Bibliography
Bibliography
The bibliography on the Möbius strip is extensive, to say the least, so much so that it is impractical, and not even necessary, to list 'all', even if that is possible. At the simplest level, a lot repeats. And at the advanced topological level, a lot is way beyond my understanding, and so is futile. Despite the opposites, I have nonetheless included such articles on occasion. Although it may seem to be not necessary, and so could easily be omitted, I have decided to include on the basis of at least 'acknowledging' the article, in that I have seen and noted it. Frequently, the titles give the possibility of a popular piece, and so could possibly have been of interest. (For example 'One-sided sources and Orientability', which is a technical expose, going into manifolds.) Therefore rather than leaving the matter open-ended, I simply document it as 'seen and noted'.
In general, for each of the more popular entries, I thus give a broad overview of the article, with those that are perhaps of more interest a more lengthy overview, albeit still within the premise of brevity. Given that a large proportion of the people here are new to me, on occasion I give brief biographies to better understand the background to their interest. This is largely at whim, and is in no way an attempt at discussing 'all' of the new people. The presentation is also influenced by other lists. For example, David Singmaster in his (spellbounding) Recreational Mathematics listing gives as a dedicated subsection on the Möbius strip, accompanied by additional commentary of interest, In general I have included this supplementary material where so, where I add at the end 'Singmaster commentary'.
The list is differentiated into sub classifications for easier finding, including books/articles, websites, blogs, videos, and Quora
Books/Articles
A
Abbott, David (General ed.). The Biographical Dictionary of Scientists. Mathematicians. Blond Educational, 1985
Möbius biography pp. 92-93, an indepth, popular account. Discusses and illustrates a Möbius strip, also crediting Listing in the discovery (who incidentally does not an entry).
Abbott's Magic. Mfg. Co. Catalog No. 21. Abbott's Magic, 1976 pp. 203, 255, 310, 428, 490.
Afghan Bands One red rag band is shown and torn through its center, making two
Abbott Magic was founded in 1934 by Percy Abbott. In the same year Recil Bordner became 50/50 partner. The business is still owned by the Bordner family. Abbott Magic is recognized as one of the largest magic manufacturing businesses in the world. It is also the host of the famous Abbott's Magic Get Together held every year in summer. Abbott Magic
Quoted by: Ask Alexander
Abbott's Magic. Mfg. Co. Catalog No. 22. Abbott's Magic, 1976 pp. 244, 312, 383, 436, 439, 451, 453
Afghan Bands One red rag band is shown and torn through its center, making two
Source: Ask Alexander
Emporium of Magic Catalog No.1, 1976, pp. 144, 329, 343
AFGHAN BANDS
Quoted by: Ask Alexander
Abraham, R. M. Winter Nights Entertainments. Constable and Constable, London, 1932, p. 26
Cutting the Paper Rings. Take three strips of paper about an inch wide and 3 feet long and gum them up into rings as follows:…
Allusion. No illustration is given.
Quoted by: David Mitchell
Winter Nights Entertainments by R M Abraham was first published by Constable and Constable in London in 1932 and later reprinted under the title 'Easy to Do Entertainment and Diversions With Coins, Cards, String, Paper and Matches' by Dover publications in 1961.
The 1932 edition does not seem to be freely available. Internet Archive has the 1951 reprint:
Bio. R. M. Abraham was a popular British creator of puzzles and games. His bag of tricks was filled with a variegated collection of ingenious problems, tricks, surprises, diversions with string, paper, wood, etc., and many other curiosities and amusements. Magicinc
https://archive.org/details/Easy-to-d0EntertainmentsAndDiversionsWithCoinsCardsStringPaperAnd/page/n33/mode/2up?q=cutting
Printed
Adair, Ian. 'Bands Together'. Magigram, 23(11):1991, pp. 557–559.
Bio. Ian Adair (1940-) writes a regular column in MAGIGRAM and is the author of numerous books on magic for the general public. Magicpedia
Magigram was a Magic Periodical for the Supreme Magic Co. edited by Ken de Courcy from September 1966 to February 1995. Magicpedia
NOT SEEN. PAYWALLED
Quoted by: Peter Prevos
Alagappan, Serena. 'The Timeless Journey of the Möbius Strip. After the disaster of 2020, let's hope we're not on a figurative one'. Scientific American Opinion, January 16, 2021
Printed
Altschuler, Eric L. and Anthony Phillips. 'The sound of topology: two dimensional manifolds in Bach'. The Musical Times, Vol 156, No. 1933, pp. 57–64
A scholarly look at crab canons on the Möbius strip.
Anderson, Gene and Francis Marshall. 'Classic Effects. Afghan Bands', Newspaper Magic Part 2. Magic Inc., Chicago, 1968, pp. 116–123.
With contributions from Gene Anderson, 'Afghan Bands', 114–116; Francis J. Rigney, 'A New Twist', 116–117; 'Chinese Version', Louis Bertol, 118–119, Martin Gardner; 'Martin Gardner on Afghan Bands', 120–122; Tommy Thompson, 'Look! No Twist', and 'Books on Paper Magic', p. 144.
https://archive.org/details/NewspaperMagicPart2-GeneAndersonFrancisMarshall/
A nice treatment on Afghan bands, with good mathematics.
Bio. Gene Anderson (1941–), a chemist by profession, is noted for his award winning newspaper magic.
He is best known for his marketed version of the Torn and Restored Newspaper, which was featured by Doug Henning. Magicpedia
Bio. Frances Ireland Marshall (1910–2002) was an accomplished magicienne, specializing in children's shows. Magicpedia
Printed
Anderson, Gene and Tadashi Tokieda. 'Squares, Hearts and MÖBIUS'. Journal of Magic Research [electronic resource] No. 7, December 2015, pp. 5–8
"A Valentine from Möbius" was the name given a 2014 Valentine's Day link on Harvard University's website…
Bio. Tadashi Tokieda (Japanese: 時枝正; born 1968) is a Japanese mathematician. He is a professor of mathematics at Stanford University; previously he was a fellow and Director of Studies of Mathematics at Trinity Hall, Cambridge. Wikipedia
Quoted by: Ask Alexander, Peter Prevos
Anderson, Gene and Tadashi Tokieda. Gene Anderson — The Bookpure GENEius. Selfpublished, 2016, p. 199
'Precocious Paper Chain' A. Introduction. B. Preview to precocious, C. The Möbius strip, D. The precocious Möbius strip E. Gene's presentation,
NOT SEEN. CONJURING ARCHIVE REFERENCE
https://www.conjuringarchive.com/list/book/1941
Annemann, Theodore. The Jinx. No. 43, April 1938
…when asked what had been deleted by them, told me the Afghan Bands were penciled out,
A brief mention in passing in the 'editrivia' column.
The first of three Annemann references.
Theodore 'Theo' Annemann (1907–1942), born Theodore John Squires, was an American professional magician who specialized in the field of Mentalism. Annemann is most famous for inventing and refining many of the standard mentalism routines that continue to be used by magicians today. Magicpedia
The Jinx was a Magic Periodical edited and published by Ted Annemann, also its major contributor, in Waverly, New York.
Jinx started in October 1934 and ran for 151 issues. Its last issue was December 15, 1941 just before Ted committed suicide. Originally put out on a monthly basis, it became a weekly publication in October of 1939. Magicpedia
Quoted by:: Ask Alexander
Annemann, Theodore. The Jinx. No. 139, 1940, p. 789
The oldest boy then did the Afghan Bands with the patter…
A brief mention in passing.
The same is repeated in June 1940.
Quoted by: Ask Alexander
Anon. [presumably prepared by the editor, Richard A. Proctor]. Trick with paper bands. Knowledge 11 January 1888, pp. 67–68.
Short description, based on La Nature, i.e. Tissandier, with copy of the illustration, omitting Poyet's name. Singmaster
Quoted by: David Singmaster
Anon. Paperfolding in Caras y Caretas (Buenos Aires edition)
Issue 252 of the Buenos Aires edition of 'Caras y Caretas', published on 1st August 1903, contained instructions showing how to flatten a mobius strip to form a regular hexagon, an effect which had originally been published in 'La Science Amusante'. Mitchell
Publication. Caras y Caretas is a weekly magazine of Argentina published from 1898 to 1941 in its first period of existence. There was a previous version published in Uruguay between 1890 and 1897. Caras y Caretas was relaunched in 2005 under the direction of historian Felipe Pigna, having been published since then. Wikipedia
Quoted by: David Mitchell
https://www.origamiheaven.com/historycarasycaretas.htm
Anon. 'Los anillos de papel' in Repertorio Completo de Todos los Juegos, 1896
Translated. The Paper Rings' in 'Complete Repertoire of All Games
Quoted by: David Mitchell
https://bdh-rd.bne.es/viewer.vm?id=0000005049&page=1
https://www.iberoamericadigital.net/BDPI/Search.do;jsessionid=131657D106293C102EFE9D631DDE87D3?numfields=1&field1=docId&field1val=bdh0000005049&field1Op=AND&advanced=true&hq=true&important=T%C3%ADtulo%3A+Repertorio+completo+de+todos+los+juegos
Anon. 'Le Livre des Amusettes' by Toto, which was published in Paris by Charles Mendel, 1899.
