Embedded Files
In the context of popular culture, the Möbius strip can be seen to have been the theme of many logos, worldwide. The literature on these varies tremendously, with for some book-length treatments (admittedly rarely) whilst others barely get a mention.
Quite how best to organise these is unclear. For the sake of a modicum of order of sorts, I place chronologically where known.
However, two logos in particular, namely the recycling symbol and Expo ‘74 symbols, so vast is the literature on these two logos, I have shown these as dedicated studies in their own right, with only a basic text here.
Researching these is trying at times. Background details range from an abundance to nothing. And then one has to assess sometimes lengthy documents for relevant details not always easily found. A lot here is simply collating material in the public domain, but is scattered. It is not a particularly creative task, but one of merely organising. Time is always a consideration. Wading through lengthy documents is not my thing for relative importance. This being so, these entries are best considered as of a basic standard, commensurate with the time allocated by myself to the task. I simply give an overview as best I can.
The intention is a comprehensive listing and survey. However, there are so many logos to document in the time I want to devote to this that this is impractical. The more and more I look, the more and more I find! Therefore, I largely concentrate on those of some renown, with minor instances merely ‘seen and noted’.The study has the potential to expand beyond all reason. As is now usual, the study expanded beyond what I anticipated as of one or two days after the February 2025 return. Primarily, this was caused by more in-depth writings. These all had to be properly documented, printed, read, and assimilated (the last as much as is possible of a first read-through), all of which takes time, much more so than one thinks it would take. Two days then became three, and then four, and so on. Each ‘extra’ day was envisaged as the last, but circumstances dictated an extension, rather than a premature end. Likely, I could continue even now, with ever finer refinements, but on the twelfth day, I have decided to end the study. It’s now undoubtedly mature and to the best of my belief the best monograph on the subject. One cannot ask for much more.
Even within the context of a ‘first look’ as detailed in the introduction, this is very much a first look! There is a lot to read and assimilate in the literature.
1. 1962+ A-1 Beer 7
2. 1967 IMPA (Possibly 1965) 12
3. 1968 Mauchly Group 13
4. 1970 Recycling Symbol 15
5. 1974 Expo ‘74 Symbol 16
6. 1975 (possibly much earlier), Canadian Mathematical Society 17
7. 1983 Parton Oil Company 18
8. 1983 International Mathematique Olympiade, Paris 19
9. 1992 International Mathematical Olympiad, Moscow 21
10. c. 1996 United Kingdom Mathematics Trust 22
11. c. 1996 Advantix Kodak 23
12. 2000? Possibly much earlier, Dresdner Bank 24
13. 2002 Belarus IMO 25
14. 2004 Möbius Beer 26
15. 2004 Caixanova 27
16. 2006 Caltrate 28
17. c. 2006 Mobius [sic]: The Journal of Social Change 29
18. c. 2006 Möbius art conservation 30
19. 2009 Commerzbank 31
20. c. 2009 UK Payments Administration 33
21. 2009 German Mathematicians Association (DMV) 34
22. 2009 Unlimited Web Hosting 35
23. 2009 Parship (likely 2002) 36
24. 2010 Age UK 37
25. 2012 Google Drive 39
26. 2018, Flarin 41
27. 2019 Léman Express 42
28. 2020 eu2020 44
Unknown Dates 45
29. NCTM 46
30. Swiss Mathematics Olympiad 47
31. Mathematisches Forschungsinstitut Oberwolfach 48
32. Swiss Federal Institute of Intellectual Property 49
33. University of Hagen 50
Appendix 1 - Table of Attributes 50
Appendix 2 - List of Inconsequential Instances 51
Chapter 1 - The Logos
The ideal is basic documentation of the date of instigation, the designer, and the reason for the use of a Möbius strip. However, this is seldom accomplished! Indeed, it is not uncommon to be found that none of these details are available, even from bodies/institutions where one would think it would be naturally available. A case in point is the National Council of Teachers of Mathematics (NCTM); there is no discussion at all on the logo! Admittedly, logos are not at the forefront of importance, but given that this is the first thing people see, one would have thought that at last some kind of explanation, no matter how brief, would be given, but no.
Generally, the name of the designer is not given. This is sometimes caused by a company using a design agency.
Frequently, the Möbius strip connection is not made in the literature, with on occasion reference made to ‘ribbon’ or ‘loops’, where one is left wondering whether the designer is fully aware of the background. As a result of all this, the study has great gaps, but this is unavoidable. I have done my best.
Perhaps somewhat surprisingly, given that the Möbius strip was discovered in 1865, the earliest known use in logos is dated as recently as 1962 (A-1 Beer). Indeed, for the rest of the century, it was used sparingly, and only in the 21st century has it become more widely seen. I find this late introduction and slow growth most surprising. I would have expected earlier usage, but the search does not show this.
32 logos are identified.
With most of the entries here, outside of a mathematical connection quite why a Möbius strip was chosen as the logo is curious. Why it appears on beer, photo films, medicines etc. with no obvious connection is decidedly odd!
For each entry, I have tried to be consistent in the presentation, of a modular nature. However, this was not always possible. The presentation is as follows:
The title
Picture
A brief introduction to the body responsible.
A discussion by myself, in which I attempt to determine basics, such as the year of instigation, the designer, and the reason for the choice.
References. Again, this is modular in form, with a clipping of text and annotations by myself, followed by a link to the source.
1. 1962+. A-1 Beer, Lancers, Carling
1. 1962+. A-1 Beer, Lancers, Carling
Fig. 1a. Lancers, 1962
Fig. 1b. Carling (1964)
Fig. 1c. Advertising Poster
The Arizona Brewing Company was founded in 1903, and A-1 beer started in 1942, but it was not until 1962 when it used the Möbius strip as the logo for its new A-1 Lancers beer.
Perhaps somewhat surprisingly, given that this reference is over 60 years old, there is considerable historical discussion and imagery on it, albeit not generally discussed (with one exception) in the context of a Möbius strip (as to be expected), with it naturally appearing on beer related sites. The Arizona Brewing Company admirably documents and illustrates the history, and Ed Sipos, a brewery historian expert, also gives even more detail (Siphos was contacted for comment, but he did not respond). The one exception is BEACH Packaging Design, who also show historic pictures, sourced in the literature.
The logo was likely designed by the Curran-Morton Advertising Agency (as mentioned by Siphos), but details are not forthcoming. Very little is known about Curran-Morton, beyond being Arizona-based. Likely the original artwork is lost.
Beginning in 1962, the Möbius strip appeared on a variety of cans, not easily unravelled, due to mergers/takeovers, in that the cans are not dated. The first appearance, with an exact date given(!), in September 29, 1962, is on a Lancers tin. Later, in 1964, Carling, upon a takeover, was also involved.
The strip itself is 3-coloured, red, blue, and green. As with most of the entries here, quite why a Möbius strip was chosen as the logo is curious; there is no obvious connection here with beer or it can be interpreted as symbolic!
References
References
Anon. Arizona Brewing Company. History
We have some history behind our brand.
About Us
Dating all the way back to 1903, The Arizona Brewing Company didn’t gain momentum until the end of Prohibition in 1933 when headlines throughout Phoenix read “Beer Here Tomorrow” in the Arizona Republic Newspaper. In 1942, The company debuted the A-1 Pilsner which would become its flagship brand. Due to its popularity, The Arizona Brewing Company commissioned famous cowboy and artist “Alonzo Lon Megargee” to create a series of prints that were used for marketing the A-1 Brand. One year later when the station KPHO graced the valley with television, The Arizona Brewing Company sponsored a gameshow which became an instant sensation…
Gives a pleasing picture and text history in the round. States that A-1 started in 1942 (without a Möbius strip logo). 1964 is the first appearance here of the Möbius strip, on a variety of products. Has a poster. No more appearances for the strip after this in the piece.
https://arizonabrewingco.com/a1-history/
Anon. Lancers A-1 Beer
A picture dated 1963 is given without the source.
https://uk.pinterest.com/pin/668080925946486621/
Anon. ‘Beer Labels Collection’. (3 March 2025)
‘Seen and noted’. Russian site, pictured referenced by BEACH Packaging Design, albeit not found.
http://www.nubo.ru/beervrn/index.htm
A-1 Beerprints
INTRODUCTION OF LANCER'S BEER. By mid 1962, Herb Lindner was well settled into his position as president. On June 18, he announced that the brewery wanted a new advertising agency, preferably a local one, "to show that we are proud to be 'Arizona-grown', to gain closer client-agency relationship geographically, and to expand our interest in the economy of our home state through increased advertising activity in the southwest." In July, Curran-Morton Advertising Company of Phoenix was awarded the account. The agency immediately began working on a new ad campaign. On September 29, 1962, a new beer was introduced under the name, Lancers A-1. Herb Lindner believed that A-1 had reached a superior stage and a new identification was in order. In addition, many other companies were causing confusion by using the A-1 name. The new beer would be lighter in flavor and different from the former A-1. The brewery expected to produce 447,000 barrels of beer by 1963.
