?Penrose inverse) ????? ??? ????? [10] ???? ??? ????? ????????? ????? ????-??????? ??????? [11] ????'?? ???????? ??? ???????????????? ??????? ??? ??????. ??. ??. ???? ????? ?????? ????? ?????? ??? ???? ??? ????????? ?????? ??? ????? ??? ?????????? ??? ??????????? ??.?. ??? ????? ??????? ?????? ??? ???? ????? ??????????? ??? ????- "tensor methods in algebraic geometry"? [12] ????? ???? ????'?? ????'? ??????? ? ????? ???? ??? ??? ???????? ??? ????? ????? ??? ????? ???? "?????????????? ??????? ???" (impossibility in its purest form)? ????? ???? ???? ??????????? ??.?? ??????? ???? ??????????? ??????? ???? ??????? ??????? ??? ???? ?????? ?????? ?????????? ?????? ????'?? ??????? ????????? ???????? ?????? [13] [14]

????????, The tribar

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

???? ??? ????'?? ???????? ?????? ??????? ???? ?? ??????? ?????????? ?????? (Minkowski space) ?????????? ?????? ???????????? ???? ?????? ??????? ???????? (?,?)? ???? ??????? ???? [16] [17]

???? ??? ??? ????'? ????? ? (Penrose tiling) ????????? ???? ????'? ????????? ????'?? ?? ?????? ???? ???? Deux types fondamentaux de distribution statistique ???? ?????????; [18] (1938; an English translation Two Basic Types of Statistical Distribution ) ???? ?????? ????????, ??????????? ??? ???????????? ??????? ??????? ???? ??? ??????? ??????? ??????? ???????????????? ??????? ???????? ?????? [19] ?????? ?? ??? ?????????? ????? ???? ???? ??? ??? ????? ??????? ????? ??????? ? ??????? ???????? ????? ??? ????????? ?????? ? ?????-???? ?????????? ????? ????? [20] ????'? ????? ?? ????'? ?????????? (Causal diagram) ???????? ????? ??????? ?????????? ?????? ???? [21]

???? ??? ?????? ???????? ???? ??????????????? ???????? ?????? ??? ?????? ??? ???????? ??? ???? ?????? ???? ?????? ??? ??? ???? [22]

??????? ???? [ ???????? ??? ]

???? ??? ????'?? ??? ?'? ?? ?????????: ? ??????? ???? ?? ??? ?'? ?? ???? ????????? (The Road to Reality: A Complete Guide to the Laws of the Universe) ??????? ???? ???? ?????????? ?? ????????? ?????? ???????? ?????????? ??????? ???????? ??? ???? ?????????? ????? ????????? ?????? ??????? ????????? ?????????? ????? ????'? ?? ?? Penrose interpretation -? ????????? ????????? ??? ?????? ????????????? ? ???? ??? ???????? ?????? ?????? ??? ??? ???????? ???????? ??- ?????-??? ??????? ????????? ??? ????????? ??????? ?????????? ????????? ????? ??? ????????? ???????????? ????? [23] [24]

???????? ???????????? [ ???????? ??? ]

??????? [ ???????? ??? ]

  • The Emperor's New Mind|The Emperor's New Mind: Concerning Computers, Minds, and The Laws of Physics (????) [25]
  • Shadows of the Mind|Shadows of the Mind: A Search for the Missing Science of Consciousness (????) [26]
  • The Road to Reality: A Complete Guide to the Laws of the Universe (????) [27]
  • Cycles of Time|Cycles of Time: An Extraordinary New View of the Universe (????) [28]
  • Fashion, Faith, and Fantasy in the New Physics of the Universe (????) [29]

??-???? ?????? [ ???????? ??? ]

  • The Nature of Space and Time ( ??????? ???? ? ????) (????) [30]
  • The Large, the Small and the Human Mind , ????? ???????, ?????? ????????? ??? ??????? ???? ? ???? (????)? [31]
  • White Mars: The Mind Set Free , ???????? ?????? ????, (????) [32]

???????????? ?????? [ ???????? ??? ]

  • Techniques of Differential Topology in Relativity (????), ??.??.??.??.   0-89871-005-7 )
  • Spinors and Space-Time: Volume 1, Two-Spinor Calculus and Relativistic Fields (???????? ????????? ????, ????) ??.??.??.??.   0-521-33707-0 (paperback)
  • Spinors and Space-Time: Volume 2, Spinor and Twistor Methods in Space-Time Geometry (???????? ????????? ????, ????) (???? ??????), ??.??.??.??.   0-521-34786-6 (????????)