Translated: The Book of Fun
Quoted by: David Mitchell
Anon. 'Die Kunst, in ein ringförmig geschlossenes band einen Knoten zu machen'. Die Zauberwelt (Vol. 5, No. 8) Aug. 1899, p. 125 ($49.50 at Lybrary)
Translated:
"The art of making a knot into a closed circle", moebius/möbius strip routine, seven different rings are cut with up to three double-twists. Conjuring Archive
Die Zauberwelt = The Magic World
Publication. The Magic World [Die Zauberwelt] is the world's first magic magazine; It was published by Carl Willmann in Hamburg from 1895 to 1904 and appeared in monthly editions. Carl Willmann was a magic equipment dealer who ran his workshop and trade in Hamburg. In January 1895 he published the first edition of The Magic World. The magazine was published regularly every month for 10 years until 1904 by Julius Sussmann. The Magic World thus became a pioneer for similar publications. In March 1895 the magic periodical Mahatma came out in the USA and in June 1895 the magazine Der Zauberspiegel, which was published by the Berlin magic dealer Friedrich Wilhelm Conrad Horster. Wikipedia translation
Die Zauberwelt was the first German magic magazine. It was an excellent publication. The content covers a wide range of magic, from tricks with cards, coins and billiard balls, to apparatus and mechanical tricks, illusions, tricks with flowers, cloths and flags, and mental and spiritualistic routines. There is even chapography, party jokes and games. Letters from readers and inquiries are also printed.
The multi-part card school, which runs over several years, is particularly worth mentioning. There are also routines and moves from very famous people such as Hofzinser and T. Nelson Downs. Translated from Lybrary
NOT SEEN. PAYWALLED.
Quoted by: Conjuring Archive
Of considerable historical importance.
Dieses Produktpacket beinhaltet 10 Produkte:
https://www.lybrary.com/zauberwelt-5-jahrgang-1899-p-923126.html No. 8 here $8 Download
Likely derived from the 1881 'pamphlet'.
Anon. 'Some Secrets of the Art of the Conjurer'. The New York Times. March 20, 1904: Vol. 53, Iss 16913, p. 11
A major discussion of conjuring in the round, including the Afghan bands. No indication of the author is given. Of historical importance.
The Afghan Bands Trick.
Another trick which can be used to advantage for drawing room entertainments is that known as the Afghan bands. The requirements consist merely of a pair of scissors. with sharp points and three or four strips of white paper, each five or six feet long and about one inch in width, pasted together at the ends, so as to form endless bands.
[Picture]
Here are the instructions: ''The performer comes forward with these bands. strung on his left arm. Taking them one by one in the right hand and showing that they are all separate. He lays them on a table or chair, or if he prefers it, hangs them around his neck. Then, taking one of them he makes a hole with the scissors in the centre of its width, and, handing the paper round, says: 'I didn't want the two rings separated. I wanted them linked one between the other. You couldn't do that? You evidently are not a conjuror. If you had been a conjuror, you would just have whispered softly to yourself, Aldiboronticophosphikoformio! and the result would have been quite different. See!' With these words he takes the second band, perforates it with the scissors, and divides it lengthwise like the other. Two bands are again formed, but the one is linked with the other, as b in the illustration.
" The secret lies in the making up of the paper bands. The first is a perfectly ordinary band, one end being brought fairly round and pasted on to the other. In the second case the strip of paper is twisted half round before the ends are pasted together. In the third case it is twisted fully round before the ends are joined. If yet another twist be given to it before joining, the band, when cut, will appear as D in the illustration.
"The chief point the novice has to bear in mind in preparing the bands is to have them long enough. The longer they are the less likely is the twisting of the bands tion." [sic]
https://archive.org/details/sim_new-york-times_1904-03-20_53_16913/page/n11/
Source: Internet Archive.
Printed
Anon. [H. W. R.] Games and Amusements. Ward, Lock & Co., London, nd [c1910??].
The mysterious paper bands, p. 128. Describes bands with 1, 2, 3 twists and cutting them in half. Singmaster
Quoted by: David Singmaster
NOT SEEN
Not to be confused with Frith's like title
Anon. 'The Magic Paper Rings'. The Daily Mirror, November 6, 1926, p. 13
THE MAGIC PAPER RINGS. A Simple, but Effective, Little Trick
This little trick with paper… Cut a long strip of paper, join the two ends together…
Illustrated, with three bands.
In a children's full-page section of the paper.
Anon. Lewiston Evening Journal. February 20, 1934
Syndicated (Hence second, third etc. entries are not listed in full but are by publication only, below)
Fun with Paper and Scissors... Trewey for the "paper rings" trick by naming it after him. However, it has been done on the stage on and off for many years. With the first you paste the two ends together to form a perfect ring. With the second, however, you twist the …
Also: Saskatoon Star-Phoenix, February 24, 1934; St Petersburg Times, February 25, 1934
Anon. Die Glocke, 1934, Jugendland, Der verhexte Papiering, Saturday, 24 November. 1934 German
Translated: The Bell. Youth country. The Bewitched Papering
https://www.deutsche-digitale-bibliothek.de/newspaper/item/OYFXYWVTELO6A5234ZTSNEM2PV2B5XUO?sort=sort.publication_date+asc&lang=en&query=%22M%C3%B6biussche+blatt%22&hit=1&issuepage=18
Appears to be a children's page. Illustrated
Anon. 'Tricks You Can Do!'. Liverpool Echo. (Junior Magazine Echo). Saturday, 23 October, 1954, p. 2
Illustrated, but not in full; concentrating on the twists.
One does not hear much about paper magic and yet it has a charm all of its own. Let us start by taking three strips of paper… AFGHAN BANDS Taking the first one, you cut down the centre with a pair of scissors
The piece credits Teach Yourself Conjuring by J. Elsden Tuffs. Nothing new but of a relatively early (BNA) historical newspaper reference.
Anon. 'A historic collection of mathematical models'. The Mathematical Gazette, Vol. 45, No. 354, December, 1961
Recently, as a result of the sale of some property belonging to the Herschel family, there came to light a chest of drawers packed with mathematical models which were evidently made by Prof. A. S. Herschel about the year 1890. The labels which accompany them indicate that some were exhibited at Munich in 1893 at an Exhibition sponsored by the Deutsche Mathematike Vereinigung; others were shown at the Royal Institution in 1897. Most of the models are of wood and seem to represent types of crystal structure. Other oddities include a Mobius strip made from part of a fashion plate,...
An interesting early (1890) account is given in the Gazette. The Prof. A. S. Herschel is Alexander Stewart Herschel (1836–1907), a leading astronomer of the day, and the grandson of the famed astronomer William Herschel. The account clearly shows they were exhibited in prestigious institutions. Quite what happed to the models and the Möbius strip in particlar is not known
The holder was given as a Miss W. A. Cooke, 6 Cherry Orchard, Stoke Pogues, Buckinghamshire. Cooke, a B.Sc, was the honorary secretary of the Cambridgese University Council 1961. She was active in 1954. A Vice President in 1966. And there the trail runs cold! What became of these models, and in particular the Möbius strip?
Anon. Chicago Tribune. October 20, 1995
William J. Lloyd, 58 was creator of recycling logo. In 1968, he joined Container Corp.,and a year later was made manager of design. It was during his years with Container Corp. that he created the three-arrow recycle logo.
NOT FULLY SEEN.
Falsely credits William J. Lloyd as the designer of the recycling symbol. More accurately, Lloyd changed the orientation of the design. That's all. That said, I agree that this is for the better, but it's a long way from being credited as the designer.
