Möbius strip (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Möbius strip" in English language version.

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Cartwright, Julyan H. E.; González, Diego L. (2016). "Möbius strips before Möbius: topological hints in ancient representations". The Mathematical Intelligencer. 38 (2): 69–76. arXiv:1609.07779. Bibcode:2016arXiv160907779C. doi:10.1007/s00283-016-9631-8. MR 3507121. S2CID 119587191.
Flapan, Erica (2000). When Topology Meets Chemistry: A Topological Look at Molecular Chirality. Outlooks. Washington, DC: Mathematical Association of America. pp. 82–83. doi:10.1017/CBO9780511626272. ISBN 0-521-66254-0. MR 1781912.
Frolkina, Olga D. (2018). "Pairwise disjoint Moebius bands in space". Journal of Knot Theory and Its Ramifications. 27 (9): 1842005, 9. arXiv:2212.02983. doi:10.1142/S0218216518420051. MR 3848635. S2CID 126421578.
Melikhov, Sergey A. (2019). "A note on O. Frolkina's paper "Pairwise disjoint Moebius bands in space"". Journal of Knot Theory and Its Ramifications. 28 (7): 1971001, 3. arXiv:1810.04089. doi:10.1142/s0218216519710019. MR 3975576. S2CID 119179202.
Kyle, R. H. (1955). "Embeddings of Möbius bands in 3-dimensional space". Proceedings of the Royal Irish Academy, Section A. 57: 131–136. JSTOR 20488581. MR 0091480.
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Larsen, Mogens Esrom (1994). "Misunderstanding my mazy mazes may make me miserable". In Guy, Richard K.; Woodrow, Robert E. (eds.). Proceedings of the Eugène Strens Memorial Conference on Recreational Mathematics and its History held at the University of Calgary, Calgary, Alberta, August 1986. MAA Spectrum. Washington, DC: Mathematical Association of America. pp. 289–293. ISBN 0-88385-516-X. MR 1303141.. See Figure 7, p. 292.
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Pook, Les (2003). "4.2: The trihexaflexagon revisited". Flexagons Inside Out. Cambridge, UK: Cambridge University Press. pp. 33–36. doi:10.1017/CBO9780511543302. ISBN 0-521-81970-9. MR 2008500.
Kühnel, W.; Banchoff, T. F. (1983). "The 9-vertex complex projective plane" (PDF). The Mathematical Intelligencer. 5 (3): 11–22. doi:10.1007/BF03026567. MR 0737686. S2CID 120926324.
Kuiper, Nicolaas H. (1972). "Tight topological embeddings of the Moebius band". Journal of Differential Geometry. 6 (3): 271–283. doi:10.4310/jdg/1214430493. MR 0314057.
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Tuckerman, Bryant (1948). "A non-singular polyhedral Möbius band whose boundary is a triangle". American Mathematical Monthly. 55 (5): 309–311. doi:10.2307/2305482. JSTOR 2305482. MR 0024138.
Bonnington, C. Paul; Nakamoto, Atsuhiro (2008). "Geometric realization of a triangulation on the projective plane with one face removed". Discrete & Computational Geometry. 40 (1): 141–157. doi:10.1007/s00454-007-9035-9. MR 2429652. S2CID 10887519.
Brehm, Ulrich (1983). "A nonpolyhedral triangulated Möbius strip". Proceedings of the American Mathematical Society. 89 (3): 519–522. doi:10.2307/2045508. JSTOR 2045508. MR 0715878.
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Hinz, Denis F.; Fried, Eliot (2015). "Translation of Michael Sadowsky's paper "An elementary proof for the existence of a developable Möbius band and the attribution of the geometric problem to a variational problem"". Journal of Elasticity. 119 (1–2): 3–6. arXiv:1408.3034. doi:10.1007/s10659-014-9490-5. MR 3326180. S2CID 119733903. Reprinted in Fosdick, Roger; Fried, Eliot (2016). The Mechanics of Ribbons and Möbius Bands (PDF). Springer, Dordrecht. pp. 3–6. doi:10.1007/978-94-017-7300-3. ISBN 978-94-017-7299-0. MR 3381564.