Seemingly taken from Ed Siphos.
https://www.a-1beerprints.net/HTML/A1%20Brewing%20Company.html
40 oz Malt Liquor
These 40s were produced well before my time by Arizona Brewing Company, and then as of 1964, Carling Brewing Company. The first bottle pictured is the oldest known 40oz, produced in 1961! The original name of this brand was A-1, but a lawsuit from Anheuser-Busch over the use of an eagle on some of their older packaging caused them to rebrand as Lancers using a knight with a lance as their logo. When former brewery owner Joseph F. Lanser passed away, they paid tribute by renaming the brand once again to J.F. Lanser's. During this time the brewery was struggling and the confusion caused by the frequent rebrandings only hurt it more until they were forced to sell to Carling in 1964.
Mostly pictorial in the form of Malt Liquor. In this context has pictures I have not seen before. I will take at face value as true for now pending more detail.
http://www.40ozmaltliquor.com/brands/a1.php
Beer Cans Plus
A site for selling beer cans! Has many pictures.
Brooks, Jay. ‘Möbius Beer’. Brookston Beer Bulletin. November 17, 2015. (27 February 2025)
I recalled seeing a famous beer label using a Möbius Strip, and a quick search revealed the one I was thinking of was Arizona Brewing’s flagship beer “A-1,” which used a multi-colored version.
[Image]
Beer History has a good article about the brewery, A-1: The Western Way to Say Welcome
by Ed Sipos. The original A-1 label had an eagle on it, but by the 1950s Anheuser-Busch, which was spreading their tentacles nationally, decided to sue Arizona Brewing claiming the eagle on their label was too close to their own, and Arizona couldn’t afford to defend the lawsuit, and decided instead to simply change the label.
[Image]
A brief discussion of A-1 in the context of generic Möbius Beer. https://brookstonbeerbulletin.com/mobius-beer/
Curran-Morton Advertising Agency
Cecilia Torres Best remisces
A year later, I started working for the Curran-Morton Advertising Agency as Ken Morton’s executive secretary.
A few mentions in passing of Curran-Morton advertising agency.
http://www.azsurvivors.com/survivorupdatesab.html
Curran-Morton Advertising Agency
Victor Wilmot Obituary
In 1962, he joined Arizona's then-leading advertising agency, Curran-Morton Co., as Director of Public Relations.
https://www.legacy.com/us/obituaries/azcentral/name/victor-wilmot-obituary?id=27648976
Davis, Deborah and Randy Ludacer. ‘Mobius [sic] Strip Branding: A-1 Beer’. BEACH Branding & Package Design. May 1, 2013. (2024)
Last night I dreamt I was at some bar, talking with the bartender about vintage beer can packaging.
Maybe he could have told me who originally designed the tri-color Mobius strip logo for A-1 beer, but I didn’t think to ask him.
The photo on the right shows the logo I’m thinking of. It’s from William Legoullon’s 2010 “A-1 Country” series.
LeGoullon became intrigued with the story of The Arizona Brewing Company as well as its flagship beer, A-1, a true symbol of southwest beer-drinking culture.…Though many people have never heard of the brewery itself, its emblematic history, the evolution of its branding, and the symbolic narrative of A-1 have become primary influences on LeGoullon’s “A-1 Country” works.
It’s true that there were many evolutionary steps to A-1’s branding and package design over the years, but, it’s those versions of the packaging with the Mobius strip logo that I’m most interested in today.
There were earlier versions of this label with the brand name “Lancers” set in a script font, but to my mind, this version (with the chunky, wave-shaped terminators in the “A-1” typography) shows A-1’s branding at its most highly evolved.
Was this version a refinement that Carling introduced after its 1964 buy out of the brand? Or was it developed sometime before that? (as suggested by the bottle label below which does not include the brand name “Carling”)
In his History of The Arizona Brewing Company, Ed Sipos mentions a Phoenix-based “Curran-Morton Advertising” agency that was brought in to help promote the brand in 1962. Maybe someone there created A-1 Beer’s Mobius strip motif.
Regarding the evolution of one small part of this label…
Sometime around 1957, Anheuser-Busch threatened a lawsuit over the eagle used in A-1’s logo since 1942. The giant brewer charged that the eagle was too similar to the one associated with Anheuser-Busch. Many local drinkers referred to A-1 as “Arizona Bud” at that time. The A-1 brewery could not afford the legal expense of a court battle, so the issue was settled quietly by discontinuing use of the eagle in their packaging altogether. In January 1958, the eagle was replaced by a knight on horseback holding a banner with the name “Lancers”.
from The History of The Arizona Brewing Company
Hence, the earlier Lancers version of the Mobius strip label had a green shield with a silhouetted knight, which was itself replaced by a green sun with knock-out facial features.
Background. Deborah Davis: A store shelf is my gallery. I am a designer specializing in retail package design for 20+ years. In 1990, together with Randy Ludacer, we founded BEACH. Beach
Here, BEACH concentrates on the Möbius strip element. A nice, popular account and discussion. Good research. Has good historical pictures, including some of billboards not seen elsewhere.
https://beachpackagingdesign.com/boxvox/a%E2%80%A21-beer-mobius-strip-branding
Printed
Duke University Libraries. Repository, Collections and Archives. ‘A Great Beer’. (3 March 2025)
Has many distinct pictures, some with minor variations. All are described as ‘1960s’.
https://repository.duke.edu/dc/oaaaarchives/AAA9981 ‘A great beer’
https://repository.duke.edu/dc/outdooradvertising/BBB0007 ‘Great for Openers’
https://repository.duke.edu/dc/outdooradvertising/AAA9978 ‘You're in A-1 country ENJOY IT’
https://repository.duke.edu/dc/outdooradvertising/AAA9986 ‘A great beer even greater’
Legoullon, William.
Has 15 pictures of A-1 Beer cans, including two with a Möbius strip.
https://williamlegoullon.com/a-1-country
Morean Auctions. (2024)
Condition/Comments: Sweet example of this blue metallic-topped label. Not quite as scarce as the JF version but perhaps as difficult to find clean due to the metallic blue field that attracts humidity so easily. This one is gorgeous and humidity free! About near mint with the zip intact on top too!
A beer can auction site. Has a picture of a can with a sale price of $627 dollars! This is part explained in that other cans I have seen on auction sites are in poor condition, but even so!
https://moreanauctions.com/Lancers_A_1_Beer_16_Ounce_Zip_Top_154_24-LOT33280.aspx
Sipos, Ed. ‘A-1: The Western Way to Say Welcome’. Beer History.com. January–February 1998. (28 February 2025)
The following article is reproduced from the January-February 1998 edition of American Breweriana Journal by permission of the author, Ed Sipos.
One of the most visible changes was the introduction of A-1 Beer in January 1943. All other brands were dropped with the exception of Dutch Treat, a private label for A. J. Bayless Markets. In addition, the brewery would now be known as the Arizona Brewing Company, Inc. Many locals would soon begin referring to the company as the "A-1 Brewery" in the same way they previously labeled the firm the "Apache Brewery"....
In July, Curran-Morton Advertising Company of Phoenix was awarded the account. The agency immediately began working on a new ad campaign. On September 29, 1962, a new beer was introduced under the name, Lancers A-1. Herb Lindner believed that A-l had reached a superior stage and a new identification was in order. In addition, many other companies were causing confusion by using the A-1 name. The new beer would be lighter in flavor and different from the former A-1. The brewery expected to produce 447,000 barrels of beer by 1963…
Era Ends When A-1 Is Buyout Victim
It was obvious that the brewery was not in as good of shape as it used to be. Something had to be done to remain in business. Workers noticed a lot of movement at the head offices, unfamiliar faces were seen, and rumors began to emerge. The rumors were true. On October 8, 1964, it was announced that the Arizona Brewing Company would be purchased by the Carling Brewing Company, Cleveland, Ohio, a subsidiary of Canadian Breweries Ltd. of Canada. The agreement was reported in a joint statement by Henry E. Russell, Carling president, and Herb Lindner, president of the A-1 brewery. The announcement came as a shock to many long-time workers. Their brewery was the victim of a buyout.