Anon. 'The creation of the logo for Germany's Presidency of the Council of the EU', 2020
https://www.eu2020.de/eu2020-en/presidency/logo-and-claim/2360188
Designed by Annette le Forte and Andre Heers. Also has a video, in German.
https://www.bundesregierung.de/breg-en/service/archive/a-symbol-of-unity-and-connectedness-1756418
Anon. 'Mobius [sic] strip design gives Shenzhen bookstore distinctive look'. 5 January 2024. CGTN
https://news.cgtn.com/news/2024-01-05/Mobius-strip-design-gives-Shenzhen-bookstore-distinctive-look-1q7lEffz8uA/p.html
CGTN is the English-language news channel of state-run China Global Television Network, based in Beijing, China.
Anon. 'A Fascinating, Improbable Shape'. 'When the World Came to Town'. Inlander. 50th anniversary commemorative edition, 2024
https://issuu.com/theinlander/docs/inlander_visitspokaneexpo50thcommemorativeedition_?fr=xPf81NTU
Repeats the Chris Bovey Carlson story at the 2014 anniversary! Nothing new on the symbol. A nice logo for the 50th celebrations, though!
Angélil, Marc and Cary Siress. 'Going Around in Circles: Regimes Of Waste'. Anyone Corporation Log, Winter 2010, No. 18 (Winter 2010), pp. 101–112
Reproduces Anderson's sketch on the first page, with a caption, but no further discussion. Seen and noted.
Art@Site
https://www.artatsite.com/Moscow/details/Nalich-A-E-Mobius-Strip-Komsomolskiy-sculpture-modern-contemporain-art-Moscow-Moskva.html
Sculpture by A. E. Naclich, a Russian artist, 1972.
Ashforth, Pat and Steve Plummer. 'Möbius Bands'. Not dated.
https://www.woollythoughts.com/mobius.html
Möbius strips of zips, in the style of Long.
Astor, V. J. Astor Katalog A Bücher, Mikromagie, Bühne und Salon. [ca. 1990?] p. 36
AFGHAN BANDS, wobei man das
Translated: Astor Catalogue A Books, Micromagic, Stage and Salon
AFGHAN BANDS, where you can
V. J. Astor (1922–2011) became interested in magic at an age of eight. His mother supported his interest but his father insisted he would become a doctor. Magicpedia
Quoted by: Ask Alexander
Printed
Astor (Victor Jamnitzky). Zaubern mit Papier, 2000, pp. 9–20
Translated: Magic with Paper
Afghan Bands. Es gibt vielleicht keinen geheimnisvolleren Körper, als das sog. Möbius Band: Ein Stück Papier…
In German. Has many cross references to Afghan Band/Möbius strip that most other articles do not. Given its substantial nature, I decided to translate.
The famous Astor (Victor Jamnitzky) collected top secret routines from his best friends. These original manuscripts were so far only available in German. Enjoy the fantastic miracles of Jahn Gallo, Joro, Bob Driebeek, Axel Velden and Mr. Schnitter.
Bio. V. J. Astor (1922–2011) became interested in magic at an age of eight. His mother supported his interest but his father insisted he would become a doctor. In 1941 he started studying medicine. In that time he earned his living at a theatre. Soon he terminated studying to become a magician but was banned because of missing authorization. After examination he received allowance. By the end of 1941 he got engagements at the Berliner Wintergarten and at the Scala using the name "Nicoletty." Magicpedia
Quoted by: Internet Archive (the only German reference!)
https://archive.org/details/Zaubern_mit_Papier__224990T_/page/9/mode/2up?q=afghan+bands
Baltzer, Richard H, F. Klein, and W. Schiebner (eds.), August Ferdinand Möbius, Gesammelte Werke (Leipzig, 1885–87).
Heinrich Richard Baltzer (1818–1887) was a German mathematician, known for his writings on determinants.
Baltzer, R., F. Klein, W. Scheibner (eds.). August Ferdinand Möbius Gesammelte Werke, 662 pp. Leipzig: S. Hirzel, 1885, Volumes 1–4
Translated: August Ferdinand Möbius Collected Works. Published by the Royal Saxon Society of Sciences
Translated: August Ferdinand Möbius Collected Works
Vol. 1, edited by R. Baltzer. Gesammelte Werke, 741 pp. (Erster Band = First Volume)
https://archive.org/details/gesammeltewerkeh01mbuoft P. 403 pentagrams. P. 411 inspiration?
Vol. 2, ed. F. Klein. Gesammelte Werke. 724 pp. (Zweiter Band = Second Volume)
https://archive.org/details/gesammeltewerkeh02mbuoft
This discusses (with a drawing of a rectangular strip) the Möbius strip, p. 484
The different shapes of the two types of zone surfaces can be clearly visualized by means of a strip of paper which has the shape of a rectangle. If A, B, B', A' (see Fig. 1) are the four corners of the rectangle,….
Vol. 3, ed. F. Klein. Gesammelte Werke. 594 pp. (Dritter Band = Third Volume)
https://archive.org/details/gesammeltewerkeh03mbuoft
Vol. 4, ed. F. Klein and W. Scheibner. Gesammelte Werke. 748 pp. (Vieter Band = Fourth Volume)
https://archive.org/details/gesammeltewerkeh04mbuoft
Banchoff, Thomas F. Beyond the Third Dimension: Geometry, Computer Graphics, and Higher Dimensions. New York: Scientific American Library: Distributed by W.H. Freeman, 1990, pp. 194–198
Chapter 8, Möbius Bands, Real Projective Planes and Klein Bottles
We should think of the band as made of some porous material through which an ink-drawn figure bleeds, leaving us no way to tell on which side of the strip the figure was originally placed. A triangle drawn on, or rather in, this two-dimensional strip can slide along the strip and come back so that it is superposed on its mirror image. There are no enantiomorphic pairs on a Mobius band.
This nicely makes a point about the transparency, or not, of the band, something that is not generally addressed.
Barber, W. 'The prevailing female fashion'. M-U-M, 54(12):625, 1965.
Quoted by: Peter Prevos
Barr, Stephen. Experiments in Topology. New York, Crowell. Original edition, 1964
https://archive.org/details/experimentsintop0000step/
All editions on the Internet Archive are one-hour loan only. The first edition has a Möbius folded triangle strip on the front cover (later ones do not). Incidentally, this is the first recorded illustration/picture of a Möbius strip on the cover of any publication (see 'Book Covers')
https://archive.org/details/experimentsintop00barr/page/207/mode/2up?q=moebius&view=theater
Bartlett, J. B. Rev. 'A Glimpse of the Fourth Dimension'. The Boy's Own Paper, 12, No. 588, 19 Apr April 26, 1890, p. 462
Illustrated with a diagram of a Möbius strip, and cuts it in an 'Afghan' style. Begins well, and then wanders into 'mystic speculations', of fourth dimension. Chiefly of interest due to its historical significance.
https://higherspace.wordpress.com/wp-content/uploads/2010/11/mobius_strip.gif
The Rev. Bartlett's column was a regular piece (Mark Blacklock)
A glimpse of the "Fourth Dimension". The Boy's Own Paper 12 (No. 588) (19 Apr 1890) 462. Simple description. Singmaster
Quoted by David Mitchell, David Singmaster
Printed
Beal, Ted. 'The Debur Afghan Bands'. In P. Naldrett, editor, More Collected Magic, 1921, pp. 31–32. Percy Naldrett, Portsmouth.
https://store.conjuringarts.org/product/pdf-more-collected-magic-percy-naldrett/
Bio. Percy Naldrett (1888–1973) was both a conjurer and great war poet. Naldrett was an editor of The Magic Circle's organ, The Magic Circular and also its printer. The latter being undertaken in his garden shed. Magicpedia
Ted Beal is only mentioned by Gardner, who quotes Nadrett!
In England at about the same time [as Carl Brema in 1920], Ted Beal thought of presenting a paper version which began with a single large band. It was cut in half to form two paper bands, one with two twists and the … Mathematics Magic and Mystery
NOT SEEN. PAYWALLED.
Quoted by: Peter Prevos
Bertol, L. 'This is old!!!' The Linking Ring, 46(1): pp. 56–57, 1966
Publication. The Linking Ring is the name of the official magazine for the International Brotherhood of Magicians.
Issue 1 Number 1 was published in January 1923. It comprised only four pages. It contained an editorial by Ernest Schieldge, a biography of Len Vintus written by Gene Gordon and a listing of all 20 members. Magicpedia
Quoted by: Peter Prevos
NOT SEEN. PAYWALLED
Bennett, G. T. 'Paradromic Rings'. Letter in Nature, June 30, 1923, p. 882
Bennett taking C. V. Boys to task for lack of credit in reply to the former's letter of 9 June 1923! Also see Anne Betts.