??????? [ ???????? ??? ]

  1. ↑ "The Nobel Prize in Physics 2020" (en-US ?????). NobelPrize.org . https://www.nobelprize.org/prizes/physics/2020/summary/ ? ???? ??? ????: 2020-10-06 .  
  2. ↑ Overbye, Dennis; Taylor, Derrick Bryson (6 October 2020). "Nobel Prize in Physics Awarded to 3 Scientists for Work on Black Holes - The prize was awarded half to Roger Penrose for showing how black holes could form and half to Reinhard Genzel and Andrea Ghez for discovering a supermassive object at the Milky Way’s center." . The New York Times . https://www.nytimes.com/2020/10/06/science/nobel-prize-physics.html ? ???? ??? ????: 6 October 2020 .  
  3. ↑ 3.0 3.1 Brookfield, Tarah (2018) (en ?????). Our Voices Must Be Heard: Women and the Vote in Ontario . UBC Press. ISBN   978-0-7748-6022-2 . https://books.google.com/books?id=LVlxDwAAQBAJ&pg=PA126 .  
  4. ↑ Rudolph Peters (1958). "John Beresford Leathes. 1864?1956". Biographical Memoirs of Fellows of the Royal Society ???? 4 : 185?191. doi : 10.1098/rsbm.1958.0016 .  
  5. ↑ Roger Penrose. Cycles of Time: Is It Possible to Discern the Previous Universe Through the Big Bang? ???????
  6. ↑ Hall, Chris (19 March 2016). "Lee Miller, the mother I never knew" (en-GB ?????). The Guardian . ISSN   0261-3077 . https://www.theguardian.com/lifeandstyle/2016/mar/19/lee-miller-the-mother-i-never-knew .  
  7. ↑ "Illustrated Mathematics" (en-GB ?????). Farleys House and Gallery. Archived from the original on 11 October 2020 . https://web.archive.org/web/20201011191035/https://www.farleyshouseandgallery.co.uk/exhibitions/illustrated-mathematics/ ? ???? ??? ????: 7 October 2020 .  
  8. ↑ 8.0 8.1 "Roger Penrose ? Biography" (en ?????). Maths History . https://mathshistory.st-andrews.ac.uk/Biographies/Penrose/ ? ???? ??? ????: 7 October 2020 .  
  9. ↑ AP and TOI staff. "Scientist of Jewish heritage among trio to win Nobel prize for black hole finds" (en-US ?????). www.timesofisrael.com . https://www.timesofisrael.com/scientist-of-jewish-heritage-among-trio-to-win-nobel-prize-for-black-hole-finds/ ? ???? ??? ????: 7 October 2020 .  
  10. ↑ Penrose, R. (1955). "A generalized inverse for matrices". Mathematical Proceedings of the Cambridge Philosophical Society ???? 51 (3): 406?413. doi : 10.1017/S0305004100030401 .  
  11. ↑ Zheng, Wenjie. "The 100th anniversary of Moore-Penrose inverse and its role in statistics and machine learning" . www.zhengwenjie.net . http://www.zhengwenjie.net/pseudoinverse/ ? ???? ??? ????: 7 October 2020 .  
  12. ↑ "Roger Penrose wins 2020 Nobel Prize in Physics for discovery about black holes" (en ?????). University of Cambridge. 6 October 2020 . https://www.cam.ac.uk/research/news/roger-penrose-wins-2020-nobel-prize-in-physics-for-discovery-about-black-holes ? ???? ??? ????: 7 October 2020 .  
  13. ↑ Welch, Chris (23 March 2012). "'Frustro' typeface applies the Penrose impossible triangle concept to words" (en ?????). The Verge . https://www.theverge.com/2012/3/23/2898025/frustro-typeface-matrzi-hegedus-penrose-triangle ? ???? ??? ????: 7 October 2020 .  
  14. ↑ Baggini, Julian (2012) (en ?????). Philosophy: All That Matters . John Murray Press. ISBN   978-1-4441-5585-3 . https://books.google.com/books?id=rws0AgAAQBAJ&newbks=0&printsec=frontcover&pg=PT21&dq=roger+penrose+%22penrose+triangle%22+%22impossibility+in+its+purest+form%22&hl=en .  
  15. ↑ "Professor Sir Roger Penrose awarded the 2020 Nobel Prize in Physics" (en-EN ?????). King's College London . https://www.kcl.ac.uk/news/professor-sir-roger-penrose-awarded-the-2020-nobel-prize-in-physics ? ???? ??? ????: 7 October 2020 .  
  16. ↑ "New Horizons in Twistor Theory | Mathematical Institute" . www.maths.ox.ac.uk . http://www.maths.ox.ac.uk/groups/mathematical-physics/events/twistors50 ? ???? ??? ????: 7 October 2020 .  