Bio. Ed Sipos is a past president of the A-1 Chapter of the Brewery Collectibles Club of America and has been the editor of the chapter’s newsletter, the A-1 Can-o-Gram, for more than fifteen years. He has written extensively for Beer Can & Brewery Collectibles magazine.
This gives an excellent history of A-1 in the round. Gives vital detail as to the introduction. Although A-1 was a brand from 1943, it was not until 1962 that ‘Lancers’ was introduced, marking the introduction of the Möbius strip logo. Also, it gives the name of the design agency seemingly responsible for the logo, Curran-Morton Advertising Company.
https://www.beerhistory.com/library/holdings/arizona-sipos.shtml (All text)
Printed
Sipos, Ed. Brewing Arizona: Century of Beer in the Grand Canyon State. University of Arizona Press; 2nd ed. Edition, 2013. NOT SEEN
Undoubtedly the defining work on Arizonian beer. Ideally, I would obtain, but judged uneconomic in terms of cost-benefit analysis, as the Möbius strip A-1 story is likely already given by Siphos in BeerHistory,com.
2. 1967, IMPA (Possibly 1965)
2. 1967, IMPA (Possibly 1965)
Fig. 2. IMPA logo
The Instituto Nacional de Matemática Pura e Aplicada (IMPA) (National Institute for Pure and Applied Mathematics) is considered to be the foremost research and educational institution of Brazil in the area of mathematics.
Quite when the logo was introduced is unclear, albeit it has a 1960s vibe, and can tentatively be dated as around 1967 by roundabout means, albeit with a degree of confidence. The exact circumstances as of its instigation remain unclear. Why was it chosen? It is stated (by IMPA) that
The shape was chosen as IMPA's logo during the management of former director Lindolpho de Carvalho Dias.
However, whether Dias was directly involved is not made explicit. IMPA gives the dates of his directorship as 1965–1969, 1971, 1979–1980. Given that the logo appears on a postage stamp commemorating the 6th Brazilian Mathematics Colloquium at IMPA in 1967, this at least gives an indication, as this correlates with his first directorship. Therefore a date of 1967 is the latest of the instigation, and possibly of 1965.
References
3. 1968, Mauchly Group
3. 1968, Mauchly Group
Anon. ‘Instituto Nacional de Matemática Pura e Aplicada’ (IMPA). Wikipedia. (19 April 2024)
Only gives minimal detail on the logo without a designer or date.
…Its logo is a stylized Möbius strip, reproducing a large sculpture of a Möbius strip on display within the IMPA headquarters.
https://en.wikipedia.org/wiki/Instituto_Nacional_de_Matem%C3%A1tica_Pura_e_Aplicada
Anon. ‘Exhibition portrays different versions of the Moebius Strip’. 11/09/2023. (2024)
IMPA is hosting the exhibition 'Elos' by sculptor Valin Branco, featuring different versions of the Moebius Strip — a topological space obtained by gluing the two ends of a strip together, which inspired the IMPA symbol…The shape was chosen as the IMPA logo during the management of former director Lindolpho de Carvalho Dias…
IMPA internal page. Gives vital detail about the instigation of the logo, but not the designer or date.
https://impa.br/en_US/noticias/exposicao-retrata-diferentes-versoes-da-faixa-de-moebius/
Lindolpho de Carvalho. Memory Center. (2024)
Director of the Institute of Pure and Applied Mathematics, IMPA (1965/1969; 1971/1979 and 1980)
Background reading on de Carvalho.
https://centrodememoria.cnpq.br/lindolpho-carvalho.html
Bursztyn, Henrique and Roberto Imbuzeiro Oliveira. ‘IMPA, Instituto de Matematica Pura e
Aplicada’. EMS Newsletter, June 2017.
Background reading on IMPA. No reference is made to the logo
Little is known to the Mauchly group. The company was apparently headed by John Mauchly, a computer pioneer (in association with John P. Eckert). Mauchley was involved in many companies, of which unravelling the trail is trying. He is also associated with Mauchly Associates, Mauchly Techniques. A subsidiary of Mauchly Group (or vice versa?)
Look Go Take Act
…Our symbol— a Moebius band— has one unending surface and only one edge— it symbolizes the control you get with a unified information program— a unified systems approach to your information needs.
A two-page spread of the Mauchly Group, where aside from the main Möbius strip large logo it is also used at a smaller scale a further four times. This reference is surprisingly the only one I have been able to find. Nothing more is known about the company and logo than is given in the text. The background to the Möbius strip is at least suitably described.
What exactly the company did is unclear. It appears to be on ‘management information’. Given its near anonymity, one can only conclude that it was taken over/dissolved in a short time.
Further, obtaining a printout is fraught with difficulty. The document is borrow only, hence one has to resort to print screen, with all the resizing difficulties thereof. Further, the text is faint, whatever one does, and is effectively unreadable; possible with great effort, yes, but so inconvenient that one quickly gives up.
References
'Look Go Take Act’. Fortune. May 1968, pp. 110–11, June 15 1968, p. 254. (11 September 2024)
https://archive.org/details/fortune77aprluce?q=%22Our+symbol%E2%80%94+a+Moebius+band%22
https://archive.org/details/fortune77aprluce/page/n5/mode/2up?q=%22moebius+band%22&view=theater (Borrow)
Publication. Fortune is an American global business magazine headquartered in New York City. It is published by Fortune Media Group Holdings, a global business media company. The publication was founded by Henry Luce in 1929. Wikipedia.
Printed
Anon. ‘John Mauchly’. Wikipedia
John Mauchly (1907–1980) was an American physicist and engineer, co-inventor in 1946, with John P. Eckert, of the Electronic Numerical Integrator and Computer (ENIAC), the first general-purpose electronic computer.
4. 1972, Recycling Symbol
4. 1972, Recycling Symbol
See the dedicated discussion for an in-depth analysis.
5. 1974, Expo ‘74
5. 1974, Expo ‘74
See the dedicated discussion for an in-depth analysis.
6. 1975 (possibly much earlier), Canadian Mathematical Society
6. 1975 (possibly much earlier), Canadian Mathematical Society
The Canadian Mathematical Society (CMS; French: Société mathématique du Canada) is an association of professional mathematicians dedicated to the interests of mathematical research, outreach, scholarship and education in Canada. The society was founded in 1945.
Surprisingly, for such a prominent institution, there is no official discussion on the logo! When it was introduced, and by whom, are not known. The earliest recorded date I have found is March 1975, in the first issue of Crux Mathematicorum (originally EUREKA). I will place it under that date pending further details. There is the potential for it much earlier. The design is also curious, in quite why there is half of a maple leaf at the side is unclear.
References
References
Anon. ‘Crux Mathematicorum’. Wikipedia
Crux Mathematicorum is a scientific journal of mathematics published by the Canadian Mathematical Society. It contains mathematical problems for secondary school and undergraduate students…The journal was established in 1975, under the name Eureka, by the Carleton-Ottawa Mathematics Association.... It took the name Crux Mathematicorum with its fourth volume, in 1978, to avoid confusion with another journal Eureka published by the Cambridge University Mathematical Society.
https://en.wikipedia.org/wiki/Crux_Mathematicorum
Anon. ‘Canadian Mathematical Society’. Wikipedia
The Canadian Mathematical Society (CMS; French: Société mathématique du Canada) is an association of professional mathematicians dedicated to the interests of mathematical research, outreach, scholarship and education in Canada. It serves the national community through the publication of academic journals, community bulletins, and the administration of mathematical competitions….The society was founded in 1945
Although the logo is displayed, there is no mention in the text.
https://en.wikipedia.org/wiki/Canadian_Mathematical_Society
Anon. ‘Canadian Mathematical Society’. Canadian Mathematical Society
Although the logo is displayed throughout, there is no mention of it in the text.
7. 1980, Parton Oil Company advert
7. 1980, Parton Oil Company advert
Parton Oil, by deduction, was formed in 1955. However, little else is known about the company. It is highly unlikely that they continued much beyond 1980, possibly being taken over, but even so, after a minimum of 35 years in business, to leave only this single trace is most surprising.
The only known references to the logo are in two adverts in Fortune magazine, which implies a 1980 date. An explanation as to why they chose the logo is given. It has a very pleasing design element, which I missed initially, but soon realised the subtlety; note the oil drop defining the inner space. Very nice!
