Editing Möbius strip (section)

==References==
{{reflist|refs=

<ref name=9vertex>{{cite journal
 | last1 = Kühnel | first1 = W.
 | last2 = Banchoff | first2 = T. F. | author2-link = Thomas Banchoff
 | doi = 10.1007/BF03026567
 | issue = 3
 | journal = [[The Mathematical Intelligencer]]
 | mr = 737686
 | pages = 11–22
 | title = The 9-vertex complex projective plane
 | url = https://www.math.brown.edu/tbanchof/howison/newbanchoff/publications/pdfs/9Vertex.pdf
 | volume = 5
 | year = 1983| s2cid = 120926324
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<ref name=ancient>{{cite journal
 | last1 = Cartwright | first1 = Julyan H. E. | author1-link = Julyan Cartwright 
 | last2 = González | first2 = Diego L.
 | arxiv = 1609.07779
 | bibcode = 2016arXiv160907779C
 | doi = 10.1007/s00283-016-9631-8
 | issue = 2
 | journal = [[The Mathematical Intelligencer]]
 | mr = 3507121
 | pages = 69–76
 | title = Möbius strips before Möbius: topological hints in ancient representations
 | volume = 38
 | year = 2016| s2cid = 119587191
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<ref name=architecture>{{cite conference
 | last1 = Thulaseedas | first1 = Jolly
 | last2 = Krawczyk | first2 = Robert J.
 | editor1-last = Barrallo | editor1-first = Javier
 | editor2-last = Friedman | editor2-first = Nathaniel
 | editor3-last = Maldonado | editor3-first = Juan Antonio
 | editor4-last = Mart\'\inez-Aroza | editor4-first = José
 | editor5-last = Sarhangi | editor5-first = Reza
 | editor6-last = Séquin | editor6-first = Carlo
 | contribution = Möbius concepts in architecture
 | contribution-url = https://archive.bridgesmathart.org/2003/bridges2003-353.html
 | isbn = 84-930669-1-5
 | location = Granada, Spain
 | pages = 353–360
 | publisher = University of Granada
 | title = Meeting Alhambra, ISAMA-BRIDGES Conference Proceedings
 | year = 2003}}</ref>

<ref name=aromaticity1>{{cite journal
 | last = Rzepa | first = Henry S.
 | date = September 2005
 | doi = 10.1021/cr030092l
 | issue = 10
 | journal = Chemical Reviews
 | pages = 3697–3715
 | title = Möbius aromaticity and delocalization
 | volume = 105| pmid = 16218564
 }}</ref>

<ref name=aromaticity2>{{cite journal
 | last1 = Yoon | first1 = Zin Seok
 | last2 = Osuka | first2 = Atsuhiro
 | last3 = Kim | first3 = Dongho
 | date = May 2009
 | doi = 10.1038/nchem.172
 | issue = 2
 | journal = Nature Chemistry
 | pages = 113–122
 | title = Möbius aromaticity and antiaromaticity in expanded porphyrins
 | volume = 1| pmid = 21378823
 | bibcode = 2009NatCh...1..113Y
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<ref name=bacon>{{cite web|url=https://www.theverge.com/2014/9/5/6110563/mobius-bacon-recipe|first=Ross|last=Miller|title=How to make a mathematically-endless strip of bacon|date=September 5, 2014|work=The Verge}}</ref>

<ref name=bagel>{{cite web|url=https://www.npr.org/sections/thesalt/2015/08/06/429437860/cut-your-bagel-the-mathematically-correct-way|publisher=NPR|title=Cut Your Bagel The Mathematically Correct Way|work=The Salt|first=Dan|last=Pashman|date=August 6, 2015}}</ref>

<ref name=bandband>{{cite magazine|url=https://magnetmagazine.com/2007/08/30/mobius-band-friendly-fire/|title=Mobius Band: Friendly Fire|magazine=[[Magnet (magazine)|Magnet]]|date=August 30, 2007|first=Andrew|last=Parks}}</ref>

<ref name=barr>{{cite book
 | last = Barr | first = Stephen
 | location = New York
 | pages = 40–49, 200–201
 | publisher = Thomas Y. Crowell Company
 | title = Experiments in Topology
 | url = https://archive.org/details/experimentsintop00barr
 | year = 1964| isbn = ((9780690278620))
 }}</ref>

<ref name=bartels-hornung>{{cite journal
 | last1 = Bartels | first1 = Sören
 | last2 = Hornung | first2 = Peter
 | doi = 10.1007/s10659-014-9501-6
 | issue = 1–2
 | journal = Journal of Elasticity
 | mr = 3326187
 | pages = 113–136
 | title = Bending paper and the Möbius strip
 | volume = 119
 | year = 2015| s2cid = 119782792
 }} Reprinted in {{harvtxt|Fosdick|Fried|2016}}, pp. 113–136. See in particular Section 5.2, pp. 129–130.</ref>

<ref name=bickel>{{cite journal
 | last = Bickel | first = Holger
 | doi = 10.1007/BF01229209
 | issue = 1–2
 | journal = Journal of Geometry
 | mr = 1675956
 | pages = 8–15
 | title = Duality in stable planes and related closure and kernel operations
 | volume = 64
 | year = 1999| s2cid = 122209943
 }}</ref>

<ref name=bjorling>{{cite journal
 | last = Mira | first = Pablo
 | doi = 10.1016/j.geomphys.2005.08.001
 | issue = 9
 | journal = Journal of Geometry and Physics
 | mr = 2240407
 | pages = 1506–1515
 | title = Complete minimal Möbius strips in <math>\mathbb{R}^n</math> and the Björling problem
 | volume = 56
 | year = 2006| bibcode = 2006JGP....56.1506M
 }}</ref>

<ref name=blackett>{{cite book
 | last = Blackett | first = Donald W.
 | isbn = 9781483262536
 | page = 195
 | publisher = Academic Press
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 | year = 1982}}</ref>