Bartels, Sören; Hornung, Peter (2015). "Bending paper and the Möbius strip". Journal of Elasticity. 119 (1–2): 113–136. doi:10.1007/s10659-014-9501-6. MR 3326187. S2CID 119782792. Reprinted in Fosdick & Fried (2016), pp. 113–136. See in particular Section 5.2, pp. 129–130.
Starostin, E. L.; van der Heijden, G. H. M. (2015). "Equilibrium shapes with stress localisation for inextensible elastic Möbius and other strips". Journal of Elasticity. 119 (1–2): 67–112. doi:10.1007/s10659-014-9495-0. MR 3326186. S2CID 53462568. Reprinted in Fosdick & Fried (2016), pp. 67–112.
Schwarz, Gideon E. (1990). "The dark side of the Moebius strip". The American Mathematical Monthly. 97 (10): 890–897. doi:10.1080/00029890.1990.11995680. JSTOR 2324325. MR 1079975.
Halpern, B.; Weaver, C. (1977). "Inverting a cylinder through isometric immersions and isometric embeddings". Transactions of the American Mathematical Society. 230: 41–70. doi:10.2307/1997711. JSTOR 1997711. MR 0474388.
Schwartz, Richard Evan (2021). "An improved bound on the optimal paper Moebius band". Geometriae Dedicata. 215: 255–267. arXiv:2008.11610. doi:10.1007/s10711-021-00648-5. MR 4330341. S2CID 220279013.
Dundas, Bjørn Ian (2018). "Example 5.1.3: The unbounded Möbius band". A Short Course in Differential Topology. Cambridge Mathematical Textbooks. Cambridge University Press, Cambridge. p. https://books.google.com/books?id=7a1eDwAAQBAJ&pg=PA101. doi:10.1017/9781108349130. ISBN 978-1-108-42579-7. MR 3793640. S2CID 125997451.
Blanuša, Danilo (1954). "Le plongement isométrique de la bande de Möbius infiniment large euclidienne dans un espace sphérique, parabolique ou hyperbolique à quatre dimensions". Bulletin International de l'Académie Yougoslave des Sciences et des Beaux-Arts. 12: 19–23. MR 0071060.
Wunderlich, W. (1962). "Über ein abwickelbares Möbiusband". Monatshefte für Mathematik. 66 (3): 276–289. doi:10.1007/BF01299052. MR 0143115. S2CID 122215321.
Schwarz, Gideon (1990). "A pretender to the title 'canonical Moebius strip'". Pacific Journal of Mathematics. 143 (1): 195–200. doi:10.2140/pjm.1990.143.195. MR 1047406.
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Richeson, David S. (2008). Euler's Gem: The Polyhedron Formula and the Birth of Topology. Princeton, New Jersey: Princeton University Press. p. 171. ISBN 978-0-691-12677-7. MR 2440945.
Godinho, Leonor; Natário, José (2014). An Introduction to Riemannian Geometry: With Applications to Mechanics and Relativity. Universitext. Springer, Cham. pp. 152–153. doi:10.1007/978-3-319-08666-8. ISBN 978-3-319-08665-1. MR 3289090.
Cantwell, John; Conlon, Lawrence (2015). "Hyperbolic geometry and homotopic homeomorphisms of surfaces". Geometriae Dedicata. 177: 27–42. arXiv:1305.1379. doi:10.1007/s10711-014-9975-1. MR 3370020. S2CID 119640200.
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Gorbatsevich, V. V.; Onishchik, A. L.; Vinberg, È. B. (1993). Lie groups and Lie algebras I: Foundations of Lie Theory; Lie Transformation Groups. Encyclopaedia of Mathematical Sciences. Vol. 20. Springer-Verlag, Berlin. pp. 164–166. doi:10.1007/978-3-642-57999-8. ISBN 3-540-18697-2. MR 1306737.
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archive.org