The third reference to 'paradromic rings' (after Tait and Rouse Ball). Curiously, mentions Listing, but not Möbius. Was Bennett ignorant of Möbius?
Bio. Geoffrey Thomas Bennett OBE (1868–1943) was an English mathematician, professor at the University of Cambridge. Wikipedia
Printed
Bergamini, David. Mathematics. Life Science Library, 1963
Picture spread, pp. 182–185. This book possibly influenced Lloyd Carlson when he designed the symbol for the Expo '74 exhibition, as related by his son, Steven, in the Inlander. However, none of the illustrations match the hexagonal outline as in the logo.
Betts, Annie D. 'A Puzzle Paper Band'. Letter in Nature, June 30, 1923, p. 882
AN easy solution of the paper-band puzzle described by Prof. C. V. Boys in NATURE of June 9, p. 774, is obtained as follows:...
Bio. Miss Annie Dorothy Betts is one of the many people who have made a huge contribution to beekeeping, but is now almost forgotten. She was born into a well known family of railway constructors on 22nd November 1884 in Surbiton, Surrey and died on 8th September 1961. Information online is rather scarce, but she is credited with being a pioneer in bee research, author, editor and worked as an aeronautical engineer during WW1. David A. Cushman
Printed
Bfinegold. [User name]. 'I've always resonated with Mobius bands — but now I know signals do too!'
AMS blog. December 4, 2013
https://blogs.ams.org/blogonmathblogs/2013/12/04/ive-always-resonated-with-mobius-bands-but-now-i-know-signals-do-too/
Bill, Max and Jacob Bill. Max Bill: Endless Ribbon 1935-95 and the Single-sided Surfaces. Benteli Verlag, 1999.
A documentation of the five versions of Bill's "Endless Ribbon" sculpture from 1935 to 1995. With essays by Max Bill, Jakob Bill, Dietmar Guderian, and Michael Hiltie. Text in English and German. First edition. 102 pp.; illustrated from photographs and drawings.
NOT SEEN
Bing, Robert. 'Surfaces'. The American Mathematical Monthly, Vol. 67, No. 7, Part 2: Elementary Point Set Topology, August-September, 1960, pp. 8–15
Begins (first three pages) in a popular sense with Möbius strips before moving on to more advanced concepts, with Klein Bottles, Tori, etc, out of my knowledge.
Part printed
Blood, S. 'Society Reports'. Abracadabra, 74, 1919, 532, 1982.
Publication. Abracadabra, widely known as just Abra, was a weekly magic magazine published in the UK that ran for a total of just over 63 years. Abra started on February 2, 1946 by Goodliffe Publications. Goodliffe successfully maintained the weekly magazine until his death near the end of 1980, afterward his family continued the business. Magicpedia
Blood is unknown.
NOT SEEN. PAYWALLED
Quoted by: Peter Prevos.
Blood, S. 'Tricks and Stunts for Christmas'. Magic Circular, 81(14):45, 1987.
Publication. The Magic Circular is the official magazine of the Magic Circle. It is the longest continuous running magic periodical in Magic's history with well over one thousand issue.
In 1906, Nevil Maskelyne edited the first issue of The Magic Circular, and on its cover were the signs of the zodiac which, together with the words "Indocilis Privata Loqui", which would become the emblem of The Magic Circle. The Latin motto, roughly translated, means "not apt to disclose secrets."
The Magic Circular has been published continuously on a monthly basis since that time.
Magicpedia
NOT SEEN. PAYWALLED
Quoted by: Peter Prevos.
Blyth, Will. Paper Magic. C. Arthur Pearson Ltd, 1920. 'An Episode of Mere Man', 1920, p. 38
It has been stated that we are indebted to some old Indian fakirs for this neat and puzzling little drawing-room trick. The secret is extremely simple, and depends entirely upon the method of making up the bands. These may be prepared beforehand, but a much better effect will be produced if the straight strips are first handed for examination and the bands then joined in front of the audience, care being taken that they do not detect the secret during the process.
[Fig. 113]
Tear three long strips of paper, each about one inch wide, to make rings No. 1, 2, and 3 of Fig. 113.
The ends of ring No. 1 are joined together in the ordinary way by means of an adhesive, or gummed paper. In joining the ends of ring No. 2 one twist must be given to the strip, while in making No. 3, the strip is twisted twice. The three rings should now appear as in Fig. 113, and if the strips are fairly long, the twists will not be noticed.
[Fig. 114]
If these bands are now cut through the centre they will appear as shown in Fig. 114
Patter…
Will J. Blyth (1873–1937) was the author of many magic books. He was elected to the position of Hon. Librarian of the Magic Circle in August of 1919, and served in that capacity until his death on January 7, 1937. Magicpedia
https://archive.org/details/Paper_Magic_Will_Blyth/page/n37/mode/1up
Book. Paper magic: being a collection of entertaining and amusing models, toys, puzzles, conjuring tricks, etc. in which paper is the only or principle material required with an introduction note by Nevil Maskelyne.
This was one of the inexpensive books which later became known as the Yellow Perils. Magicpedia
Quoted by: David Mitchell
Boas, Ralph P., Jr. 'Möbius Shorts'. Mathematics Magazine, April, 1995
Boi, Luciano. 'Images et diagrammes des objets et de leurs transformations dans l'espace'. Visible, No. 5, 2009
Translated. Images and diagrams of objects and their transformations in space.
Largely popular account. Has many references to the Mobius strip throughout, but without being of a dedicated nature.
Bio. Is Senior Scientist and Associate Professor (with tenure since January 1, 1998) in Ecole des Hautes Etudes en Sciences Sociales.
https://www.unilim.fr/visible/324 (in English)
https://www.unilim.fr/visible/324&file=1/
Bonola, Roberto and Horatio Scott Carslaw. Non-Euclidean Geometry. A Critical and Historical Study of Its Development. Chicago, Open Court Publishing Company, 1912, pp. 148-149
An example of a one-sided surface is given by the Leaf of MOBIUS [Mobiussche Blatt], which can be easily constructed as follows: Cut a rectangular strip ABCD. Instead of joining the opposite sides AB and CD and thus obtaining a cylindrical surface, let these sides be joined after one of them, e. g., CD, has been rotated through two right angles about its middle point. Then what was the upper face of the rectangle, in the neighbourhood of CD, is now succeeded by the lower face of the original rectangle. Thus on Mobius' Leaf the distinction between the two faces becomes impossible.
Of note is the use of 'Möbius leaf' for the strip, which suggests the standard term used today had not become fully adopted. However, this may be down to the translation (from Italian?) Mobiussche Blatt]= sheet.
Bowers, Dawn. Expo `74 World's Fair Spokane. Spokane: Expo '74 Corp.
https://archive.org/details/expo74worldsfair0000bowe/
Official commemorative, 128 pp. Skim viewed (missing pages 63,64). Very nice treatment of the Expo '74 event. The text has many photographs accompanying it. However, the symbol is not discussed, nor appears in any of the photos! It is only shown as a line drawing on the frontispiece and pages 4 and 103.
Boys, C. V. 'A Puzzle Paper Band'. Letter in Nature of 9 June 1923, p. 774.
A Möbius strip is described but not credited to any one person. The letter sparked further correspondence, from G. T. Bennett and Annie D. Betts. Bennett takes Boys to task for improper credit where Bennett has a subtle and amusing dig at him in the last paragraph.
Interestingly, the term 'Möbius strip' or alternates had evidently still not come into common parlance. Boys, Bennett and Betts discuss 'paper bands' and not a strip/band as such.
Bio. Sir Charles Vernon Boys, FRS (1855–1944) was a British physicist, known for his careful and innovative experimental work in the fields of thermodynamics and high-speed photography, and as a popular science communicator through his books, inventions, and his public lectures for children. Wikipedia
Printed
Brand, Louis. Vector and Tensor Analysis. New York, J. Wiley, 1947, p. 218
A brief mention in passing.
The simplest unilateral surface is the Möbius strip; this may be materialized by taking a rectangular strip of paper, giving it one twist, and pasting the ends ab and a'b' together (Fig. 100a). This surface has but one side; if we move a point P along its median line and make a complete circuit of the strip it will arrive at the point P' directly underneath. Since we can travel on a continuous path from one side of the Möbius Strip to the opposite, these sides cannot be distinguished. This is not the case with a spherical surface,...
https://archive.org/details/vectortensoranal00branrich
Breitenberger, E. 'Johann Benedict Listing'. Neue Deutsche Biographie. 1952;14.:700–701.