<ref name=blanusa>{{cite journal
 | last = Blanuša | first = Danilo | author-link = Danilo Blanuša
 | journal = Bulletin International de l'Académie Yougoslave des Sciences et des Beaux-Arts
 | mr = 71060
 | pages = 19–23
 | title = Le plongement isométrique de la bande de Möbius infiniment large euclidienne dans un espace sphérique, parabolique ou hyperbolique à quatre dimensions
 | volume = 12
 | year = 1954}}</ref>

<ref name=bon-nak>{{cite journal
 | last1 = Bonnington | first1 = C. Paul
 | last2 = Nakamoto | first2 = Atsuhiro
 | doi = 10.1007/s00454-007-9035-9
 | issue = 1
 | journal = [[Discrete & Computational Geometry]]
 | mr = 2429652
 | pages = 141–157
 | title = Geometric realization of a triangulation on the projective plane with one face removed
 | volume = 40
 | year = 2008| s2cid = 10887519
 | doi-access = free
 }}</ref>

<ref name=brecher>{{cite conference
 | last = Brecher | first = Kenneth
 | editor1-last = Swart | editor1-first = David
 | editor2-last = Séquin | editor2-first = Carlo H.
 | editor3-last = Fenyvesi | editor3-first = Kristóf
 | contribution = Art of infinity
 | contribution-url = https://archive.bridgesmathart.org/2017/bridges2017-153.html
 | isbn = 978-1-938664-22-9
 | location = Phoenix, Arizona
 | pages = 153–158
 | publisher = Tessellations Publishing
 | title = Proceedings of Bridges 2017: Mathematics, Art, Music, Architecture, Education, Culture
 | year = 2017}}</ref>

<ref name=brehm>{{cite journal
 | last = Brehm | first = Ulrich
 | doi = 10.2307/2045508
 | issue = 3
 | journal = [[Proceedings of the American Mathematical Society]]
 | mr = 715878
 | pages = 519–522
 | title = A nonpolyhedral triangulated Möbius strip
 | volume = 89
 | year = 1983| jstor = 2045508
 }}</ref>

<ref name=bridges>{{cite journal
 | last = Séquin | first = Carlo H. | author-link = Carlo H. Séquin
 | date = January 2018
 | doi = 10.1080/17513472.2017.1419331
 | issue = 2–3
 | journal = [[Journal of Mathematics and the Arts]]
 | pages = 181–194
 | title = Möbius bridges
 | volume = 12| s2cid = 216116708 }}</ref>

<ref name=briefmarken>{{cite journal
 | last1 = Decker | first1 = Heinz
 | last2 = Stark | first2 = Eberhard
 | issue = 7
 | journal = Praxis der Mathematik
 | mr = 720681
 | pages = 207–215
 | title = Möbius-Bänder: ...und natürlich auch auf Briefmarken
 | volume = 25
 | year = 1983}}</ref>

<ref name=can-ind>{{cite journal
 | last1 = Candeal | first1 = Juan Carlos
 | last2 = Induráin | first2 = Esteban
 | date = January 1994
 | doi = 10.1016/0165-1765(94)90045-0
 | issue = 3
 | journal = [[Economics Letters]]
 | pages = 407–412
 | title = The Moebius strip and a social choice paradox
 | volume = 45}}</ref>

<ref name=cantwell-conlon>{{cite journal
 | last1 = Cantwell | first1 = John
 | last2 = Conlon | first2 = Lawrence
 | arxiv = 1305.1379
 | doi = 10.1007/s10711-014-9975-1
 | journal = [[Geometriae Dedicata]]
 | mr = 3370020
 | pages = 27–42
 | title = Hyperbolic geometry and homotopic homeomorphisms of surfaces
 | volume = 177
 | year = 2015| s2cid = 119640200
 }}</ref>

<ref name=chirality>{{cite book
 | last = Flapan | first = Erica | author-link = Erica Flapan
 | doi = 10.1017/CBO9780511626272
 | isbn = 0-521-66254-0
 | mr = 1781912
 | pages = [https://books.google.com/books?id=ytjLCgAAQBAJ&pg=PA82 82–83]
 | publisher = Mathematical Association of America | location = Washington, DC
 | series = Outlooks
 | title = When Topology Meets Chemistry: A Topological Look at Molecular Chirality
 | title-link = When Topology Meets Chemistry
 | year = 2000}}</ref>

<ref name=chords>{{cite journal
 | last = Tymoczko | first = Dmitri | author-link = Dmitri Tymoczko
 | bibcode = 2006Sci...313...72T
 | date = July 7, 2006
 | doi = 10.1126/science.1126287
 | issue = 5783
 | journal = [[Science (journal)|Science]]
 | jstor = 3846592
 | pages = 72–4
 | pmid = 16825563
 | title = The geometry of musical chords
 | url = http://dmitri.mycpanel.princeton.edu/voiceleading.pdf
 | volume = 313| s2cid = 2877171 }}</ref>

<ref name=coaster1>{{cite book
 | last = Easdown | first = Martin
 | isbn = 9781782001522
 | page = 43
 | publisher = Bloomsbury Publishing
 | title = Amusement Park Rides
 | url = https://books.google.com/books?id=jjTDCwAAQBAJ&pg=PA43
 | year = 2012}}</ref>

<ref name=coaster2>{{cite book
 | last = Hook | first = Patrick
 | isbn = 9780785835776
 | page = 20
 | publisher = Chartwell Books
 | title = Ticket To Ride: The Essential Guide to the World's Greatest Roller Coasters and Thrill Rides
 | url = https://books.google.com/books?id=a7vdDwAAQBAJ&pg=PA20
 | year = 2019}}</ref>