Nothing more is known about the logo; this is the only reference I have found. No designer's name is given, nor to the subtlety of the design. Likely, they were acquired. Researching this reference is frustrating; aside from the advert, there is no trace of the company, and so no discussion!
References
‘The Road Never Ends’ (advert, Parton Oil Company). Fortune. October 6, 1980, p. 90; December 1, 1980, p. 112. (11 September 2024)
In the thirty-five years we’ve been in business… We’ve adopted a new corporate symbol that represents our philosophy of continuing business .. . choosing an illustration from the pioneering work of A.F. Mobius [sic et al], a genius in the mathematical field of topology - the study of surfaces.
The Mobius strip is a fascinating construction whose surface is continuous. That is, it has only one "side". You can prove this to yourself by constructing your own simple Mobius strip (see diagram ) and drawing a pencil line down the middle. You'll eventually come full circle, leaving one continuous line which joins itself. . . an endless line over an endless surface.
https://archive.org/details/fortune102octluce/page/n391/mode/2up?q=%22Parton+Oil+Company%22
8. 1983, International Mathematique Olympiade, Paris
8. 1983, International Mathematique Olympiade, Paris
The International Mathematical Olympiad, a mathematical olympiad for pre-university students held every year since 1959 (1980 was an exception) has incorporated a logo for each year. However, this is poorly documented; the IMO page does not specifically mention logos. Little interest is shown externally. A great aid in viewing these is by TUE = Eindhoven University of Technology, who have compiled a select listing. However, this is not a complete set, and beyond a pictorial reference, there is no other detail as to how any one logo was selected and by whom. I find the lack of information in general most surprising.
In 1983, the 24th Olympiad was held in Paris, France (Fig. 8). Beyond that, nothing more is known about the background! The logo has proved impossible to research; I have nothing to add! An observation is that it is a highly symmetrical composition, within a regular hexagonal outline and an inner equilateral triangle. What the object is in the centre is unclear.
Oddly, this sighting is not in the TUE listing but is rather found in Robert Ferréol’s Mathcurve page (the only known instance).
The first of two known Möbius strip IMO logos. Also see the 1992 entry.
References
Ferréol, Robert. ‘Möbius Strip’. Mathcurve.
https://mathcurve.com/surfaces.gb/mobius/mobius.shtml
Gronau, Hans-Dietrich, Hanns-Heinrich Langmann, Dierk Schleicher Eds. 50th IMO - 50 Years of International Mathematical Olympiads. Springer, 2011.
‘Seen and noted’. Arguably, the defining book on the Olympiad, with the potential for the appearance and discussion of the logo. However, no logos are pictured, with only a passing reference to the German logo of 1965.
International Mathematical Olympiad. Wikipedia
The International Mathematical Olympiad (IMO) is a mathematical olympiad for pre-university students, and is the oldest of the International Science Olympiads. It is “the most prestigious” mathematical competition in the world. The first IMO was held in Romania in 1959. It has since been held annually, except in 1980. More than 100 countries participate. Each country sends a team of up to six students, plus one team leader, one deputy leader, and observers…
https://en.wikipedia.org/wiki/International_Mathematical_Olympiad
International Mathematical Olympiad Logos. TUE = Eindhoven University of Technology
Pictorial references of logos through the years, albeit seemingly a selection of what is available; not all years are shown.
9. 1992, International Mathematical Olympiad, Moscow
9. 1992, International Mathematical Olympiad, Moscow
Again, as with the Paris Olympiad, this logo has proved impossible to research; I have nothing at all!
The 33rd International Mathematical Olympiad (IMO) was held in Moscow, Russia from July 10–21, 1992. The only known pictures are at TUE (in black and white) and at IMO (in red).
References
International Mathematical Olympiad Logos. TUE = Eindhoven University of Technology. (6 May 2024)
Pictorial references of logos through the years, albeit seemingly a selection of what is available; not all years are shown.
https://olympiads.win.tue.nl/imo/logos/index.html
IMO, 1992
10. C. 1996. United Kingdom Mathematics Trust
10. C. 1996. United Kingdom Mathematics Trust
The United Kingdom Mathematics Trust (UKMT) is a charity founded in 1996 to help with the education of children in mathematics within the UK.
This logo has proved impossible to research; surprisingly, there is simply no discussion of it at all in their literature! I have only been able to find out when the trust was formed, in 1996, and so I tentatively place the logo under that date. Interestingly, there are two versions, likely updates, the second is that as shown currently on their website. The second logo was apparently by Northern Bear Design Agency in Lichfield, England, at least since 2014.
References
United Kingdom Mathematics Trust (UKMT). Wikipedia
The United Kingdom Mathematics Trust (UKMT) is a charity founded in 1996 to help with the education of children in mathematics within the UK…
The logo is neither displayed nor discussed!
https://en.wikipedia.org/wiki/United_Kingdom_Mathematics_Trust
The UK Mathematics Trust Yearbook 2002-2003. UKMT
The logo is displayed, thus giving a 2022 date (Fig. 9a).
https://archive.org/details/isbn_095368234x/page/n1/mode/2up?q=strip+of+paper+ABCD
The Northern Bear
Northern Bear is a creative agency, proud to work with inspiring organisations that have a positive impact in the world.
We provide valuable, effective work that helps our clients to boost awareness, funds and impact.
The design agency. The page states ‘Proud to work with’, showing 12 logos, including UKMT.
11. C. 1996. Advantix Kodak
11. C. 1996. Advantix Kodak
Advantix was Kodak's brand name for Advanced Photo System (APS) film and cameras. APS was a consumer film format that was popular from 1996 until it was discontinued in 2011. Advanced Photo System (APS) is a discontinued film format for still photography first produced in 1996. It was marketed by Eastman Kodak under the brand name Advantix, by FujiFilm under the name Nexia, by Agfa under the name Futura and by Konica as Centuria. Only on Kodak was the Möbius logo used.
Researching, as with many of the entries here, is frustrating, in that no background detail is given! Kodak used a Möbius strip on the new range of Advantix film introduced in 1996, ad so the date is based on that.
The logo was seemingly devised by Bryan Kirkey Design, a US design agency. Details about Kirkey are scant. His website is mainly pictorial, with no biographical detail. The logo is shown, but without further detail (as with the other images). He does at least mention the Möbius element, but without elaborating. Elsewhere, it is said that Kirkey is an instructor in the Department of Applied Photography/Media Production in the US. He is apparently head of Ecoshel.
References
Bryan Kirkey
https://bryanjkirkey.myportfolio.com/copy-of-timber-frame-aerial
https://bryanjkirkey.myportfolio.com/copy-of-1
Advantix
ON 22 April 1996, consumers around the world began buying and using products and services from an entirely new photographic system: the Advantix Advanced Photo System (APS). The products' simultaneous introduction worldwide by 45 different companies made photo industry history.
https://www.pmi.org/learning/library/kodak-advantix-photographic-system-project-3275
12. 2000? Possibly much earlier, Dresdner Bank
12. 2000? Possibly much earlier, Dresdner Bank
Dresdner Bank AG was a German bank, founded in 1872 in Dresden, then headquartered in Berlin from 1884 to 1945 and in Frankfurt from 1963 onwards after a postwar hiatus. Long Germany's second-largest bank behind Deutsche Bank, it was eventually acquired by Commerzbank in May 2009.
Researching this entry is most frustrating, with uncertainties to the fore. Dresdner Bank does not discuss the logo on any of its pages. Yet more complications ensue as the bank no longer exists as Dresdner Bank, being taken over by Commerzbank, which has retained the logo, albeit changing the colour. Next to no detail as to the instigation is known. Different designers are credited, namely Ansgar Seelen and Otl Aicher, with a 30-year difference! The logo has changed at various times with mergers and acquisitions. Unravelling all the machinations is a nightmare.
It can be seen that the design is highly stylised, although presumably a Möbius strip is intended. The earliest dated use of the logo is 2000 (outside a London branch), so I will tentatively date from there. It could be much earlier, possibly decades.
References
Dresdner Bank
The Dresdner Bank logo after integration of the company into the Allianz Group. Design by Ansgar Seelen / BBDO Identity. The picturemark ("Ponto-Eye") was continued from its predecessor - designed by Otl Aicher.
https://commons.wikimedia.org/wiki/File:Dresdner-Bank-Logo.svg
Dresdner Bank AG
https://www.britannica.com/money/Dresdner-Bank-AG
Dresdner Bank
Dresdner Bank AG was a German bank, founded in 1872 in Dresden, then headquartered in Berlin from 1884 to 1945 and in Frankfurt from 1963 onwards after a postwar hiatus. Long Germany's second-largest bank behind Deutsche Bank, it was eventually acquired by Commerzbank in May 2009.