  17. ↑ "twistor space in nLab" . ncatlab.org . https://ncatlab.org/nlab/show/twistor+space#TwistorsFor4dMinkowskiSpacetime ? ???? ??? ????: 7 October 2020 .  
  18. ↑ Jaromir Kor?ak (1938): Deux types fondamentaux de distribution statistique. Prague, Comite d'organisation, Bull. de l'Institute Int'l de Statistique, vol. 3, pp. 295?299.
  19. ↑ Steinhardt, Paul (1996). "New perspectives on forbidden symmetries, quasicrystals, and Penrose tilings" . Proceedings of the National Academy of Sciences ???? 93 (25): 14267?14270. doi : 10.1073/pnas.93.25.14267 . PMID   8962037 .  
  20. ↑ "Penrose on Spin Networks" . math.ucr.edu . https://math.ucr.edu/home/baez/penrose/ ? ???? ??? ????: 7 October 2020 .  
  21. ↑ "Penrose diagrams" (en ?????). jila.colorado.edu . https://jila.colorado.edu/~ajsh/insidebh/penrose.html ? ???? ??? ????: 7 October 2020 .  
  22. ↑ "Roger Penrose at Rice, 1983?87" . Rice History Corner . 22 May 2013 . http://ricehistorycorner.com/2013/05/22/roger-penrose-at-rice-1983-87/ .  
  23. ↑ Johnson, George (27 February 2005). "'The Road to Reality': A Really Long History of Time" . The New York Times, USA . https://www.nytimes.com/2005/02/27/books/review/the-road-to-reality-a-really-long-history-of-time.html?_r=0 ? ???? ??? ????: 3 April 2017 .  
  24. ↑ "If an Electron Can Be in Two Places at Once, Why Can't You?" . Archived from the original on 1 November 2012 . https://web.archive.org/web/20121101130211/http://discovermagazine.com/2005/jun/cover/article_view?b_start:int=0&-C= ? ???? ??? ????: 27 October 2008 .  
  25. ↑ Penrose, Roger (1989) (en ?????). The Emperor's New Mind . https://books.google.com/books?id=_ibtvQEACAAJ&newbks=0&hl=en .  
  26. ↑ Penrose, Roger (1994) (en ?????). Shadows of the Mind: A Search for the Missing Science of Consciousness . Oxford University Press. ISBN   978-0-19-510646-6 . https://books.google.com/books?id=gDbOAK89tmcC&newbks=0&printsec=frontcover&dq=Shadows+of+the+Mind:+A+Search+for+the+Missing+Science+of+Consciousness&hl=en .  
  27. ↑ Penrose, Roger (31 March 2016) (en ?????). The Road to Reality: A Complete Guide to the Laws of the Universe . Random House. ISBN   978-1-4464-1820-8 . https://books.google.com/books?id=VWTNCwAAQBAJ&newbks=0&hl=en .  
  28. ↑ Penrose, Roger (6 September 2011) (en ?????). Cycles of Time: An Extraordinary New View of the Universe . Knopf Doubleday Publishing Group. ISBN   978-0-307-59674-1 . https://books.google.com/books?id=gv8o1XydoCQC&newbks=0&printsec=frontcover&dq=Cycles+of+Time:+An+Extraordinary+New+View+of+the+Universe&hl=en .  
  29. ↑ Penrose, Roger (5 September 2017) (en ?????). Fashion, Faith, and Fantasy in the New Physics of the Universe . Princeton University Press. ISBN   978-0-691-17853-0 . https://books.google.com/books?id=9XKYDwAAQBAJ&newbks=0&printsec=frontcover&dq=Fashion,+Faith,+and+Fantasy+in+the+New+Physics+of+the+Universe&hl=en .  
  30. ↑ Hawking, Stephen W.; Penrose, Roger (1996) (en ?????). The Nature of Space and Time . Princeton University Press. ISBN   978-0-691-03791-2 . https://books.google.com/books?id=8RatQgAACAAJ&newbks=0&hl=en .  
  31. ↑ Penrose, Roger; Shimony, Abner; Cartwright, Nancy; Hawking, Stephen (28 April 2000) (en ?????). The Large, the Small and the Human Mind . Cambridge University Press. ISBN   978-0-521-78572-3 . https://books.google.com/books?id=jWHqlijAjyMC&newbks=0&printsec=frontcover&dq=The+Large,+the+Small+and+the+Human+Mind&hl=en .  
  32. ↑ Aldiss, Brian W.; Penrose, Roger (19 May 2015) (en ?????). White Mars; or, The Mind Set Free: A 21st-Century Utopia . Open Road Media. ISBN   978-1-5040-1028-3 . https://books.google.com/books?id=K_-jBwAAQBAJ&newbks=0&printsec=frontcover&dq=White+Mars:+The+Mind+Set+Free(1999)&hl=en .  

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