<ref name=courant>{{cite journal
 | last = Courant | first = Richard | author-link = Richard Courant
 | doi = 10.1080/00029890.1940.11990957
 | journal = [[The American Mathematical Monthly]]
 | jstor = 2304225
 | mr = 1622
 | pages = 167–174
 | title = Soap film experiments with minimal surfaces
 | volume = 47
 | year = 1940| issue = 3 }}</ref>

<ref name=crowell>{{cite magazine|magazine=Scientific American|last=Crowell|first=Rachel|date=September 12, 2023|title=Mathematicians solve 50-year-old Möbius strip puzzle|url=https://www.scientificamerican.com/article/mathematicians-solve-50-year-old-moebius-strip-puzzle/}}</ref>

<ref name=darkside>{{cite journal
 | last = Schwarz | first = Gideon E.
 | doi = 10.1080/00029890.1990.11995680
 | issue = 10
 | journal = [[The American Mathematical Monthly]]
 | jstor = 2324325
 | mr = 1079975
 | pages = 890–897
 | title = The dark side of the Moebius strip
 | volume = 97
 | year = 1990}}</ref>

<ref name=ddg>{{cite web
 | last = Knöppel | first = Felix
 | date = Summer 2019
 | title = Tutorial 3: Lawson's Minimal Surfaces and the Sudanese Möbius Band
 | url = https://dgd.service.tu-berlin.de/wordpress/ddg2019/2019/04/29/tutorial-3-lawsons-minimal-surfaces-and-the-sudanese-mobius-band/
 | work = DDG2019: Visualization course at TU Berlin}}</ref>

<ref name=defy>{{cite magazine|url=https://www.quantamagazine.org/mobius-strips-defy-a-link-with-infinity-20190220/|title=Möbius strips defy a link with infinity|first=Evelyn|last=Lamb|magazine=[[Quanta Magazine]]|date=February 20, 2019}}</ref>

<ref name=dna>{{cite web|url=https://arstechnica.com/science/2010/10/chemical-origami-used-to-create-a-dna-mobius-strip/|title=Chemical origami used to create a DNA Möbius strip|work=[[Ars Technica]]|first=Diana|last=Gitig|date=October 18, 2010|access-date=2022-03-28}}</ref>

<ref name=dooner-seirig>{{cite book
 | last1 = Dooner | first1 = David B.
 | last2 = Seireg | first2 = Ali
 | contribution = 3.4.2 The cylindroid
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 | isbn = 9780471045977
 | pages = 135–137
 | publisher = John Wiley & Sons
 | series = Wiley Series in Design Engineering
 | title = The Kinematic Geometry of Gearing: A Concurrent Engineering Approach
 | volume = 3
 | year = 1995}}</ref>

<ref name=dundas>{{cite book
 | last = Dundas | first = Bjørn Ian
 | contribution = Example 5.1.3: The unbounded Möbius band
 | doi = 10.1017/9781108349130
 | isbn = 978-1-108-42579-7
 | mr = 3793640
 | page = https://books.google.com/books?id=7a1eDwAAQBAJ&pg=PA101
 | publisher = Cambridge University Press, Cambridge
 | series = Cambridge Mathematical Textbooks
 | title = A Short Course in Differential Topology
 | year = 2018| s2cid = 125997451
 }}</ref>

<ref name=emmer>{{cite journal
 | last = Emmer | first = Michele
 | date = Spring 1980
 | issue = 2
 | journal = [[Leonardo (journal)|Leonardo]]
 | pages = 108–111
 | title = Visual art and mathematics: the Moebius band
 | url = https://muse.jhu.edu/article/599337/summary
 | volume = 13| doi = 10.2307/1577979
 | jstor = 1577979
 | s2cid = 123908555
 }}</ref>

<ref name=escher1>{{cite book
 | last = Crato | first = Nuno
 | contribution = Escher and the Möbius strip
 | doi = 10.1007/978-3-642-04833-3_29
 | pages = 123–126
 | publisher = Springer
 | title = Figuring It Out: Entertaining Encounters with Everyday Math
 | year = 2010| isbn = 978-3-642-04832-6
 }}</ref>

<ref name=escher2>{{cite web|url=https://www.escherinhetpaleis.nl/escher-today/mobius-strip-i/?lang=en|title=Möbius Strip I|publisher=[[Escher in the Palace]]|first=Erik|last=Kersten|date=March 13, 2017|access-date=2022-04-17}}</ref>

<ref name=expo74>{{cite news |url=https://news.google.com/newspapers?id=v9kvAAAAIBAJ&pg=5133%2C4421507 |newspaper=[[The Spokesman-Review]] |title=Expo '74 symbol selected |date=March 12, 1972 |page=1}}</ref>

<ref name=flapan>{{cite book
 | last = Flapan | first = Erica | author-link = Erica Flapan
 | doi = 10.1090/mbk/096
 | isbn = 978-1-4704-2535-7
 | mr = 3443369
 | pages = 99–100
 | publisher = American Mathematical Society | location = Providence, Rhode Island
 | title = Knots, Molecules, and the Universe: An Introduction to Topology
 | url = https://books.google.com/books?id=q4RbCwAAQBAJ&pg=PA99
 | year = 2016}}</ref>

<ref name=fomenko-kunii>{{cite book
 | last1 = Fomenko | first1 = Anatolij T. | author1-link = Anatoly Fomenko
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 | isbn = 9784431669562
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 | publisher = Springer
 | title = Topological Modeling for Visualization
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 | year = 2013}}</ref>

<ref name=fuchs-tabachnikov>{{cite book
 | last1 = Fuchs | first1 = Dmitry | author1-link = Dmitry Fuchs
 | last2 = Tabachnikov | first2 = Serge | author2-link = Sergei Tabachnikov
 | contribution = Lecture 14: Paper Möbius band
 | doi = 10.1090/mbk/046
 | isbn = 978-0-8218-4316-1
 | mr = 2350979
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 | publisher = American Mathematical Society | location = Providence, Rhode Island
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<ref name=francis>{{cite book
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 | year = 1987}}</ref>