Although the logo is pictured, it is not discussed in the main text.
https://en.wikipedia.org/wiki/Dresdner_Bank
Logomark. 14 December 2017
Dresdner Bank #logo by Otl Aicher, c.1970.
Seemingly credits Aicher as the designer, but I am not so sure.
https://x.com/logomarkco/status/941427695321153536
PhilippvonRosenGalerie
This is no longer an office system, but is more reminiscent of company logos (one thinks of the “green band of sympathy” of the former Dresdner Bank or the logo of Deutsche Bank and other trademarks).
https://www.philippvonrosen.com/wp-content/uploads/2024/06/UI_2024_Presse_EN.pdf
Good Logo
A 1970 date is stated.
13. 2002, Belarusian Mathematical Olympiad
13. 2002, Belarusian Mathematical Olympiad
Nothing is known about this logo beyond the date! Although dated 2002, the Olympiad was held in Glasgow, possibly this is the specific Belarusian logo team. Again, frustrating to research
This is not on the TUE listing, nor Ferréol. Possibly, my own finding.
References
Belarusian Mathematical Olympiad. Minsk Publishing Centre, BSU, 2002.
The front page shows the logo. Possibly ‘proceedings’ of the Olympiad?
https://www.scribd.com/doc/153349221/Belarus-2002
Bakonkurs
Has many incarnations of the logo.
14. 2004, Möbius Beer
14. 2004, Möbius Beer
No certain picture is available.
Robert Spencer introduced Mobius beer in 2004. Subsequently, there appear to have been other Möbius beers, leading to confusion as to the original. As such, with such uncertainty, and without a certain 2004 picture, I refrain from adding a possible incorrect image.
Details here are scant. Clifford Pickover (my source) briefly mentions ‘Möbius Beer’ in his listing and is also discussed (in relative detail) in a single newspaper report and briefly on a webpage. Whether ‘Möbius Beer’ is the actual title or a generic description I am unsure of.
References
Brooks, Jay. ‘Möbius Beer’. November 17, 2015.
Today is the birthday of mathematician August Ferdinand Möbius, for whom several mathematical items are named, although the most famous is certainly the Möbius Strip…
Apparently there’s also a Mobius Infused Lager that looks like a gimmicky contract beer. It appears to be a generic lager “infused with taurine, ginseng, and caffeine.” Ugh, does that sound like a bad idea.
In a brief article on ‘Möbius Beer’ an indirect quote is seemingly taken from Pickover, as he repeats parts, seemingly made to Spencer’s Beer. As an aside, Brooks also briefly discusses A-1 Beer.
https://brookstonbeerbulletin.com/mobius-beer/
Jahn, Dirk. ‘Mobius [sic] Beer‘. January 12, 2018.
Mobius beer is part of “Mobius Projects” as the starting point for the Brewery activity.
One possible modern-day reference that could be confused with the 2004 reference.
https://www.distillery.news/places/belgium/walloon-region/sombreffe/breweries/mobius-beer/
Pickover, Clifford A. The Möbius Strip: Dr. August Möbius's marvelous band in mathematics, games, literature, art, technology, and cosmology. New York: Thunder's Mouth Press, 2006, p. xix (Introduction)
In 2004, Mobius beer, infused with taurine, ginseng, caffeine, and thiamine, went on sale in Charleston, South Carolina, each can emblazoned with the Mobius strip. "Mobius beer will keep you going on and on all night long," says the company literature.
A brief mention of Möbius beer in the context of the Möbius strip in a ‘variety of settings’.
Smith, Bruce. ‘Brewer marketing new energy beer’. Wilmington Star-News. 26 November 2004. (27 February 2025)
CHARLESTON, S.C. - Robert Spencer, a tall former college basketball player, looks up from his table in a busy Charleston restaurant.
“Do you have any Mobius beer?” he asks, but only gets a quizzical look from the waitress.
Mr. Spencer, who began selling his new “energy beer” earlier this month, isn’t fazed. “In a year,” he says, “I think we’ll be worldwide.”
Mobius Infused Lager went to market Nov. 8 and already you can order a bottle in at least 30 locations in this city known for its dining and nightlife…
Mobius is the name of a 19th century mathematician who discovered the Mobius strip – a strip of paper twisted and glued together so that is has only one side. The sideways figure 8, the symbol of infinity, is used on the packaging…
This appears to be what Pickover is referring to. No pictures are shown. Gives a brief background to Möbius. Throughout, no umlauts are in Möbius’s name.
https://eu.starnewsonline.com/story/news/2004/11/26/brewer-marketing-new-energy-beer/30243525007/
15. c. 2004, Caixanova
Caixanova appears to have been a Spanish bank but is likely to have subsequently merged, with name changes.
Details are scant, with much uncertainty. Little is known here! Certainly, what appears to be the latest form, CaixaBank, as of this writing (2025) no longer uses the logo. The earliest reference I have is 2004, on a bank card. The latest is 2012. I will take the 2004 date at face value
Marta Macho Stadler quotes this.
References
Brand Finance
Location Spain. Industry Banking
https://brandirectory.com/brands/caixanova-banco-novagalicia
Caixanova. Logopedia. (26 February 2025)
In 2010 Caixa Galicia and Caixanova merged to form NovaCaixaGalicia, which in 2014, would become Abanca.
https://logos.fandom.com/wiki/Caixanova
Colnect.com
https://colnect.com/en/bank_cards/bank_card/11976-Caixa_Nova-Caixa_Nova-Spain
https://colnect.com/en/bank_cards/bank_card/714-Caixa_Nova-Caixa_Nova-Spain
16. 2006, Caltrate
Caltrate is a brand-name calcium supplement sold by Haleon.
Nothing is known at all as to the designer and reason of use! However, a tentative date of 2006 can be given, in that this is the date of Clifford Pickover’s book reference to this. As of this writing (2025), it appears to have been discontinued; a different logo is now used.
Source: Clifford Pickover, Marta Macho Stadler
References
Caltrate. Wikipedia
Caltrate is a brand name calcium supplement sold by Haleon.
17. C. 2006, Mobius: The Journal of Social Change
Mobius: The Journal of Social Change began as a quarterly print journal in 1989, before becoming an online journal in 2009. It publishes challenging fiction and poetry that deals with social change as either a primary or a secondary theme.
Details are scant, the only reference being Clifford Pickover, of a name check in a listing of logos. No date is given. However, given that Pickover’s book was published in 2006, this at least gives a ‘no later than’ by date. There is no discussion about the logo or why it is titled Mobius [sic] on the journal’s website.
References
About. We became an online-only journal, published quarterly in March, June, September, and December, in 2009.
Established in 1989 as a quarterly print journal with local free distribution in Madison, Wisconsin, Mobius strives to publish challenging fiction and poetry that deals with social change as either a primary or a secondary theme. Social Change
18. C. 2006. Möbius art conservation
MÖBIUS: art conservation provides expert consultations and fine art services in the Monterey Bay and San Francisco Bay areas.
Details are scant. The company’s website does not discuss the logo or background naming of the company.
I’m not even sure if this is actually a Möbius strip, although certainly intended as such! It may be an ‘illusory ring’!
From a reference by Clifford Pickover. Arguably could be excluded/downgraded to ‘minor’ instances, but as Pickover has referenced it I will retain it in the main listing.
References
Möbius Art Conservation
About. Chris J. Kenney is the Principal Conservator at MÖBIUS: art conservation inc. which spans 35 years of providing expert consultations and fine art services in the Monterey Bay and San Francisco Bay areas. MAC
The same text appears here:
https://patch.com/california/santacruz/business/listing/315701/mobius-art-conservation-inc
Pickover, Clifford A. The Möbius Strip: Dr. August Möbius's marvelous band in mathematics, games, literature, art, technology, and cosmology. New York: Thunder's Mouth Press, 2006, p. xix (Introduction)
It's the name of a Santa Cruz, California, company that specializes in the conservation and restoration of oil paintings.
A brief mention in the context of the Möbius strip in a ‘variety of settings’.
19. 2009, Commerzbank
Commerzbank is a leading corporate bank in Germany and Europe, as well as a leading capital markets house, established in 1870.
Unlike most of the entities, this is discussed extensively, albeit not entirely satisfactorily. Detailed background discussion to the logo is given by the company and a logo site, although no direct mention is made to the Möbius strip, but is rather alluded to, in the form of ‘ribbons’! It is stated that it is based on the Dresdner Bank logo, which it acquired. No mention is made of the designer.