Pickover, Clifford A. (2005). The Möbius Strip: Dr. August Möbius's Marvelous Band in Mathematics, Games, Literature, Art, Technology, and Cosmology. Thunder's Mouth Press. pp. 28–29. ISBN 978-1-56025-826-1.
Barr, Stephen (1964). Experiments in Topology. New York: Thomas Y. Crowell Company. pp. 40–49, 200–201. ISBN 9780690278620.

arstechnica.com

Gitig, Diana (October 18, 2010). "Chemical origami used to create a DNA Möbius strip". Ars Technica. Retrieved 2022-03-28.

artnet.com

news.artnet.com

Gopnik, Blake (October 17, 2014). "Pedro Reyes Makes an Infinite Love Seat". Artnet News.

arxiv.org

Cartwright, Julyan H. E.; González, Diego L. (2016). "Möbius strips before Möbius: topological hints in ancient representations". The Mathematical Intelligencer. 38 (2): 69–76. arXiv:1609.07779. Bibcode:2016arXiv160907779C. doi:10.1007/s00283-016-9631-8. MR 3507121. S2CID 119587191.
Frolkina, Olga D. (2018). "Pairwise disjoint Moebius bands in space". Journal of Knot Theory and Its Ramifications. 27 (9): 1842005, 9. arXiv:2212.02983. doi:10.1142/S0218216518420051. MR 3848635. S2CID 126421578.
Melikhov, Sergey A. (2019). "A note on O. Frolkina's paper "Pairwise disjoint Moebius bands in space"". Journal of Knot Theory and Its Ramifications. 28 (7): 1971001, 3. arXiv:1810.04089. doi:10.1142/s0218216519710019. MR 3975576. S2CID 119179202.
Hinz, Denis F.; Fried, Eliot (2015). "Translation of Michael Sadowsky's paper "An elementary proof for the existence of a developable Möbius band and the attribution of the geometric problem to a variational problem"". Journal of Elasticity. 119 (1–2): 3–6. arXiv:1408.3034. doi:10.1007/s10659-014-9490-5. MR 3326180. S2CID 119733903. Reprinted in Fosdick, Roger; Fried, Eliot (2016). The Mechanics of Ribbons and Möbius Bands (PDF). Springer, Dordrecht. pp. 3–6. doi:10.1007/978-94-017-7300-3. ISBN 978-94-017-7299-0. MR 3381564.
Schwartz, Richard Evan (2021). "An improved bound on the optimal paper Moebius band". Geometriae Dedicata. 215: 255–267. arXiv:2008.11610. doi:10.1007/s10711-021-00648-5. MR 4330341. S2CID 220279013.
Schwartz, Richard (2023). "The optimal paper Moebius band". arXiv:2308.12641 [math.MG].
Schleimer, Saul; Segerman, Henry (2012). "Sculptures in $S 3$ ". In Bosch, Robert; McKenna, Douglas; Sarhangi, Reza (eds.). Proceedings of Bridges 2012: Mathematics, Music, Art, Architecture, Culture. Phoenix, Arizona: Tessellations Publishing. pp. 103–110. arXiv:1204.4952. ISBN 978-1-938664-00-7.
Cantwell, John; Conlon, Lawrence (2015). "Hyperbolic geometry and homotopic homeomorphisms of surfaces". Geometriae Dedicata. 177: 27–42. arXiv:1305.1379. doi:10.1007/s10711-014-9975-1. MR 3370020. S2CID 119640200.
Yamashiro, Atsushi; Shimoi, Yukihiro; Harigaya, Kikuo; Wakabayashi, Katsunori (2004). "Novel electronic states in graphene ribbons: competing spin and charge orders". Physica E. 22 (1–3): 688–691. arXiv:cond-mat/0309636. Bibcode:2004PhyE...22..688Y. doi:10.1016/j.physe.2003.12.100. S2CID 17102453.