<ref name=franzoni>{{cite journal
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<ref name=gardner>{{cite book
 | last = Gardner | first = Martin | author-link = Martin Gardner
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 | publisher = Dover Books
 | title = Mathematics, Magic and Mystery
 | year = 1956}}</ref>

<ref name=gdrive>{{cite news|url=https://sg.news.yahoo.com/did-google-drive-copy-icon-091053776.html|title=Did Google Drive Copy its Icon From a Chinese App?|first=Steven|last=Millward|date=April 30, 2012|work=Tech in Asia|via=Yahoo! News|access-date=2022-03-27}}</ref>

<ref name=godinho-natario>{{cite book
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<ref name=graphene>{{cite journal
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<ref name=hilbert-cohn-vossen>{{cite book
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 | publisher = Chelsea
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<ref name=huggett-jordan>{{cite book
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<ref name=impa>{{cite web|url=https://impa.br/en_US/noticias/para-quem-e-fa-do-impa-dez-curiosidades-sobre-o-instituto/|title=Símbolo do IMPA|work=Para quem é fã do IMPA, dez curiosidades sobre o instituto|publisher=IMPA|access-date=2022-03-27|date=May 7, 2020}}</ref>

<ref name=isham>{{cite book
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 | volume = 61
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<ref name=jab-rad-saz>{{cite journal
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<ref name=kazakh>{{cite news
 | last = Wainwright | first = Oliver
 | date = October 17, 2017
 | newspaper = [[The Guardian]]
 | title = 'Norman said the president wants a pyramid': how starchitects built Astana
 | url = https://www.theguardian.com/cities/2017/oct/17/norman-foster-president-pyramid-architects-built-astana}}</ref>

<ref name=kuiper>{{cite journal
 | last = Kuiper | first = Nicolaas H. | author-link = Nicolaas Kuiper
 | doi = 10.4310/jdg/1214430493
 | journal = [[Journal of Differential Geometry]]
 | mr = 314057
 | pages = 271–283
 | title = Tight topological embeddings of the Moebius band
 | volume = 6
 | year = 1972| issue = 3 | doi-access = free
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<ref name=kyle>{{cite journal
 | last = Kyle | first = R. H.
 | journal = Proceedings of the Royal Irish Academy, Section A
 | jstor = 20488581
 | mr = 0091480
 | pages = 131–136
 | title = Embeddings of Möbius bands in 3-dimensional space
 | volume = 57
 | year = 1955}}</ref>

<ref name=larsen>{{cite conference
 | last = Larsen | first = Mogens Esrom
 | editor1-last = Guy | editor1-first = Richard K. | editor1-link = Richard K. Guy
 | editor2-last = Woodrow | editor2-first = Robert E.
 | contribution = Misunderstanding my mazy mazes may make me miserable
 | isbn = 0-88385-516-X
 | mr = 1303141
 | pages = 289–293
 | publisher = Mathematical Association of America | location = Washington, DC
 | series = MAA Spectrum
 | title = Proceedings of the Eugène Strens Memorial Conference on Recreational Mathematics and its History held at the University of Calgary, Calgary, Alberta, August 1986
 | year = 1994}}. See [https://books.google.com/books?id=FsH2DwAAQBAJ&pg=PA292 Figure 7, p. 292].</ref>

<ref name=lawson>{{cite journal
 | last = Lawson | first = H. Blaine Jr. | author-link = H. Blaine Lawson
 | doi = 10.2307/1970625
 | journal = [[Annals of Mathematics]]
 | jstor = 1970625
 | mr = 270280
 | pages = 335–374
 | series = Second Series
 | title = Complete minimal surfaces in <math>S^3</math>
 | volume = 92
 | year = 1970| issue = 3 }} See Section 7, pp. 350–353, where the Klein bottle is denoted <math>\tau_{1,2}</math>.</ref>

<ref name=lopez-martin>{{cite journal
 | last1 = López | first1 = Francisco J.
 | last2 = Martín | first2 = Francisco
 | doi = 10.1353/ajm.1997.0004
 | issue = 1
 | journal = [[American Journal of Mathematics]]
 | mr = 1428058
 | pages = 55–81
 | title = Complete nonorientable minimal surfaces with the highest symmetry group
 | volume = 119
 | year = 1997| s2cid = 121366986
 }}</ref>

<ref name=magic>{{cite book
 | last = Prevos | first = Peter
 | location = Kangaroo Flat
 | publisher = Third Hemisphere
 | title = The Möbius Strip in Magic: A Treatise on the Afghan Bands
 | year = 2018
 | url = https://horizonofreason.com/pdf/afghan-bands-sample.pdf }}</ref>

<ref name=mangahas>{{cite book
 | last = Mangahas | first = Johanna
 | editor1-last = Clay | editor1-first = Matt
 | editor2-last = Margalit | editor2-first = Dan
 | contribution = Office Hour Five: The Ping-Pong Lemma
 | date = July 2017
 | doi = 10.1515/9781400885398
 | pages = 85–105
 | publisher = Princeton University Press
 | title = Office Hours with a Geometric Group Theorist| isbn = 9781400885398
 }} See in particular Project 7, pp. 104–105.</ref>

<ref name=maps1>{{cite journal
 | last = Tobler | first = Waldo R. | author-link = Waldo R. Tobler
 | journal = Surveying & Mapping
 | page = 486
 | title = A world map on a Möbius strip
 | url = https://books.google.com/books?id=2j44AAAAIAAJ&pg=PA486
 | volume = 21
 | year = 1961}}</ref>

<ref name=maps2>{{cite journal
 | last1 = Kumler | first1 = Mark P. | author1-link = Waldo R. Tobler
 | last2 = Tobler | first2 = Waldo R.
 | date = January 1991
 | doi = 10.1559/152304091783786781
 | issue = 4
 | journal = Cartography and Geographic Information Systems
 | pages = 275–276
 | title = Three world maps on a Moebius strip
 | volume = 18| bibcode = 1991CGISy..18..275K }}</ref>