A Robert Ferréol reference.
This Mobius strip is left-handed strip with 3 half-twists.
References
1000 Logos
Commerzbank is the name of one of the largest and most reputable financial institutions in Europe, which was established in Hamburg, Germany, in 1870. Today the bank successfully operates not only in European countries but has its subsidiaries on different continents. The yearly revenue of Commerzbank is about 8,5 billion Euro.
Since the bank boasts a very long history, its visual identity has undergone several redesigns throughout the years. There were different styles and color palettes adopted for the Commerzbank logo, from classic seals to modern abstract symbols. Let’s check the development of the German bank’s visual identity below.
When Commerzbank acquired Dresdner Bank in 2008, it adopted a new brand identity, which also reflected this acquisition.
The ribbon design seen on the current Commerzbank logo was borrowed from the logo of Dresdner Bank. According to the company, each of the three segments of the ribbon has a meaning: they represent employees, customers, and business partners. The three dimensions symbolize dynamism, continuity, and stability. The bank used to have a flat logo earlier, though.
Gives a detailed history of the evolution of the logo.
https://1000logos.net/commerzbank-logo/
Logos World
…The bank presented its current icon in October 2009. This is a tape bent in three places, which forms an isosceles triangle. It is taken over from Dresdner Bank. According to the concept, each stripe symbolizes close contact between bank employees, customers, and partners. Moreover, the logo expresses the dynamism, stability, and continuity of these business ties.
Gives a detailed history.
https://logos-world.net/commerzbank-logo/
https://www.commerzbank.com/media/konzern_1/geschichte/download_8/hist_CB_Logos_en.pdf
iF Design
After the merger of Commerzbank and Dresdner Bank in May 2009, a new brand was born that underscores the bank’s claim to leadership in the German banking market and sends a clear signal for the integration of the two financial institutions. Therefore the logotype was updated with a new, modern typeface and the brand mark was transformed into a three-dimensional image and accented with yellow, the bank’s primary color. The new brand conveys quality and confidence and highlights the key qualities of the bank: partnership and performance.
No allusion to the
https://ifdesign.com/en/winner-ranking/project/commerzbank/62967
Commerzbank
‘Mercury’s wings, the four winds and yellow ribbon’.
…Re-launched a brand rich in tradition – The merger of Commerzbank and Dresdner Bank has brought a new Commerzbank into being. In October 2009, the bank unveiled its new brand. The joint new brand identity is a visible symbol of this integration. The new brand and logotype is composed of three elements: the Commerzbank name in new font, the colour yellow and a three-dimensional ribbon, enhancing the Dresdner Bank logo. Since November 2012, the new brand positioning „fairness and competence“ and the new claim „The bank at your side“ clearly align Commerzbank’s actions on customers’ interest and their satisfaction.
A detailed explanation of the evolution of the logo. The best discussion.
https://www.commerzbank.de/group/who-we-are/history/download/logos-overview.pdf
Sueddeutsche Zeitung
20. C. 2009, UK Payments Administration
The UK Payments Administration Ltd (UKPA) is a United Kingdom service company that provides people, facilities and expertise to the UK payments industry.
Little detail is known. No explanation is given on UK Payments website (or elsewhere) as to the reason for the Möbius strip logo. Again, this is frustrating to research, with no detail. The logo appears to have been discontinued upon a name change to UK Pay.
References
‘UK Payments Administration’. Wikipedia. (8 May 2024)
The UK Payments Administration Ltd (UKPA) is a United Kingdom service company that provides people, facilities and expertise to the UK payments industry.
UKPA was created on 6 July 2009,...
A broad, short outline.
21. 2009, German Mathematicians Association (DMV)
The German Mathematical Society (German: Deutsche Mathematiker-Vereinigung, DMV) is the main professional society of German mathematicians and represents German mathematics within the European Mathematical Society (EMS) and the International Mathematical Union (IMU). It was founded in 1890.
Researching this is frustrating. I have a date for the introduction of a new logo, 2009, with a desire for a change, and that’s about it! This is even more surprising from such a major mathematical body!
References
Schaffrinna, Achim. ‘German Mathematical Society DMV with new logo’. January 26, 2009
The German Mathematical Society DMV is introducing a new logo. Despite the changed appearance, one thing remains the same: a penchant for MCEscher.
After there were numerous events last year as part of the “Year of Mathematics”, the association obviously wants to take some of the momentum and dynamism of the previous year with it. “There should also be movement in terms of the look,” says Ziegler, former DMV president. “The old logo is like a Volvo,” adds Lück, “the new one is like a Smart.”
Good. First of all, I don't think my anthracite-colored Volvo V50 is uglier, more conservative or more old-fashioned than a Smart, quite the opposite, but as we all know, tastes differ, and so do interpretations of the image of car brands and models.
The new logo takes the form of a Möbius strip. This theme was most recently used in the redesign of Grant Thornton. This two-dimensional, spatial structure has only one surface and was discovered in the middle of the 19th century by the two mathematicians Listing and Möbius. “The object merges into itself in such a way that if you start to color the surface on one of the apparently two sides, you will end up having colored the entire object.” (Source: Wikipedia )
Visually, the new logo makes a good impression: the colors are consistent, the typography is clear, and the overall logo is very balanced. However, the new logo could also stand for a chip manufacturer or a machine manufacturer. This risk of confusion certainly did not exist with the constructed letter arrangement of the predecessor. The clarity in terms of the interpretation of the logo is greater in the predecessor than in the new logo due to the somewhat "quirky" design language. But it was precisely this widespread cliché that mathematicians always have something quirky about them that was clearly something they wanted to counteract.
A nice discussion. A Möbius strip is detailed.
https://www.designtagebuch.de/deutsche-mathematiker-vereinigung-dmv-mit-neuem-logo/
Dambeck, Holger. ‘Mathematicians want to become smarter’. SPEIGEL Science, January 23, 2009. (2024)
…The DMV wants to say goodbye to the image of a dusty association and has just given itself a new logo (see photo gallery). Instead of square, three-dimensional letters, an almost esoterically curved Möbius strip in blue and orange now represents the DMV. "The visual aspect should also be movement," says Ziegler. "The old logo is like a Volvo," adds Lück, "the new one is like a Smart."
Deutsche Mathematiker-Vereinigung
22. 2009-2017, 2017-2025 Unlimited Web Hosting
Unlimited Web Hosting is a web hosting company that provides hosting services for businesses and individuals. They were formed in 2009.
Unlimited Web Hosting logo has seemingly used a Möbius strip as their logo, in two incarnations. Or at least that is my interpretation. No discussion on the logo is given on their website or Facebook page.
References
Unlimited Web Hosting
About. Since 2009, our goal has always been to clarify the UK's hosting market with simple, exhaustive, easy to comprehend hosting products and back them with the best customer support we can provide.
https://www.unlimitedwebhosting.co.uk/about
UK Unlimited Web Hosting Company - Simply A New Way To Host
Apparently deprecated, in that the last post was 2017.
23. 2009, Parship (likely 2002)
Parship is an online dating agency based in Hamburg, Germany, founded in 2002. It has since expanded to 13 other countries, including the UK.
Details on the logo are non-existent. The logo is not discussed on Parship’s site or elsewhere. Dating the logo is problematic, in that it appears to have been discontinued, having been replaced by a heart-shaped logo at an unknown date. The new logo predominates in searches. These are the only two distinct types shown. The earliest association I have with Möbius strip logo is 4 May 2009. Given that there are only two known logos, likely the Möbius strip logo was introduced from the start. Given the uncertainty, I will place it under the associated date pending confirmation.
References
Parship. Wikipedia
Parship (or Parship GmbH) is an online dating agency based in Hamburg, Germany. It was part of the Georg von Holtzbrinck Publishing Group. Its stated goal is to encourage and forge long-term partnerships. Founded in 2000,...Since 2002, Parship has expanded to 13 countries in addition to Germany: Austria, Belgium, Denmark, France, Ireland, Italy, Mexico, The Netherlands, Norway, Spain, Sweden, Switzerland, United Kingdom.
https://en.wikipedia.org/wiki/Parship
Wikimedia Commons File: PARSHIP Logo 130911.svg
May 4, 2009 (presumably uploaded)
https://de.wikipedia.org/wiki/Datei:Logo_Parship.svg
Macho, Marta Stadler. ‘Listing, Möbius y su famosa banda’. In Un paseo por la Geometria (Not Seen), Universidad del País Vasco, Bilbao, 2009, pp. 59–78. (6 February 2025)
Translated. ‘Listing, Möbius and his famous band’.