Breitenberger, Ernst, "Listing, Johann Benedikt" in: Neue Deutsche Biographie 14 (1985), pp. 700-701 [online version]; URL:
https://www.deutsche-biographie.de/pnd117063193.html#ndbcontent
Breitenberger, E. 'Gauss und Listing: Topologie und Freundschaft'. Gauss-Ges Gottingen Mitt. 1993; 30:3–56.
NOT SEEN
Breitenberger, E. Johann Benedict Listing. In: James IM, editor. History of Topology. Amsterdam: 1999; 909–924.
https://www.google.co.uk/books/edition/History_of_Topology/7iRijkz0rrUC?hl=en
PART PREVIEW
Lots here of interest.
Ernst Breitenberger (1925-2020)
Brown, Richard (ed.). 30-Second Maths. The Möbius Strip, pp. 120-121
Standard fare.
Bruckner, Max. Vielecke und Vielflache, Theorie und Geschichte. Leipzig B.G. Teubner, 1900. (Polygons and polyhedrals, theory and history) Mobius blatt, p. 54-55
https://archive.org/details/vieleckeundvielf00bruoft/
Illustrates a Möbius strip
Möbiusschen blatts = Möbius sheets
Bullivant, Cecil. H. The Drawing Room Entertainer. C. Arthur Pearson, London, 1903.
Paper rings, p. 48. Cuts various rings in half. Singmaster
Bio. Cecil Henry Bullivant (fl. 1900–1910) was author of several magic books. Magicpedia
Quoted by: David Singmaster
NOT SEEN. PAYWALLED
Bullivant, Cecil H. Home Fun. New York Dodge Publishing Company, 1910, pp. 501–502
THE MYSTERIOUS BANDS Take a full sheet of a large newspaper, e.g. the first and last pages (which make one sheet) of a paper like the New York Times, and cut three straight strips (a, b, c) about three inches wide, as shown in Fig. 23. Now join the ends of these strips in the following manner in order to make three loops...
https://archive.org/details/homefun00bull/page/501/mode/1up?view=theater
Allusion. Illustrated and discussed.
Printed
Quoted by: David Mitchell
Blyth, Will. Paper Magic., first published in London in 1920, as 'An Episode of Mere Man', 1920
Quoted by: David Mitchell
Cantor, Moritz. Review of 'In ein ringförmig geschlossenes Band einen Knoten zu machen", und verwandter merkwürdiger Probleme' by Oscar Simonyi ("To make a knot in a ring-shaped band", and related strange problems)
The 'Tait pamphlet' reference!
I translated all the text (typed up by hand), given its importance
The speaker read this little book with even greater interest because, by a strange coincidence, the subject was being discussed experimentally in the Heidelberg Mathematical Society at the very time when the request was made that we should express our opinion on the content. Mr. Georg Wallenberg from Danzig, using thick paper tapes with gummed ends, showed us the most important of Simony's experiments and thus made our judgment much easier, whereas without the dexterity of this young mathematics student, our personal lack of spatial imagination would not have been able to adequately explain the results, even in spite of the excellent illustrations. Perhaps other readers have had the same experience and have thereby become biased towards things that they were unable to imagine…
Bio. Moritz Benedikt Cantor (1829–1920) was a German historian of mathematics. Wikipedia
Carroll, Lewis. Letter of June 1890 to Princess Alice.
Letter of Jun 1890 to Princess Alice. Not in Cohen. In 1890, Carroll met Princess Alice (whose father, Prince Leopold had been a student at Christ Church and had been enamoured of the original Alice, then aged 18, but the Queen prevented such a marriage), then age 6 and became friends. This letter has the plan of a Möbius strip. This letter was advertised for sale by Quaritch's at the 2001 Antiquarian Book Fair in London. Carroll refers to it in his letter of 12 Aug 1890 to R. H. Collins and Cohen's note quotes Sylvie and Bruno Concluded, qv below, and explains the object. Singmaster
I have not seen the letter.
Quoted by: David Singmaster
Carroll, Lewis. Sylvie and Bruno Concluded. Macmillan, 1893. Chapter 7, pp. 96‑112, esp., pp. 99‑105.
Discusses Möbius band ("puzzle of the Paper Ring"), Klein bottle and projective plane. Quoted, with extended discussion in John Fisher; The Magic of Lewis Carroll; op. cit. in 1; pp. 230-234. Cf Carroll-Gardner, pp. 6-7. Singmaster
Quoted by: David Singmaster
Cartwright, Julyan and Diego L. González. 'Möbius strips before Möbius: Topological hints in ancient representations'. The Mathematical Intelligencer, June 2016, Volume 38, Issue 2, pp. 69–76
Historical predecessors by two theoretical physicists. A very nice, popular treatment.
Printed
Chapman, S. J. The dissection of rectangles, cylinders, tori, and Möbius bands into squares. November 1993. Duke Math. J. 72(2): 467-485 (November 1993).
NOT SEEN
Christopher, Milbourne. 'The Afghan Bands - The Möbius Strip', January 1946. Hugard's Magic Monthly (Vol. 3 No. 8) p. 185
NOT SEEN. PAYWALLED
Bio. Milbourne Christopher (1914–1984) was a prominent American illusionist, magic historian, and author.
President of the Society of American Magicians, an honorary vice-president to The Magic Circle, and one of the founding members of the Committee for Skeptical Inquiry, Christopher wrote a number of books, including a biography of Harry Houdini titled Houdini: The Untold Story, a chronicle of his own craft titled The Illustrated History Of Magic, and thousands of essays relating to magic and mentalism. Wikipedia
MMM mentions him
Quoted by: Conjuring Archive, Peter Prevos
Clarke, S. W. 'Magic books'. In The Annals of Conjuring, pages 123–124. The Miracle Factory, Seattle, Washington. Originally Published in The Magic Wand (1923–1928), 2001.
Publication. The Annals of Conjuring was advertised beginning in 1919. The prohibitive cost of book production and illustration, coupled with the disappointing response by intending purchasers, prevented the work being issued as originally intended. Thus it was first published serially in the pages of The Magic Wand from March, 1924 to 1928, then later in book form in 1929 (four copies), 1983 (reprint), 2001 (reprint). Magicpedia
It was a landmark in the recorded history of conjuring, representing the most detailed work on the subject at the time (and possibly even now) covering magic in England and Europe up until the early 1900's.
Publication. The Magic Wand was a British Magic Periodical that ran for 47 years from Vol. 1, No. 1 (September 1910) to Vol. 46, No. 256 (December 1957). It was equivalent to the US published Sphinx in terms of influence, longevity and time-frame.
The Magic Wand was a actually continuation of P. T. Selbit's magazine The Wizard, which was renamed when it was handed over to George Munro.
It started out as a monthly, suspended for a time during World War I, was transformed into a quarterly in 1921 after George Johnson had taken over, and finally became an undated "four-part book" until the last issue which bore the number 256. Magicpedia
Quoted by: Peter Prevos.
Coar?, Henry I. 'Double Surfaces', Science, Vol. xxii, No. 56, December 15, 1893, pp. 328-329
…has been called after his name, "Blatt des Moebius."
A detailed explanation as to the whys and wherefores of the number of twists.
References Dingeldey's, Topologische Studien…
Coleman. 'Hilo Hawaiian Bands. A brand new version of an old effect'.
NOT SEEN. PAYWALLED
Quoted by: Peter Prevos.
Conrad, G. 'Paging the Ladies: A New Use for Afghan Bands'. 1938, Genii,
2(9):321.
NOT SEEN. PAYWALLED.
Quoted by: Peter Prevos.
Cornell Study Bulletin for Teachers - Issue 3 - Page 73, 1908
Snippet view
.. Möbius 'surface" offers opportunity for testing visualization. Cut a slip of paper about three inches wide and twenty long. Paste the ends together after making a half twist in the strip . ( 1 ) Can you paint or water - color one
Courant, Richard and Herbert Robbins. What is Mathematics? Oxford University Press, second edition, 1960. First published in 1941
P. 235
One of the great geometers of the time was A. F. Moebius (1790-1868), a man whose lack of self-assertion destined him to the career of an insignificant astronomer in a second-rate German observatory. At the age of sixty-eight he submitted to the Paris Academy a memoir on "one-sided" surfaces that contained some of the most surprising facts of this new kind of geometry. Like other important contributions before it, his paper lay buried for years in the files of the Academy until it was eventually made public by the author. Independently of Moebius, the astronomer J. B. Listing (1808-1882) in Goettingen had made similar discoveries, and at the suggestion of Gauss had published in 1847 a little book, Vorstudien zur Topologie. …
And following, scattered discussion. His commentary on Möbius seems a bit harsh!