<ref name=maschke>{{cite journal
 | last = Maschke | first = Heinrich | author-link = Heinrich Maschke
 | doi = 10.2307/1986401
 | issue = 1
 | journal = [[Transactions of the American Mathematical Society]]
 | mr = 1500522
 | page = 39
 | title = Note on the unilateral surface of Moebius
 | volume = 1
 | year = 1900| jstor = 1986401 | doi-access = free
 }}</ref>

<ref name=massey>{{cite book
 | last = Massey | first = William S.
 | isbn = 0-387-97430-X
 | mr = 1095046
 | page = 49
 | publisher = Springer-Verlag | location = New York
 | series = Graduate Texts in Mathematics
 | title = A Basic Course in Algebraic Topology
 | url = https://books.google.com/books?id=laSfDwAAQBAJ&pg=PA49
 | volume = 127
 | year = 1991}}</ref>

<ref name=meeks>{{cite journal
 | last = Meeks | first = William H. III | author-link = William Hamilton Meeks, III
 | doi = 10.1215/S0012-7094-81-04829-8
 | issue = 3
 | journal = [[Duke Mathematical Journal]]
 | mr = 630583
 | pages = 523–535
 | title = The classification of complete minimal surfaces in <math>\mathbb{R}^3</math> with total curvature greater than <math>-8\pi</math>
 | volume = 48
 | year = 1981}}</ref>

<ref name=melikhov>{{cite journal
 | last = Melikhov | first = Sergey A.
 | doi = 10.1142/s0218216519710019
 | issue = 7
 | journal = [[Journal of Knot Theory and Its Ramifications]]
 | mr = 3975576
 | pages = 1971001, 3
 | title = A note on O. Frolkina's paper "Pairwise disjoint Moebius bands in space"
 | volume = 28
 | year = 2019| arxiv = 1810.04089
 | s2cid = 119179202
 }}</ref>

<ref name=music>{{cite web
 | last = Moskowitz | first = Clara | author-link = Clara Moskowitz
 | date = May 6, 2008 | access-date = 2022-03-21
 | title = Music reduced to beautiful math
 | url = https://www.livescience.com/strangenews/080507-math-music.html
 | website = [[Live Science]]}}</ref>

<ref name=nak-tsu>{{cite journal
 | last1 = Nakamoto | first1 = Atsuhiro
 | last2 = Tsuchiya | first2 = Shoichi
 | doi = 10.1016/j.disc.2011.06.007
 | issue = 14
 | journal = [[Discrete Mathematics (journal)|Discrete Mathematics]]
 | mr = 2921579
 | pages = 2135–2139
 | title = On geometrically realizable Möbius triangulations
 | volume = 312
 | year = 2012| doi-access = free
 }}</ref>

<ref name=nascar>{{cite magazine
 | last = Muret | first = Don
 | date = May 17, 2010
 | magazine = Sports Business Journal
 | title = NASCAR Hall of Fame 'looks fast sitting still'
 | url = https://www.sportsbusinessjournal.com/Journal/Issues/2010/05/17/This-Weeks-News/NASCAR-Hall-Of-Fame-Looks-Fast-Sitting-Still.aspx}}</ref>

<ref name=olson>{{cite book
 | last = Byers | first = Mark
 | isbn = 9780198813255
 | pages = 77–78
 | publisher = Oxford University Press
 | title = Charles Olson and American Modernism: The Practice of the Self
 | url = https://books.google.com/books?id=U1ZYDwAAQBAJ&pg=PA77
 | year = 2018}}</ref>

<ref name=optimal>{{cite arXiv|first=Richard|last=Schwartz|author-link=Richard Schwartz (mathematician)|title=The optimal paper Moebius band|date=2023 |eprint=2308.12641|class=math.MG}}</ref>

<ref name=paradromic>{{cite journal
 | last = Bennett | first = G. T. | author-link = Geoffrey Thomas Bennett
 | date = June 1923
 | doi = 10.1038/111882b0
 | issue = 2800
 | journal = [[Nature (journal)|Nature]]
 | page = 882
 | title = Paradromic rings
 | volume = 111| bibcode = 1923Natur.111R.882B | s2cid = 4099647 | doi-access = free
 }}</ref>

<ref name=parameterization>{{cite book
 | last = Junghenn | first = Hugo D.
 | isbn = 978-1-4822-1927-2
 | mr = 3309241
 | page = 430
 | publisher = CRC Press | location = Boca Raton, Florida
 | title = A Course in Real Analysis
 | url = https://books.google.com/books?id=nE63BgAAQBAJ&pg=PA430
 | year = 2015}}</ref>
 
<ref name=parker>{{cite book
 | last = Parker
 | first = Phillip E.
 | editor-last = Del Riego
 | editor-first = L.
 | contribution = Spaces of geodesics
 | contribution-url = http://www.math.wichita.edu/~pparker/research/sog/sog1.zip
 | mr = 1304924
 | pages = 67–79
 | publisher = Soc. Mat. Mexicana, México
 | series = Aportaciones Mat. Notas Investigación
 | title = Differential Geometry Workshop on Spaces of Geometry (Guanajuato, 1992)
 | volume = 8
 | year = 1993
 | access-date = 2022-03-21 
 | archive-date = 2016-03-13 
 | archive-url = https://web.archive.org/web/20160313115359/http://www.math.wichita.edu/~pparker/research/sog/sog1.zip
 | url-status = bot: unknown
 }}</ref>

<ref name=pasta>{{cite news|newspaper=[[The New York Times]]|title=Pasta Graduates From Alphabet Soup to Advanced Geometry|url=https://www.nytimes.com/2012/01/10/science/pasta-inspires-scientists-to-use-their-noodle.html|first=Kenneth|last=Chang|date=January 9, 2012}}</ref>