Page 77 shows seven Möbius strip logos (one faux), including Parship. No discussion is given.
This is the source.
24. 2010. Age UK
Age UK is a charity that helps older (50+!) people in the UK. They offer advice, companionship, and support. Upon merging in 2009 with Age Concern and Help the Aged, Age UK was founded in 2010.
For the founding, a new logo was designed. Basic details of this are given a ‘Third Sector’ discussion. Although the logo is pictured, it is not discussed in the text but is rather referred to as a ‘life loop’, without discussing that the Möbius strip underpins the design. A branding agency, Corporate Edge, is credited with the design.
References
Age UK. Wikipedia
Age UK is a registered charity in the United Kingdom, formed on 25 February 2009 and launched on 1 April 2009, as a merging of Age Concern England and Help the Aged…
https://en.wikipedia.org/wiki/Age_UK
Donovan, Tristan. ‘Age UK logo revealed’. Third Sector. 16 March 2010. (14 August 2024)
'Life loop' is the branding choice of charity formed by the merger of Help the Aged and Age Concern
Age UK's long-awaited logo has made its debut on the charity's election manifesto, in advance of the new charity's formal launch in April.
The logo, called the 'life loop', has also appeared on the websites of Age Concern England and Help the Aged, which are merging to form Age UK.
It was designed by branding agency Corporate Edge.
"It shows life in the round," said a spokeswoman. "Not a straight line that starts with young and ends with old, but a loop of vitality, a circle of life. It represents the continuous, seamless support that Age UK offers."
The charity intends to launch its new identity officially next month but decided to start familiarising people with it in advance.
"We wanted to prepare people for it and show them the new look before it is official," said another spokesman.
He said the charity would unveil the logo officially in April, coinciding with the expected date of the start of the general election. "It was important to put the logo on our election manifesto as we will be using that in the months ahead."
The manifesto, Our Power is Our Number, was launched in February.
https://www.thirdsector.co.uk/age-uk-logo-revealed/communications/article/990186
Age UK Guidelines
The Age UK brand
Our shared brand is a valuable asset for the whole network, and has become widely recognised in our communities. It is trusted by millions of older people, their carers and their families. The elements that make up our brand design – logo, fonts, colours and photography – are what makes our brand distinctive. These guidelines contain some simple rules about how to use these elements, examples of how they can be used, and some of the templates that are available on Brand D1 for you to use.
Age UK Brand Partner logos consist of the life loop, Age UK and a geographical descriptor.
McCathie, Charlie. ‘Photon snaps up design company Corporate Edge’. Campaign 5 Sept 2007. (5 March 2025)
LONDON - Photon Group UK has acquired the branding agency Corporate Edge, which launched internet bank Egg, and the Nectar loyalty scheme.
https://www.campaignlive.co.uk/article/photon-snaps-design-company-corporate-edge/735883
25. 2012, Google Drive
Google Drive is a cloud-based service that allows users to store, organize, and share files online. It's part of Google Workspace and integrates with other Google services like Gmail, Docs, and Sheets. It began on 24 April 2012
There are three versions of the logo, of a identical outline, beginning 2012. Somewhat surprisingly, with a prominent body, little background detail is in the public domain. The logo was designed by Strohl Inc., a Graphic Design Studio in San Francisco. They state:
Inspired by the Möbius strip, the symbol represents the syncing, sharing and accessibility of your files and data.
And that’s it! No single artist is credited on their site, albeit at least the Möbius strip is alluded to. No reference is made to the colouring. However, other logo sites give more detail. However, somewhat disarmingly, no reference is made to the Möbius strip. And furthermore, basic descriptions are inaccurate. Therefore, although I take the background given at face value, this is largely at trust.
References
Millward, Steven. ‘Did Google Drive Copy its Icon From a Chinese App?’. 30 April 2012.
Chinese startups and apps often get a lot of flack - including from us - for cloning and copying, and generally coming up with ideas that seem strikingly similar to what has been done before. But that ‘inspiration’ is a two-way street, as seen with the stylish triangular icon and logo for Google Drive, the new cloud storage service that’s already blocked in China, which bears a striking resemblance to that of the Chinese-made Vplayer app (pictured above)...
Google's inspiration could have been anything from a Möbius strip - the most likely - to the globally-recognizable recycling logo
Speculations on the likeness of the logo to a Chinese design.
https://sg.news.yahoo.com/did-google-drive-copy-icon-091053776.html
1000 Logos
Google Drive is a service created by Google to store, synchronize and share files. The software was launched in 2012 and today has over one billion users worldwide. Google Drive offers not only websites but also applications for both iOS and Android operating systems…
https://1000logos.net/google-drive-logo/
A detailed discussion, but no mention of the Möbius strip or ribbons! I would not be surprised if the author was unaware of the connection.
Logos World. ’Google Drive Logo’. Update: June 13, 2024
The Google Drive logo is bright and eye-catching. The image shows different facets of the software. The emblem encodes various file types, ways to work with them, and directions for which the service will be useful…
Again, a detailed discussion, but no mention of the Möbius strip!
https://logos-world.net/google-drive-logo/
Strohl, Inc.
Inspired by the Möbius strip, the symbol represents the syncing, sharing and accessibility of your files and data.
The impression given is that Strohl was the designers.
https://strohlsf.com/googledrive/
Logopedia
https://logos.fandom.com/wiki/Google_Drive#2014%E2%80%932020
Schade, Ruben. ‘Did Google Drive rip off Vplayer? Not really!’. Monday 30 April 2012.
One of the current memes surrounding Google Drive seems to be how their logo was copied from Vplayer. As a logo nerd, I felt it my duty to clear the air!...
While copying isn't unexpected behaviour from Google necessarily, I find TechInAsia's claim that their new logo was a copy of Vplayer to be a bit of a stretch. As far as I can tell, both services are employing Möbius Strip-like designs in their logos…
Examines the case for piracy. As an aside, this shows the UK Payments logo, which is likely where I sourced this.
26. 2018, Flarin
Infirst Limited, a pharmaceutical manufacturing company, produces Flarin. Flarin is a unique ibuprofen that helps to stop pain, relieve swelling and ease stiffness of the joints.
Nothing is known as to the designer and reasons for use. The strip’s portrayal is unusual in that it is concave, in which the designer attempts to echo the letter ‘A’.
Researching this, amid a myriad of health sites, is a trying business.
References
Jones, Caroline. ‘They promise to be better than your go-to treatments, but are they really worth the cost of a medicine cabinet upgrade’. Daily Mail 2 September 2019. (27 February 2025)
Last year (i.e. 2018), Flarin, a type of ibuprofen with a special ‘lipid’ formulation, was released to reduce the risk of stomach problems.
A date of 2018 is implied.
Lloyds Pharmacy
Flarin is a unique ibuprofen that helps to stop pain, relieve swelling and ease stiffness of the joints. This over the counter medicine has been proven to be as effective as prescription strength ibuprofen. Flarin has a unique lipid formulation.
27. 2019, Léman Express
The Léman Express is a recent (2019) cross-border rail network that connects France and Switzerland. It's one of the largest regional rail networks in Europe.
The rail network's logo is formed of a Möbius strip of “fjord blue” colour recalling the general shape of Lake Geneva as well as the colour of the water and is formed of two lines reminiscent of railway rails.
The logo was designed by Base Design, an international network of creative studios specializing in branding and communications. Reference is made by the agency (2017) to the Möbius strip, which seemingly translates to a travel premise.
The Möbius strip is left-handed with one half-twist.
References
Marchand, Victoria. ‘Base Design designed the visual identity of the Léman Express’. icominmag.ch, December 18, 2019
For the Léman Express, Base Design developed a symbol, an exclusive typography, graphic elements and a sound identity.
But why a Mœbius strip for the Léman Express?
The particularity of the Mœbius strip lies in the fact that the two sides are one… We arrive at the other side without ever changing face.
Many years of work have made it possible to build a railway link between Switzerland and France, allowing the Léman Express to connect the inhabitants of the entire greater Geneva region.
What could be better, then, than the Mœbius strip that takes the shape of Lake Geneva to represent this great project? A symbol with modernist inspirations for a new mobility tool for the Lake Geneva region.
https://cominmag.ch/base-design-a-concu-lidentite-visuelle-du-leman-expreess/
Rigal, Herve. ‘Léman Express. Ce qui se cache derrière le logo’. August 15, 2017
Translated. Léman Express. What is behind the logo.