books.google.com

Flapan, Erica (2000). When Topology Meets Chemistry: A Topological Look at Molecular Chirality. Outlooks. Washington, DC: Mathematical Association of America. pp. 82–83. doi:10.1017/CBO9780511626272. ISBN 0-521-66254-0. MR 1781912.
Massey, William S. (1991). A Basic Course in Algebraic Topology. Graduate Texts in Mathematics. Vol. 127. New York: Springer-Verlag. p. 49. ISBN 0-387-97430-X. MR 1095046.
Rouse Ball, W. W. (1892). "Paradromic rings". Mathematical Recreations and Problems of Past and Present Times (2nd ed.). London & New York: Macmillan and co. pp. 53–54. ISBN 9780608377803.
Larsen, Mogens Esrom (1994). "Misunderstanding my mazy mazes may make me miserable". In Guy, Richard K.; Woodrow, Robert E. (eds.). Proceedings of the Eugène Strens Memorial Conference on Recreational Mathematics and its History held at the University of Calgary, Calgary, Alberta, August 1986. MAA Spectrum. Washington, DC: Mathematical Association of America. pp. 289–293. ISBN 0-88385-516-X. MR 1303141.. See Figure 7, p. 292.
Junghenn, Hugo D. (2015). A Course in Real Analysis. Boca Raton, Florida: CRC Press. p. 430. ISBN 978-1-4822-1927-2. MR 3309241.
Dooner, David B.; Seireg, Ali (1995). "3.4.2 The cylindroid". The Kinematic Geometry of Gearing: A Concurrent Engineering Approach. Wiley Series in Design Engineering. Vol. 3. John Wiley & Sons. pp. 135–137. ISBN 9780471045977.
Pook, Les (2003). "4.2: The trihexaflexagon revisited". Flexagons Inside Out. Cambridge, UK: Cambridge University Press. pp. 33–36. doi:10.1017/CBO9780511543302. ISBN 0-521-81970-9. MR 2008500.
Dundas, Bjørn Ian (2018). "Example 5.1.3: The unbounded Möbius band". A Short Course in Differential Topology. Cambridge Mathematical Textbooks. Cambridge University Press, Cambridge. p. https://books.google.com/books?id=7a1eDwAAQBAJ&pg=PA101. doi:10.1017/9781108349130. ISBN 978-1-108-42579-7. MR 3793640. S2CID 125997451.
Flapan, Erica (2016). Knots, Molecules, and the Universe: An Introduction to Topology. Providence, Rhode Island: American Mathematical Society. pp. 99–100. doi:10.1090/mbk/096. ISBN 978-1-4704-2535-7. MR 3443369.
Richeson, David S. (2008). Euler's Gem: The Polyhedron Formula and the Birth of Topology. Princeton, New Jersey: Princeton University Press. p. 171. ISBN 978-0-691-12677-7. MR 2440945.
Godinho, Leonor; Natário, José (2014). An Introduction to Riemannian Geometry: With Applications to Mechanics and Relativity. Universitext. Springer, Cham. pp. 152–153. doi:10.1007/978-3-319-08666-8. ISBN 978-3-319-08665-1. MR 3289090.
Seifert, Herbert; Threlfall, William (1980). A Textbook of Topology. Pure and Applied Mathematics. Vol. 89. Translated by Goldman, Michael A. New York & London: Academic Press. p. 12. ISBN 0-12-634850-2. MR 0575168.
Fomenko, Anatolij T.; Kunii, Tosiyasu L. (2013). Topological Modeling for Visualization. Springer. p. 269. ISBN 9784431669562.
Isham, Chris J. (1999). Modern Differential Geometry for Physicists. World Scientific lecture notes in physics. Vol. 61 (2nd ed.). World Scientific. p. 269. ISBN 981-02-3555-0. MR 1698234.
Gorbatsevich, V. V.; Onishchik, A. L.; Vinberg, È. B. (1993). Lie groups and Lie algebras I: Foundations of Lie Theory; Lie Transformation Groups. Encyclopaedia of Mathematical Sciences. Vol. 20. Springer-Verlag, Berlin. pp. 164–166. doi:10.1007/978-3-642-57999-8. ISBN 3-540-18697-2. MR 1306737.
Easdown, Martin (2012). Amusement Park Rides. Bloomsbury Publishing. p. 43. ISBN 9781782001522.
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Tobler, Waldo R. (1961). "A world map on a Möbius strip". Surveying & Mapping. 21: 486.
Byers, Mark (2018). Charles Olson and American Modernism: The Practice of the Self. Oxford University Press. pp. 77–78. ISBN 9780198813255.
Peterson, Ivars (2002). "Recycling topology". Mathematical Treks: From Surreal Numbers to Magic Circles. MAA Spectrum. Mathematical Association of America, Washington, DC. pp. 31–35. ISBN 0-88385-537-2. MR 1874198.
Gardner, Martin (1956). "The Afghan Bands". Mathematics, Magic and Mystery. New York: Dover Books. pp. 70–73.

bridgesmathart.org

archive.bridgesmathart.org

Séquin, Carlo H. (2005). "Splitting tori, knots, and Moebius bands". In Sarhangi, Reza; Moody, Robert V. (eds.). Renaissance Banff: Mathematics, Music, Art, Culture. Southwestern College, Winfield, Kansas: Bridges Conference. pp. 211–218. ISBN 0-9665201-6-5.
Schleimer, Saul; Segerman, Henry (2012). "Sculptures in $S 3$ ". In Bosch, Robert; McKenna, Douglas; Sarhangi, Reza (eds.). Proceedings of Bridges 2012: Mathematics, Music, Art, Architecture, Culture. Phoenix, Arizona: Tessellations Publishing. pp. 103–110. arXiv:1204.4952. ISBN 978-1-938664-00-7.
Brecher, Kenneth (2017). "Art of infinity". In Swart, David; Séquin, Carlo H.; Fenyvesi, Kristóf (eds.). Proceedings of Bridges 2017: Mathematics, Art, Music, Architecture, Education, Culture. Phoenix, Arizona: Tessellations Publishing. pp. 153–158. ISBN 978-1-938664-22-9.
Thulaseedas, Jolly; Krawczyk, Robert J. (2003). "Möbius concepts in architecture". In Barrallo, Javier; Friedman, Nathaniel; Maldonado, Juan Antonio; Mart\'\inez-Aroza, José; Sarhangi, Reza; Séquin, Carlo (eds.). Meeting Alhambra, ISAMA-BRIDGES Conference Proceedings. Granada, Spain: University of Granada. pp. 353–360. ISBN 84-930669-1-5.

brown.edu

math.brown.edu

Kühnel, W.; Banchoff, T. F. (1983). "The 9-vertex complex projective plane" (PDF). The Mathematical Intelligencer. 5 (3): 11–22. doi:10.1007/BF03026567. MR 0737686. S2CID 120926324.

doi.org

Cartwright, Julyan H. E.; González, Diego L. (2016). "Möbius strips before Möbius: topological hints in ancient representations". The Mathematical Intelligencer. 38 (2): 69–76. arXiv:1609.07779. Bibcode:2016arXiv160907779C. doi:10.1007/s00283-016-9631-8. MR 3507121. S2CID 119587191.
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