<ref name=peterson>{{cite book
 | last = Peterson | first = Ivars | author-link = Ivars Peterson
 | contribution = Recycling topology
 | contribution-url = https://books.google.com/books?id=RMH2DwAAQBAJ&pg=PA31
 | isbn = 0-88385-537-2
 | mr = 1874198
 | pages = 31–35
 | publisher = Mathematical Association of America, Washington, DC
 | series = MAA Spectrum
 | title = Mathematical Treks: From Surreal Numbers to Magic Circles
 | year = 2002}}</ref>

<ref name=phillips>{{cite magazine
 | last = Phillips | first = Tony
 | date = November 25, 2016
 | magazine = [[Plus Magazine]]
 | title = Bach and the musical Möbius strip
 | url = https://plus.maths.org/content/topology-music-m-bius-strip}} Reprinted from an American Mathematical Society Feature Column.</ref>

<ref name=pickover>{{cite book
 | last = Pickover | first = Clifford A. | author-link = Clifford A. Pickover
 | isbn = 978-1-56025-826-1
 | pages = 28–29
 | publisher = Thunder's Mouth Press
 | title = The Möbius Strip: Dr. August Möbius's Marvelous Band in Mathematics, Games, Literature, Art, Technology, and Cosmology
 | url = https://archive.org/details/mbiusstripdrau00pick
 | year = 2005}}</ref>

<ref name=polarization>{{cite journal
 | last1 = Bauer | first1 = Thomas
 | last2 = Banzer | first2 = Peter
 | last3 = Karimi | first3 = Ebrahim
 | last4 = Orlov | first4 = Sergej
 | last5 = Rubano | first5 = Andrea
 | last6 = Marrucci | first6 = Lorenzo
 | last7 = Santamato | first7 = Enrico
 | last8 = Boyd | first8 = Robert W.
 | last9 = Leuchs | first9 = Gerd
 | date = February 2015
 | doi = 10.1126/science.1260635
 | issue = 6225
 | journal = [[Science (journal)|Science]]
 | pages = 964–966
 | title = Observation of optical polarization Möbius strips
 | volume = 347| pmid = 25636796
 | bibcode = 2015Sci...347..964B
 | s2cid = 206562350
 }}</ref>

<ref name=pook>{{cite book
 | last = Pook | first = Les
 | contribution = 4.2: The trihexaflexagon revisited
 | contribution-url = https://books.google.com/books?id=MlKL1aG781QC&pg=PA33
 | doi = 10.1017/CBO9780511543302
 | isbn = 0-521-81970-9
 | mr = 2008500
 | pages = 33–36
 | publisher = Cambridge University Press | location = Cambridge, UK
 | title = Flexagons Inside Out
 | year = 2003}}</ref>

<ref name=ramirez-seade>{{cite book
 | last1 = Ramírez Galarza | first1 = Ana Irene
 | last2 = Seade | first2 = José
 | isbn = 978-3-7643-7517-1
 | location = Basel
 | mr = 2305055
 | pages = 83–88, 157–163
 | publisher = Birkhäuser Verlag
 | title = Introduction to Classical Geometries
 | year = 2007}}</ref>

<ref name=resistor>{{cite magazine
 | date = September 25, 1964
 | issue = 13
 | magazine = [[Time (magazine)|Time]]
 | title = Making resistors with math
 | url = https://content.time.com/time/subscriber/article/0,33009,876181,00.html
 | volume = 84}}</ref>

<ref name=resonator>{{cite journal
 | last = Pond | first = J. M.
 | bibcode = 2000ITMTT..48.2465P
 | doi = 10.1109/22.898999
 | issue = 12
 | journal = IEEE Transactions on Microwave Theory and Techniques
 | pages = 2465–2471
 | title = Mobius dual-mode resonators and bandpass filters
 | volume = 48
 | year = 2000}}</ref>

<ref name=resonator2>{{cite journal
 | last1 = Rohde | first1 = Ulrich L.
 | last2 = Poddar | first2 = Ajay
 | last3 = Sundararajan | first3 = D.
 | date = November 2013
 | issue = 11
 | journal = Microwave Journal
 | title = Printed resonators: Möbius strip theory and applications
 | url = https://synergymwave.com/articles/2013/11/article.pdf
 | volume = 56}}</ref>

<ref name=reyes>{{cite web|url=https://news.artnet.com/art-world/pedro-reyes-makes-an-infinite-love-seat-133150|work=Artnet News|title=Pedro Reyes Makes an Infinite Love Seat|first=Blake|last=Gopnik|date=October 17, 2014}}</ref>

<ref name=richeson>{{cite book
 | last = Richeson | first = David S. | author-link = David Richeson
 | isbn = 978-0-691-12677-7
 | mr = 2440945
 | page = [https://books.google.com/books?id=BFeXDwAAQBAJ&pg=PA171 171]
 | publisher = Princeton University Press | location = Princeton, New Jersey
 | title = Euler's Gem: The Polyhedron Formula and the Birth of Topology
 | title-link = Euler's Gem
 | year = 2008}}</ref>

<ref name=ringel-youngs>{{cite journal
 | last1 = Ringel | first1 = G. | author1-link = Gerhard Ringel | last2 = Youngs | first2 = J. W. T.
 | bibcode = 1968PNAS...60..438R
 | doi = 10.1073/pnas.60.2.438 | doi-access = free
 | issue = 2
 | journal = [[Proceedings of the National Academy of Sciences of the United States of America]]
 | volume = 60
 | pages = 438–445
 | mr = 0228378
 | pmc = 225066
 | pmid = 16591648
 | title = Solution of the Heawood map-coloring problem
 | year = 1968}}</ref>

<ref name=ringvan>{{cite magazine|url=https://www.pressreader.com/uk/prog/20210209/281535113669133|title=Ring Van Möbius|magazine=[[Prog (magazine)|Prog]]|date=February 9, 2021|first=Dom|last=Lawson}}</ref>