Coxeter, H.S.M. 'Coloured Symmetry'. In M.C. Escher Art and Science, by H. S. M. Coxeter (Editor), M. Emmer (Editor), R. Penrose (Editor), M.L. Teuber (Editor), North-Holland, 1986.
Pp. 15–33
P. 27. Recalling that Escher did not hesitate to draw a finite version of his Horsemen on an ingeniously twisted cylinder [6, p.100], we might easily imagine his going on to draw such a finite version of his Butterflies.
'[6, p.100]' refers to Magic Mirror. Coxeter seems to be referring to a Möbius strip here. Note that Ernst does not use the exact phrase twisted cylinder but is rather Coxeter's own interpretation. He does not use the 'Möbius strip' in the discussion. This has the potential for confusion. A topological cylinder is not a Möbius strip!
Cramer, Stuart. 'Remarkable Evolution of the Afghan Bands'. In Germain the Wizard. The Miracle Factory, Seattle, 2002.
Details: The master of the fine art of magic returns! Germain the Wizard combines the redesigned text of Stuart Cramer's enthralling books on the life and art of Karl Germain with Germain's scrapbook and notebook. All Magic
NOT SEEN.
Quoted by: Peter Prevos.
Crato, Nuno. 'Escher and the Möbius Strip' in Figuring It Out Entertaining Encounters with Everyday Math. Heidelberg; New York: Springer, pp. 123–126.
https://archive.org/details/figuringitoutent0000crat
One hour loan
Seems to be based on the account of Ernst. From what I've seen, nothing original save for a mention of a logo for Banco Totta & Açores / Azulejo Publicitário Português logo
Cundy, H. Martyn and A. P. Rollett. Mathematical Models. Oxford University Press 1977
A popular, albeit brief, account of Möbius strips, pp. 191–193 in Chapter 4.5, Other Models in Solid Geometry.
Curtis, M. L. 'Amazing Mobius [sic] Bands'. Boys' Life, December 1960.
Standard fare, of a popular level.
Scout Life (formerly Boys' Life) is the monthly magazine of the Boy Scouts of America (BSA). Its target readers are children between the ages of 6 and 18. The magazine's headquarters are in Irving, Texas.[3][4][5] Wikipedia
The entire run had been digitised, with a search facility, so I took a look. Also see September 1970 and April 1987, for a further treatments, not documented here (juvenile material).
Davey, Gina. 'The Prints of M.C. Escher and the Fractal Boundaries Within Print Processes'. Thesis, 1999
Occasional reference to Möbius themes, Horseman. Flatters to deceive in general. I do not recall any new insight in the round. Seen and noted.
Dalal, S. 'Presentation for the Afghan Bands'. Swami, 18
Sam Dalal (b.1946) was the editor of Swami and Mantra. After phasing out of performing, he started his own magic manufacturing business called "Funtime Innovations." Magicpedia
NOT SEEN.
Quoted by: Peter Prevos.
Dayton, R. 'The Whole Art of Clippo'. Hades Publications, 1986
Clippo is the marketed name for a cut and restored paper effect by Will De Seive (William H. Wilson) around 1937 (as seen in Thayer advertising in Genii).... The effect has been marketed under various names, including Clip-It, Clipper and Scissoring Caesar's. Magicpedia
NOT SEEN. PAYWALLED
Quoted by: Peter Prevos.
D'Amore, Bruno. 'Visual Art and Mathematics: Common Characteristics of Order'. Leonardo, Summer, 1981, Vol. 14, No. 3 (Summer, 1981), pp. 230–231
A brief, in effect, 'note'.
Bio. Bruno D'Amore (1946-) is an Italian mathematician and author. Wikipedia
Printed
Debur, Paul. 'The Afghan Bands with Debur Improvement'. Conjurer 4, 29, p. 156
Debur is not known on Magicpedia
NOT SEEN. PAYWALLED
Quoted by: Peter Prevos.
DeMuth, Fred. 'How to conceal the twist in the Afghan bands'. The Sphinx, Vol. 22 (1):21.,1923
NOT SEEN (Paywalled at Lybrary)
Bio. Fred DeMuth (1885–1961) was a Corning Glass employee and amateur magician who created the DeMuth Milk Bottle (a precursor to the Milk Pitcher) and Improved Bottomless Glass. Magicpedia
Quoted by: Lybrary, Peter Prevos
de Muth, Fred. 'The Siamese matrimonial bands patter for Afghan bands'. The Linking Ring, 15(12),1971
Bio. Fred DeMuth (1885-1961) was a Corning Glass employee and amateur magician who created the DeMuth Milk Bottle (a precursor to the Milk Pitcher) and Improved Bottomless Glass. Magicpedia
NOT SEEN. PAYWALLED
Quoted by: Peter Prevos.
Design Week. 'Recycling logo just keeps coming back for more', June 2, 2000
https://www.designweek.co.uk/issues/1-june-2000/recycling-logo-just-keeps-coming-back-for-more/
Credits (erroneously) William J. Lloyd (of CCA) as the designer of the recycling symbol.
Devant, David. Tricks for Everyone. C. Arthur Pearson Ltd, 1910.
Curious paper patterns, pp. 20-21. Cutting rings with 0, 1, 2 half-twists in half. Singmaster
Bio. David Devant (1868–1941) born David Wighton in Holloway, London was an English magician, shadowgraphist and film exhibitor. His name is sometimes incorrectly spelt with a trailing 'e'. He was a member of the famous Maskelyne & Cook company and performed regularly at the Egyptian Hall in Piccadilly, London. In 1905 he became a partner with John Nevil Maskelyne. He was succeeded by Oswald Williams. Magicpedia
Quoted by: David Singmaster
Paywalled
NOT SEEN
Dexter, Will. Everybody's Book of Magic. Arco Publishers Limited, 1956
NOT SEEN. Not in Internet Archive.
Refers to Afghan bands
https://littleegyptmagic.com/ourmag.htm
Will Dexter (1906 - 1985) was a close-up worker, mentalist and writer. Born William Thomas Pritchard in England, Dexter was a professional journalist who started in 1928.…He ghosted several books for Robert Harbin. Magicpedia
Dingeldey, Friedrich. Topologische Studien über die aus ringförmig geschlossenen Bändern durch gewisse Schnitte erzeugbaren Gebilde. B. G. Teubner, Leipzig, 1890.
Translated. Topological studies on the structures that can be created from ring-shaped closed bands through certain cuts.
See page (foreword) v Mobisusche blatt
https://archive.org/details/topologischestu01dinggoog/mode/1up
Friedrich Dingeldey (1859–1939) was a German mathematician. In 1890 Dingeldey had a pamphlet published with a brief history of topology and basic results on knot theory obtained by various mathematicians.
Douglas, Jesse. 'One-sided minimal surfaces with a given boundary. Transactions of the American Mathematical Society. 1932, pp. 731-
A mention essentially in passing (Möbius strip) in regards of Plateau's problem, pp. 731 and 733.
Jesse Douglas (1897–1965) was an American mathematician and Fields Medalist known for his general solution to Plateau's problem. Wikipedia
https://www.ams.org/journals/tran/1932-034-04/S0002-9947-1932-1501661-8/S0002-9947-1932-1501661-8.pdf
'Dr Z…'. 'Les Anneaux Mysterieuse'. Recreations Scientifique. La Nature 709, 1st January 1887
(Afghan Bands) (Source: David Mitchell)
Translated: The Mysterious Rings
Dudeney, Henry. Cutting-out paper puzzles. Cassell's Magazine ?? (Dec 1909) 187-191 & 233-
235.
Calls it "paradromic ring" and says it is due to Listing, 1847. Probably based on Lucas. Singmaster
Quoted by: David Singmaster
NOT SEEN
Dunaway, Finis. 'The Recycling Logo and the Aesthetics of Environmental Hope'. In Seeing Green, Chapter Six, Oxford University Press, 2015, pp. 96-106
Google Books has a limited preview, but fortunately has most of the desired chapter! A nice scholarly piece, with quotations from Anderson. Reference is made to the Möbius strip, and illustrated with Escher's two themed prints.
https://academic.oup.com/chicago-scholarship-online/book/17329/chapter-abstract/174781160?redirectedFrom=fulltext
Limited preview (first page) only seen (paywalled).