Invented by the mathematician August Möbius in 1858, the Möbius strip is a surface that has the particularity of having only one side and one face. The Möbius strip is obtained by gluing together two opposite sides of a rectangular strip that is first twisted half a turn.
"If you run your finger around this strip, you automatically arrive at the other side."
Léman Express. Wikipedia. (6 May 2024)
Although the logo is shown, it is not discussed in the text.
28. 2020, Eu2020
The logo of the German EU Council Presidency, 2020, July through December.
The presidency of the Council rotates among the EU member states every six months. During this six-month period, the presidency chairs meetings at every level in the Council, helping to ensure the continuity of the EU's work in the Council.
A rationale for the Möbius strip is given:
It's a very special thing - because it has properties that are so completely contrary to our everyday ideas that you really don't expect: The Möbius strip is a structure with only one side and one edge. A twisted surface embedded in three-dimensional space. An object without such a clear top and bottom, inside and outside. Seen from the right angle, it is reminiscent of the symbol of infinity. A Möbius strip was currently designed for the logo of the German EU Council Presidency - "A strong bond for a united Europe" .
Friedrich-verlag
References
Anon. ‘A strong band for a united Europe’.
…Our faith in Europe’s innovative abilities is also reflected in our Presidency logo with its distinctive Möbius strip – a strong band symbolising a united Europe.
The Möbius strip is the classic example of a single-sided surface in algebraic topology. It takes the form of a loop with only one edge and one side making it impossible to distinguish between the loop’s top and bottom or inside and outside.
Descriptions of the Möbius strip were first penned more than 160 years ago in 1858 when two German scientists discovered such single-sided surfaces independently from one another. The strip was named after one of them, August Ferdinand Möbius (1790-1868). Born in Leipzig, the mathematician and astronomer was the son of a dancing teacher and a descendant of Martin Luther. Carl Friedrich Gauss appointed him adjunct professor and later director of the Leipzig Observatory.
Today the Möbius strip is not only at home in the natural sciences. Famous depictions of the two-dimensional twisted loop can be found in the visual arts, films, video games and literature. In mathematical terms, the Möbius strip, in the form of an infinite loop, is a non-orientable manifold. No matter where you start and what direction you go, you always end up on the same side.
The strip symbolises an innovative and integrated Europe in which dialogue to reconcile differing interests creates what we share. A strong band symbolising a united Europe. A Europe rooted in a shared spirit of solidarity.
You can learn more about the creation of the logo for Germany's Presidency of the Council of the EU in the following film from the German Ministry of Finance. (see below)
https://www.eu2020.de/eu2020-en/presidency/logo-and-claim/2360188
There is also a video, in German.
The designer speaks, in German. Alexander Meier Gestalder der Wort- und Bildmarke designer of the word and logo.
https://vms.auswaertiges-amt.de/getMedium/Default/4fe99c5713ff136073559c82cbb67128.mp4
Anon. August Ferdinand Möbius and the Möbius strip
A Möbius strip is the logo of Germany’s Presidency of the Council of the European Union in 2020 – it is entwined and can never be separated. But what is it? Where did it get its name? And why was it chosen as a symbol? Here’s an overview and some instructions on how to make your own Möbius strip…. It has only one side although that does not appear to be the case at first sight. This property of the Möbius strip symbolises the European Union and European decision-making processes in the logo of Germany’s Presidency of the European Union.
It doesn’t matter what side of the Möbius strip you start on, or what direction you move in, you will always meet up on the same side. The EU member states are also interconnected, in spite of all their differences, their national interests and their divergent opinions. And they move forward together along the European path.
https://www.bundesregierung.de/breg-en/service/archive/background-logo-moebius-strip-1756434
Anon. Mr. Möbius and his Band
The logo of the current EU Council Presidency shows an exciting mathematical object. With paper, glue, scissors and our downloadable worksheet, you are well equipped for a single or double lesson of systematic exploration….A Möbius strip has recently been designed for the logo of the German EU Council Presidency - "A strong band for a united Europe" .
Unknown Dates
Despite my best efforts, some logos have defied even an approximation as to date. This being so, I have collected these together under ‘Unknown Dates’. These include:
NCTM (National Council of Teachers of Mathematics)
Swiss Mathematics Olympiad
Mathematisches Forschungsinstitut Oberwolfach
Swiss Federal Institute of Intellectual Property
The University of Hagen
29. NCTM (National Council of Teachers of Mathematics)
Founded in 1920, the National Council of Teachers of Mathematics (NCTM) is the world's largest mathematics education organisation.
Researching this logo has proved surprisingly frustrating, even more so coming from a mathematical body of which one would have expected to sing about it from the rooftops. I cannot find any discussion on the official NCTM website or their publications! At some point, there has been a ‘recent’ (loosely defined) change. I saw a shield logo, with NTCM inside, of 1973 and again in 1988. Modern instances (2023 and 2024) abound, but not earlier. There is notable gap. Given the notable difference in years between 1988 and 2024, rather than an indicative placement I have placed it under not dated.
References
NCTM
There is no indication of any discussion on their website.
‘National Council of Teachers of Mathematics’. Wikipedia
Although the logo is pictured, it is very small and is not discussed in the text.
Founded in 1920, The National Council of Teachers of Mathematics (NCTM) is a professional organization for schoolteachers of mathematics in the United States. One of its goals is to improve the standards of mathematics in education. NCTM holds annual national and regional conferences for teachers and publishes five journals.
https://en.wikipedia.org/wiki/National_Council_of_Teachers_of_Mathematics
30. Swiss Mathematics Olympiad
This logo has proved impossible to research; I have nothing at all!
References
Schweizer Mathematik-Olympiade. In Wikipedia.
The Swiss Mathematics Olympiad (SMO for short or OSM for French: Olympiades Suisses de Mathématiques) is the Swiss student competition in the field of mathematics for students under the age of 20 who have not yet started studying. It has been organised annually since 2004 by the Imosuisse Association and is structured in two rounds. https://de.wikipedia.org/wiki/Schweizer_Mathematik-Olympiade
31. Mathematisches Forschungsinstitut Oberwolfach
The Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics) is an international research centre situated in the German Black Forest.
Details are effectively non-existent! I have not been able to determine the background (date and designer) of this logo.
References
Mathematisches Forschungsinstitut Oberwolfach
The Mathematisches Forschungsinstitut Oberwolfach (MFO, Oberwolfach Research Institute for Mathematics) is an international research centre situated in the German Black Forest. Leading experts from all over the world meet at the Institute in order to pursue their research activities, to discuss recent developments in their field with others, and to generate new ideas. The Institute is a member of the Leibniz Association and is funded jointly by the German federal government and the state governments.
History
The MFO was founded in 1944 shortly before the end of World War II.
32. Swiss Federal Institute of Intellectual Property
The Swiss Federal Institute of Intellectual Property (IPI), based in Bern, is an agency of the federal administration of Switzerland responsible for patents, trademarks, geographical indications, industrial designs and copyright.
No detail of the strip is known. Although the logo is pictured, it is not discussed in the text. This has proved surprisingly difficult to research. I have not been able to find any discussion. Even a tentative date is not possible.
References
Swiss Federal Institute of Intellectual Property. Wikipedia
The Swiss Federal Institute of Intellectual Property (IPI), based in Bern, is an agency of the federal administration of Switzerland responsible for patents, trademarks, geographical indications, industrial designs and copyright.
https://en.wikipedia.org/wiki/Swiss_Federal_Institute_of_Intellectual_Property
33. The University of Hagen
The University of Hagen is a public research university that is primarily focused on distance teaching. While its main campus is located in Hagen, North Rhine-Westphalia, Germany, the university maintains more than 50 study and research centres in Germany and throughout Europe.
Details of this logo are scant in the extreme, described (by Robert Ferréol) as ‘Logo of a German university left-handed strip with 3 half-twists’ and nothing more! The link gives The University of Hagen. However, the logo is no longer extant.
References
The University of Hagen. Wikipedia
The University of Hagen is a public research university that is primarily focused on distance teaching. While its main campus is located in Hagen, North Rhine-Westphalia, Germany, the university maintains more than 50 study and research centres in Germany and throughout Europe.
Appendix 1
Table of Attributes
Not that not all the entries are straightforwardly placed/described, in that there are certain grey areas of interpretation. On occasion, I have simplified, sometimes greatly so. A case in point is that of ‘Presentation’.
Created 20 May 2025 From existing text. Last updated 23 May 2025
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