<ref name=roman>{{cite journal
 | last = Larison | first = Lorraine L.
 | bibcode=1973AmSci..61..544L
 | issue = 5
 | journal = [[American Scientist]]
 | jstor = 27843983
 | pages = 544–547
 | title = The Möbius band in Roman mosaics
 | volume = 61
 | year = 1973}}</ref>

<ref name=rouseball>{{cite book|title=Mathematical Recreations and Problems of Past and Present Times|edition=2nd|publisher=Macmillan and co.|location=London & New York|year=1892|last=Rouse Ball|first=W. W.|author-link=W. W. Rouse Ball|contribution=Paradromic rings|pages=53–54|contribution-url=https://books.google.com/books?id=IwDvAAAAMAAJ&pg=PA53}}</ref>

<ref name=sadowsky-translation>{{cite journal
 | last1 = Hinz | first1 = Denis F.
 | last2 = Fried | first2 = Eliot
 | doi = 10.1007/s10659-014-9490-5
 | issue = 1–2
 | journal = Journal of Elasticity
 | mr = 3326180
 | pages = 3–6
 | title = 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"
 | volume = 119
 | year = 2015| arxiv = 1408.3034
 | s2cid = 119733903
 }} Reprinted in {{cite book
 | last1 = Fosdick | first1 = Roger
 | last2 = Fried | first2 = Eliot
 | doi = 10.1007/978-94-017-7300-3
 | isbn = 978-94-017-7299-0
 | mr = 3381564
 | pages = 3–6
 | publisher = Springer, Dordrecht
 | title = The Mechanics of Ribbons and Möbius Bands
 | year = 2016| url = https://openresearch.lsbu.ac.uk/download/7bba3852893aa5916361a1c98259f2aee64381672fa60a5dcfb7e926228a4197/6644159/Starostin-Heijden2015_Article_EquilibriumShapesWithStressLoc.pdf
 }}</ref>

<ref name=schleimer-segerman>{{cite conference
 | last1 = Schleimer | first1 = Saul
 | last2 = Segerman | first2 = Henry
 | editor1-last = Bosch | editor1-first = Robert
 | editor2-last = McKenna | editor2-first = Douglas
 | editor3-last = Sarhangi | editor3-first = Reza
 | arxiv = 1204.4952
 | contribution = Sculptures in {{math|''S''<sup>3</sup>}}<!-- html math so formula is properly bluelinked -->
 | contribution-url = https://archive.bridgesmathart.org/2012/bridges2012-103.html
 | isbn = 978-1-938664-00-7
 | location = Phoenix, Arizona
 | pages = 103–110
 | publisher = Tessellations Publishing
 | title = Proceedings of Bridges 2012: Mathematics, Music, Art, Architecture, Culture
 | year = 2012}}</ref>

<ref name=schwartz>{{cite journal
 | last = Schwartz | first = Richard Evan | author-link = Richard Schwartz (mathematician)
 | arxiv = 2008.11610
 | doi = 10.1007/s10711-021-00648-5
 | journal = [[Geometriae Dedicata]]
 | mr = 4330341
 | pages = 255–267
 | title = An improved bound on the optimal paper Moebius band
 | volume = 215
 | year = 2021| s2cid = 220279013 }}</ref>

<ref name=schwarz>{{cite journal
 | last = Schwarz | first = Gideon
 | issue = 1
 | journal = [[Pacific Journal of Mathematics]]
 | mr = 1047406
 | pages = 195–200
 | title = A pretender to the title 'canonical Moebius strip'
 | url = https://projecteuclid.org/euclid.pjm/1102646207
 | volume = 143
 | year = 1990| doi = 10.2140/pjm.1990.143.195
 | doi-access = free
 }}</ref>

<ref name=seifert-threlfall>{{cite book
 | last1 = Seifert | first1 = Herbert | author1-link = Herbert Seifert
 | last2 = Threlfall | first2 = William | author2-link = William Threlfall
 | translator-last = Goldman | translator-first = Michael A.
 | isbn = 0-12-634850-2
 | location = New York & London
 | mr = 575168
 | page = 12
 | publisher = Academic Press
 | series = Pure and Applied Mathematics
 | title = A Textbook of Topology
 | url = https://books.google.com/books?id=rsb8zjP0XHoC&pg=PA12
 | volume = 89
 | year = 1980}}</ref>

<ref name=soap>{{cite journal
 | last1 = Goldstein | first1 = Raymond E. | author1-link = Raymond E. Goldstein
 | last2 = Moffatt | first2 = H. Keith | author2-link = Keith Moffatt
 | last3 = Pesci | first3 = Adriana I. | author3-link = Adriana Pesci
 | last4 = Ricca | first4 = Renzo L. | author4-link = Renzo L. Ricca
 | date = December 2010
 | doi = 10.1073/pnas.1015997107
 | issue = 51
 | journal = [[Proceedings of the National Academy of Sciences]]
 | pages = 21979–21984
 | title = Soap-film Möbius strip changes topology with a twist singularity
 | volume = 107| bibcode = 2010PNAS..10721979G | doi-access = free | pmc = 3009808}}</ref>

<ref name=spivak>{{cite book
 | last = Spivak | first = Michael | author-link = Michael Spivak
 | edition = 2nd
 | location = Wilmington, Delaware
 | page = 591
 | publisher = Publish or Perish
 | title = A Comprehensive Introduction to Differential Geometry, Volume I
 | year = 1979}}</ref>
 