Eckl, E. 'Gardyloo. Ed Eckl's First Lecture Notes'. 1977, 32 pp.
Bio. Ed Eckl (1934–2018) was a prominent figure in the Upper New York State magic scene and a performer at Eddie Fechter's Fork Hotel. As proprietor of Unikorn Magic, he published the magazine Precursor. Magicpedia
NOT SEEN. PAYWALLED
Quoted by: Peter Prevos.
Eckl, Ed. 'The Mobius Zip' 1984 (ca.). Described as 'using zippers for mobius strip/Afghan band effects, topological', p. 3
In Magic of my Friends. Philip Reed Willmarth 6 pages (Loose-leave collection). Self published, Illustrated with drawings by Dick Schick. Also published "Gardyloo" lecture notes
Quoted by: Conjuring Archive
NOT SEEN. PAYWALLED
Eldin, Peter. Great Book of Magic. Hauppauge, NY: Barrons, 2008, p. 40
The Afghan Bands has been a popular trick since the time of Adelaide Herrmann, and may be even older. It was first called "The Afghan Bands" by Professor Hoffmann, who wrote many books on the art of magic.
Juvenile, but of interest.
'Ellisdon for Novelties'. News Chronicle, January 4, 1939, p. 4
Afghan Bands. Startling Paper Cutting Mystery. Three long circular bands…
Full-page advert within Ellisdon's wide range. Illustrated with a maigicn doing the trick (small scale).
Background. The Ellisdon family established the London shop that inspired generations of magicians who visited or used their mail order service. Prior to this, the Ellisdons had been through boom, bust and scandal which led them to flee to the other side of the world.
Emch, Arnold. 'On a Special Class of Connected Surfaces'. The Kansas University Quarterly, Volume 3, Issues 1-4 1895, pp. 154-156, plate xiii,
... surfaces is, therefore, that they must have the same connectivity. Now we can give an example which is an ... unilateral and bilateral surfaces, as Moebius calls them, has already been treated several times, and many years ago . I ...
https://www.google.co.uk/books/edition/The_Kansas_University_quarterly/ozZ14kULNeYC?hl=en&gbpv=1&dq=unilateral+surfaces&pg=PA154&printsec=frontcover
Arnold F. Emch (1871–1959) was an American mathematician, known for his work on the inscribed square problem. Wikipedia
Emmer, Michele. 'Visual Art and Mathematics: The Moebius Band'. Leonardo, Spring, 1980, Vol. 13, No. 2 (Spring, 1980), pp. 108–111
Discusses contributions of Max Bill (Swiss architect, artist, painter, typeface designer, industrial designer and graphic designer), Corrado Caglian (Italian painter), and José de Riviera (American abstract sculptor). Discusses (and illustrates) Escher's Möbius Band I and Möbius Band II (p. 110) but not Horseman and Swans, possibly suggesting a dichotomy.
Printed
Emmer, Michele. 'Mathematics and Art: Bill and Escher'. In Bridges: Mathematical Connections in Art, Music, and Science Conference Proceedings, R. Sarhangi, ed. 2000
Dedicated pieces on Bill and Escher. Shows and discusses Bill's Endless Ribbon and Escher's Möbius Strip II
Printed
Enright, Diane. 'Shadowland. Princess Lotus Blossom's Afghan Bands'. M-U-M, 94(10):43;53, 2005.
Publication. M-U-M, Magic-Unity-Might, is the official organ of the Society of American Magicians. Magicpedia
M-U-M began in 1911. Between 1927 and 1951 it was published as a special section of other magicians' magazines (The Sphinx from 1927-1941, and 1947-1951; Genii from 1941-1947). It became a standalone magazine again in 1951. Prior to M-U-M becoming into existence, S.A.M. reports were published in the Sphinx magazine starting in 1902. The Online Books Page
NOT SEEN
Quoted by: Peter Prevos.
Epple, Moritz. 'Topology, Matter, and Space, I: Topological Notions in 19th-century Natural Philosophy'. Archive for History of Exact Scences. February 1998, Volume 52, 1998, pp. 297–392.
A first impression is that the subject matter is primarily on knots, which is strictly outside my interests (and ability). But scattered throughout are matters related to the Möbius study, and so is thus of interest. Four references are made to Möbius bands, pp. 346, 365, 375. Also on Tait championing Listing's work, pp. 375-379.
A lengthy, albeit nice, scholarly treatment but is still at a popular level.
Moritz Epple (1960-) is a German mathematician and historian of science… His habilitation thesis on the history of knot theory.… Wikipedia.
https://www.maths.ed.ac.uk/~v1ranick/papers/epple4.pdf
Printed (relevant pages)
Epple, Moritz. Die Entstehung der Knotentheorie: Kontexte und Konstruktionen einer modernen mathematischen Theorie. Vieweg+Teubner Verlag, 1999
Translation. The Emergence of Knot Theory: Contexts and Constructions of a Modern Mathematical Theory
Despite the title, without an indication of direct Möbius interest, there are related pages, and by chance others, including Escher! Pp. 89, 177, 181 Mobius strip is discussed. See p. 177 where Simonyi/Mobius/Listing is discussed.
P. 178 has a intersecting spiral band in the same broad nature as Barbaro's 1569 rendering and Escher's Spirals band in Magic Mirror, p. 98. The caption on p. 178 (Fig. 6.1) gives:
Ein von Simony zerschnittittener Schlauch (Simony 1884, Tafel I)
Translated. A hose cut by Simony (Simony 1884, Plate I)
I can't find the 1884 publication/
Listing is discussed beginning on p. 80, but then the preview is cut off!
'Experimental Topologie' p. 177, with Simonyi and Slade mentions.
Part preview
https://www.google.co.uk/books/edition/Die_Entstehung_der_Knotentheorie/Im31BQAAQBAJ?hl=en&gbpv=1&dq=%22In+ein+ringf%C3%B6rmig+geschlossenes+Band+einen+Knoten+zu+machen%22&pg=PA177&printsec=frontcover
Printed select pages of interest.
Erickson, Jeff. Book title unknown. Chapter 6. Surface Maps
https://jeffe.cs.illinois.edu/teaching/comptop/2017/chapters/06-combinatorial-surfaces.pdf
Regrettably, I have been unable to establish the book the excerpt is derived from.
Gives a most pleasing, considered, unravelling of Möbius-Listing priority matters, below. He also gives detail on (Henry) Slade, quoted by Tait, who previously I could not determine who he was. And incidentally, a salutary lesson on Slade of the swiftness of vanishing of contemporary fame! I for one had never heard of him.
Most historical sources observe that described the Möbius strip in July 1858, two months before its first appearance in Möbius's private notes, and first published it five years later. However, Listing merely mentions the one-sided strip in passing, in a footnote, stating only that "such surfaces have very different properties"; whereas, Möbius described the one-sided strip in much more detail, giving both a formal construction from five triangles and an intuitive construction from twisted paper strip, as part of the first formal investigation of non-orientable surfaces. On the other hand, a construction of the Möbius strip is already implicit in another paper of Listing, published more than a decade earlier [56, pp. 857–858]. Listing observed that if two threads are twisted around each other and their ends tied together, the result is either two (possibly linked) cycles or one (possibly knotted) cycle, depending on whether the threads are twisted an integral or half-integral number of times. Tait [78] eloquently described a popular application of Listing's observation:
…This remark of Listing's forms the sole basis of a work which recently had a large sale in Vienna: - showing how, in emulation of the celebrated Slade, to tie an irreducible knot on an endless string!
Henry Slade was an 19th century American spiritualist who claimed, among his many supernatural talents, the ability to introduce knots into a string whose ends had been tied together and covered with wax. When he was arrested for fraud in London, Slade was defended several prominent physicists, who argued that he was passing the string into the fourth dimension [76,91,92]. The Vienna street-magic trick described by Tait has been improved and generalized many times by magicians, most commonly under the rubric "The Afghan Bands". Perhaps the most famous version of the Afghan Bands was designed by James C. Wobensmith and performed by Harry Blackstone, Sr. using prepared strips of muslin [30].
I'm a computational geometer/topologist/graphophile with more general interests in algorithms, data structures, and lower bounds. I also have a growing interest in computer science education research, especially in understanding how students learn to design algorithms.
https://jeffe.cs.illinois.edu/cv.pdf
Ernst, Bruno. The Magic Mirror of M.C. Escher. Tarquin Publications, 1985. First Published January 1976.