<ref name=split-tori>{{cite conference
 | last = Séquin | first = Carlo H. | author-link = Carlo H. Séquin
 | editor1-last = Sarhangi | editor1-first = Reza
 | editor2-last = Moody | editor2-first = Robert V.
 | contribution = Splitting tori, knots, and Moebius bands
 | contribution-url = https://archive.bridgesmathart.org/2005/bridges2005-211.html
 | isbn = 0-9665201-6-5
 | location = Southwestern College, Winfield, Kansas
 | pages = 211–218
 | publisher = Bridges Conference
 | title = Renaissance Banff: Mathematics, Music, Art, Culture
 | year = 2005}}</ref>

<ref name=starostin-vdh>{{cite journal
 | last1 = Starostin | first1 = E. L.
 | last2 = van der Heijden | first2 = G. H. M.
 | doi = 10.1007/s10659-014-9495-0
 | issue = 1–2
 | journal = Journal of Elasticity
 | mr = 3326186
 | pages = 67–112
 | title = Equilibrium shapes with stress localisation for inextensible elastic Möbius and other strips
 | volume = 119
 | year = 2015| s2cid = 53462568
 | doi-access = free
 }} Reprinted in {{harvtxt|Fosdick|Fried|2016}}, pp. 67–112.</ref>

<ref name=stillwell>{{cite book
 | last = Stillwell | first = John | author-link = John Stillwell
 | contribution = 4.6 Classification of isometries
 | doi = 10.1007/978-1-4612-0929-4
 | isbn = 0-387-97743-0
 | mr = 1171453
 | pages = 96–98
 | publisher = Springer | location = Cham
 | series = Universitext
 | title = Geometry of Surfaces
 | year = 1992}}</ref>

<ref name=sudanese>{{cite web
 | last = Gunn | first = Charles
 | access-date=2022-03-17
 | title = Sudanese Möbius Band
 | url = https://vimeo.com/286360639
 | website = Vimeo| date = August 23, 2018
 }}</ref>

<ref name=synthesis>{{cite journal
 | last1 = Walba | first1 = David M.
 | last2 = Richards | first2 = Rodney M.
 | last3 = Haltiwanger | first3 = R. Curtis
 | date = June 1982
 | doi = 10.1021/ja00375a051
 | issue = 11
 | journal = [[Journal of the American Chemical Society]]
 | pages = 3219–3221
 | title = Total synthesis of the first molecular Moebius strip
 | volume = 104| bibcode = 1982JAChS.104.3219W
 }}</ref>

<ref name=systolic>{{cite journal
 | last1 = Pesci | first1 = Adriana I. | author1-link = Adriana Pesci
 | last2 = Goldstein | first2 = Raymond E. | author2-link = Raymond E. Goldstein
 | last3 = Alexander | first3 = Gareth P.
 | last4 = Moffatt | first4 = H. Keith | author4-link = Keith Moffatt
 | doi = 10.1103/PhysRevLett.114.127801
 | issue = 12
 | journal = [[Physical Review Letters]]
 | mr = 3447638
 | page = 127801
 | title = Instability of a Möbius strip minimal surface and a link with systolic geometry
 | volume = 114
 | year = 2015| pmid = 25860771 | bibcode = 2015PhRvL.114l7801P | url = http://wrap.warwick.ac.uk/74286/7/WRAP_PRL114_127801_2015_alexander.pdf }}</ref>

<ref name=szilassi>{{cite journal
 | last = Szilassi | first = Lajos | author-link = Lajos Szilassi
 | doi = 10.1007/s00454-007-9033-y
 | issue = 3
 | journal = [[Discrete & Computational Geometry]]
 | mr = 2443291
 | pages = 395–400
 | title = A polyhedral model in Euclidean 3-space of the six-pentagon map of the projective plane
 | volume = 40
 | year = 2008| s2cid = 38606607 | doi-access = free
 }}</ref>

<ref name=tietze>{{cite journal
 | last = Tietze | first = Heinrich | author-link = Heinrich Tietze
 | journal = Jahresbericht der Deutschen Mathematiker-Vereinigung
 | pages = 155–159
 | title = Einige Bemerkungen zum Problem des Kartenfärbens auf einseitigen Flächen
 | url = https://sites.math.washington.edu/~mathcircle/circle/2014-15/advanced/mc-14a-w8.pdf
 | volume = 19
 | year = 1910}}</ref>

<ref name=tuckerman>{{cite journal
 | last = Tuckerman | first = Bryant | author-link = Bryant Tuckerman
 | doi = 10.2307/2305482
 | journal = American Mathematical Monthly
 | jstor = 2305482
 | mr = 24138
 | pages = 309–311
 | title = A non-singular polyhedral Möbius band whose boundary is a triangle
 | volume = 55
 | year = 1948| issue = 5 }}</ref>

<ref name=woll>{{cite journal
 | last = Woll | first = John W. Jr.
 | date = Spring 1971
 | doi = 10.2307/3026946
 | issue = 1
 | journal = [[The Two-Year College Mathematics Journal]]
 | jstor = 3026946
 | pages = 5–18
 | title = One-sided surfaces and orientability
 | volume = 2}}</ref>

<ref name=wunderlich>{{cite journal
 | last = Wunderlich | first = W.
 | doi = 10.1007/BF01299052
 | journal = [[Monatshefte für Mathematik]]
 | mr = 143115
 | pages = 276–289
 | title = Über ein abwickelbares Möbiusband
 | volume = 66
 | year = 1962| issue = 3
 | s2cid = 122215321
 }}</ref>

<ref name=zimmermann>{{cite news|first=Nancy J. |last=Thomas |title=Making a Mobius a matter of mathematics|newspaper=[[The Times (Trenton)]]|date=October 4, 1998|page=aa3 |url= https://infoweb.newsbank.com/apps/news/openurl?ctx_ver=z39.88-2004&rft_id=info%3Asid/infoweb.newsbank.com&svc_dat=AWNB&req_dat=0F1B56E1B179D300&rft_val_format=info%3Aofi/fmt%3Akev%3Amtx%3Actx&rft_dat=document_id%3Anews%252F11B7A8B696793450 |via=[[NewsBank]]}}</ref>

}}