Extensive discussion on Möbius strips in Chapter 14, 'Marvellous Designs of Nature and Mathematics', Moebius Strips, pp. 99–101.
Ernst, Bruno. M. C. Escher's Legacy, pp. 5–23 A Centennial Celebration: Collection of articles coming from the M.C. Escher Centennial Conference, Rome, 1998
We reproduce in Fig. 9 [periodic drawing 67] one of his most attractive and ingenious examples. It is one of the few regular divisions he also used for a print - the color wood engraving Horseman (1946) in which a topologically interesting band is rendered.
Interestingly, rather than simply (and obviously) stating 'Möbius strip', Ernst gives 'topologically interesting band'. This implies that it is not a Möbius strip. But It is not clear his intention here.
Ernst, Bruno. Escher Tovenaar op papier [Escher Magician onpaper], Kunsthal Rotterdam, Waanders Uitgevers, Zwolle, M.C. Escher Foundation, Baarn, 1998.
NOT SEEN
Ervin, E. 'A variation of the Afghan bands'. The Sphinx, 22(3):87, 1923
Bio. Dr. E(dward) G(eorge) Ervin DDS (1875-1947) was a dentist in Kansas City, Missouri. He was also an amateur magician who invented several tricks. Dr. Ervin had originally been instructed in the art of Magic by William Ellsworth Robinson, a personal friend of Ervin's father. Of Robinson, Ervin said, " A great magician, a kind preceptor. I shall never forget him." Magicpedia
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Quoted by: Peter Prevos.
Escher, Maurits. M. C. Escher The Graphic Work. Taschen, 1992. First published in 1959
Möbius Band I and Möbius Band II are discussed, p. 12, but only in a bare-bones, simple description. In connection with the possibility of other prints being a Möbius strip, Horseman and Swans are not discussed, which suggests a distinction.
Escher, Maurits. Phoenix, monthly journal of the visual arts, Volume 2, No. 4, June 1947; in the column 'Graphic Artists of the Netherlands Speak of Their Work'.
NOT SEEN.
Estralella, Jose. Ciencia Recreativa, Gustavo Gili in Barcelona, 1918.
Source: David Mitchell
Falletta, Nicholas. The Paradoxicon: A collection of contradictory challenges, problematical puzzles and impossible illustrations, Wellingborough: Turnstone, 1985, pp.153-160
If you take a strip of paper, 2 inches by 14 inches, and paste its narrow ends as shown in Figure 83, you would form a band. This band has two edges, one upper and one lower, and two surfaces or planes, one interior and one exterior. Now, if you take an identical strip of paper, but before the ends are pasted give it a half twist, how many edges and surfaces will this band have?...
Bio. Nicholas Falletta is a mathematics writer and the author of McGraw Hill-Education's SSAT/ISEE. Google Books
Popular treatment, likely taken from other sources. Discusses Escher's Mobus Stirp II print, with ants, relating an earlier 'Victorian version' reference (which he is not exact about). I must find!
https://archive.org/details/paradoxiconcolle0000fall/page/152/mode/2up
Fajuri, Gabe. Potter & Potter - 02 - Market Place Auction of Magic Apparatus, Posters, Ephemera, Houdiniana & Books No. 2, January, 2009
[Apparatus] [Harry Blackstone, Sr.] Harry Blackstone, Sr.'s Afghan Bands fro. Known in the Blackstone show as the "red as the Afghan Bands), throughout his career, and was one of the few effects he performed on
Source: Ask Alexander
Fauvel, John, Raymond Flood, and Robin Wilson (eds). Möbius and his Band. Mathematics and Astronomy in Nineteenth-century Germany, Oxford University Press, 1993
August Mobius was one of the 19th century's most influential mathematicians and astronomers. Written by six distinguished contributors, this book explores the work of Mobius and his brilliant German contemporaries. ..Norman Biggs traces his role in the development of topological ideas. Finally, Ian Stewart explores the legacy Mobius left to mathematics in our own century.
A major scholarly work, albeit only Norman Biggs and Ian Stewart discusses the strip aspect, and even then not throughout. Stewart shows the pictures in Gesselmelte. The books flatters to deceive in terms of the Möbius strip, in that this may be thought to be predominantly on the strip, which it is not, albeit the title implies a study in the round. In fact, there is no dedicated discussion on the strip in any chapter, but is rather discussed in the round when so addressed.
The preface states… it is a set of essays on topics reflecting the context, life, work, and influence of an nineteenth century academic.
Escher's Möbius Strip II (Ants) as the frontispiece. Chapters 1-4 are essentially on non Möbius strip matters, save for passing mentions. These can thus effectively be diregarded.
Chapter 5, The development of topology, by Norman Biggs, illustrates and references the Brazil impa stamp of 1967. P. 108 Möbius and one sideness. LIsting p. 109. A very good, popular discussion as to background. Chapter 6, Möbius's modern legacy, Ian Stewart, p. 121 pictures p. 122, p. 159 summary
https://archive.org/details/mobiushisbandmat00john/mode/1up
One-hour loan, without printing facility.
Flament, Dominique and Jean-Jacques Szczeciniarz. August Ferdinand Möbius: Entre polyèdres et corrélation élémentaire. Hermann Glassin, 2013, 465 pp.
Quoted by: Klaus Möbius.
Fleckenstein, J. 'Patter for Afghan Bands used by Flecky'. The Linking Ring, 27(2): 1947, pp. 43–44
Fleckenstein is not known at Magicpedia
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Quoted by: Peter Prevos.
Fleron, Julian, Philip Hotchkiss, Volker Ecke, Christine von Renesse. Discovering the Art of Mathematics Art and Sculpture. 2017. (The book appears to be in 'permanent' draft mode.)
Chapter 3 The Magical Möbius Band: Cultural Icon and Engineering Marvel. 3.5 Basic Mobius Topology, pp. 59-82
A very nice, in-depth treatment, largely at a popular level. Of note includes: Recycling symbol, pp. 73-74. Paper clip interlinking (not seen this before), pp. 75-80
Somewhat curiously, the Möbius strip chapter begins wih a topological discussion in general, focusing on maps, before beginning in earnest on p. 59.
https://www.artofmathematics.org/books/art-and-sculpture
Forsyth, A. R. Theory Of Functions Of A Complex Variable. Cambridge University Press, 1918. First published 1900
Consider a surface made out of a long rectangular slip of paper, which is twisted once (or any odd number of times) and then has its ends fastened together.
Describes a Möbius strip without naming it as such.
Andrew Russell Forsyth, FRS, FRSE (1858–1942) was a British mathematician. Wikipedia
Foster, Leslie. Mathematics Encyclopedia. Grisewood and Dempsey Ltd, 1985 (W. H. Smith Edition).
'Moebius and his Merry Band', pp 114-115.
Juvenile material. For a child's book, a good treatment of the strip, with systematic experiments.
Frankel, E.T. 'Loop of surprising length'. The Linking Ring, 24 1 p. 40-
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Quoted by: Peter Prevos.
Fréchet, M. and K. Fan. Initiation to Combinatorial Topology. Boston, Prindle, Weber & Schmidt, 1967
From a reference in Larrison. The impression Larrison gives is that Fréchet and Fan do original scholarly research into the matter, but they do not, seemingly simply quoting Tietze as their source.
See pages 29-35,107. See 14. Unilateral surfaces. A footnote gives credit to Listing. Quotes Tietze as an authority.
https://archive.org/details/initiationtocomb00frec_0
René Maurice Fréchet (1878–1973) was a French mathematician. He made major contributions to general topology and was the first to define metric spaces. He also made several important contributions to the field of statistics and probability, as well as calculus. Wikipedia
Freeman, Mae and Ira Freeman. Fun with Geometry. Reprinted by Kaye & Ward 1969. First published by Edmund Ward (Publishers) Limited, 1958
See 'One sided piece of Paper', pp. 46-47
Juvenile. Describes (and illustrates) a Möbius strip without naming it as such, or mentions of Möbius. This is perhaps understandable given the intended audience. Standard fare.
The same publication is also known as Fun with Figures:
https://archive.org/details/FunWithFigures_505
Frith, Henry. 'The Paper Rings', in Scientific Amusements. Ward, Locke and Co Ltd, London, New York and Melbourne, 1890. Translated from the French of Gaston Tissandier.
Quoted by: David Mitchell
https://archive.org/details/cu31924031296126/page/n14/mode/1up