Coup de Poing

Introduction

Chapter 1 - Entries (1892–1941)

Summary

References

Appendix - Translations and Original Text in La Science Amusante and the Trade Card

Introduction

A little-known curiosity of the Möbius strip—dating as far back as 1892—is what the French call coup de poing = a blow with the fist, or more accurately, what one person, Arthur Good—also known as Tom Tit—called it, and what has become known. When performed on a suitably prepared Möbius strip, this act results in a regular hexagon forming in outline. Despite the seemingly violent name, the action is better described as a firm press rather than an actual blow. With so few sources, I hesitate to assign it an ‘official’ designation. However, since the term has been used historically, retaining the striking (pun intended) description seems reasonable.

To achieve this effect, a generic Möbius strip simply won’t suffice. The strip must be of a specific mathematical composition, involving square roots. A standard Möbius strip, when pressed flat, would produce a variety of outlines—none of particular interest. This specific instance, yielding a regular hexagon, is therefore especially noteworthy.

As mentioned above, the connection between coup de poing and the Möbius strip remains little known. Given that all known references are in non-mathematical literature—mostly popular science, this obscurity is understandable. To my knowledge, it is not discussed in either academic or popular Möbius strip literature.

The origins are paradoxically both clear and unclear. Clear in that a definite source and date of the term and context is stated, L'Illustration, 1892, but unclear in how it was derived, but likely it was from a mathematical source (both detailed below).
Researching and finding instances of the term is challenging. The term to me (and likely most non-French people) was unknown before this research, is also used almost exclusively for fighting, and so one has to wade through a series of spurious results. The British Newspaper Archive (BNA) has 200+ references, although these are all in regard to fighting per se, and so not the desired entity here. An indication of the terms fall from use is that there are no references since 1999! Chronicling America has 2000+ references, but all seem to be spurious. And again, the term seems to have fallen out of favour, with the last entry of 1950 to 1959. Gallica has 2,000+ results, but as above, all spurious. This is also exacerbated in that it is shown without the coup de poing attribution, found only as a byproduct when searching for related Möbius terms, such as a ‘strip of paper’. Unsurprisingly, coup de poing yields no relevant results in general UK searches. French searches offer little more—mostly references to fighting and related topics. The Internet Archive and Google Books are similarly saturated with unrelated material. One could spend considerable time searching with minimal return. While other archives might offer something, the likelihood of success seems low, and the effort disproportionate. For now, I content myself with a general survey, with the option to revisit should more details emerge.
I must acknowledge the groundbreaking work of David Mitchell in bringing this phenomenon to light—an offshoot of his interest in paperfolding, and the foundation on which I lean heavily. Mitchell alone has brought this to relative prominence. I know of no other writings of comparable substance. The phenomenon occasionally appears in passing on French websites, particularly as a trade card illustration, but such instances are rare. 

Chapter 1

Entries

The presentation consists of a broad bibliographic citation with annotations. For each entry, the first instance is presented with text from the paper and a comment thereof. Where a second, repeat instance is found, I merely show a clipping, referring back to the first. This is followed by metadata, such as whether the content was syndicated (a common occurrence), the source if not by me, and the archive resource.

At-a-Glance Chronology

1892. Tom Tit. ‘Coup de Poing’. L'Illustration 2588, 1st October, 1892.

1893. Tom Tit. La Science Amusante, Volume 3. ‘L'hexagone construit d'un coup de poing’, 1893

1898. Somerville Gibney. ‘So simple! The hexagon, the enlarged ring,…’.The Boy's Own Paper, 1898.

1903. Tom Tit. ‘Figura Geométrica Hecha de un Puñetazo’. Caras y Caretas

1903. Mansfield Daily Shield (US), November 28, 1903, pp. 9–12. 

1903.The Clinton Morning Age (US), November 29, 1903, p. 6.

1903.The Coalville Times (US), December 4, 1903, not paginated

1903.The Goodland Republic (US), December 11, 1903, p. not paginated

1904.The Afro-American-Ledger (US), January 16, 1904, p. 3.

1918. C. G. Knott (Trans). 'To Construct a Hexagon by Finger Pressure'. In Scientific Amusements
1941.The Age (Australia), Saturday, August 9, 1941, p. 16. 

1892 (1)

Tom Tit (Arthur Good). ‘Coup de Poing’. L'Illustration 2588, 1st October, 1892.

The earliest known reference (and likely the first for Good reason, pardon the pun) under ‘coup de poing’ dates back to October 1892, in L'Illustration, a French illustrated weekly newspaper published in Paris. This had contributions by Tom Tit, a pseudonym for the Frenchman (and not Englishman as I originally thought), Arthur Good. Tom Tit is the more commonly used form in the publication, which I will use ongoing.

Interestingly, Louis Poyet (1846–1913), who drew the Möbius strip-themed Gaston Tissandier's three magic rings (Afghan Bands) illustrations, was also the illustrator here. Subsequent references largely repeat the illustration in various forms.

The basic form of the illustration is then repeated by Tit in three other publications and others are simplified (as line drawings) in newspaper syndications.
Source: David Mitchell 

1893 (1)

Tom Tit, La Science Amusante, Troisième Serie, Larousse (Paris), 1893, pp. 159–161.

II – POLYGONES

Construire d’un coup de poing un l’hexagone régulier.

Collez ensemble les extrémités d’une bande de papier, de façon, à obtenir une bande sans fin, mais en donnant à l’un des bouts, avant de le coller, une demi-torsion; vous obtenez ainsi un bracelet de papier ayant l’aspect de la figure 1 de notre dessin… (See Appendix 1 for all text)

The same illustration first published in L'Illustration was republished in 1893 in La Science Amusante, a compendium of articles focused on scientific experiments using everyday materials. Both publications were closely associated with Tom Tit, whose involvement explains the visual and textual continuity between them.

It seems likely that Tom Tit first encountered the effect in a mathematics journal and chose to adapt it for a broader audience, presenting it in a more expressive and accessible form. His treatment spans three pages and includes a detailed illustration, making it the earliest known published account of coup de poing. Given its historical significance, I translated the full text.

What’s particularly satisfying is Tit’s clarity in explaining the construction. He not only outlines the geometric principles—invoking square roots—but also provides a practical approximation of the proportions: 26 to 5. This balance of mathematical rigour and everyday accessibility exemplifies his approach to popular science, and it’s likely what allowed the phenomenon to reach a wider readership.
Source: David Mitchell 

1898 (1)

The Boy's Own Paper, June 4, 1898, pp. 573–574.

So Simple

The Hexagon, the Enlarged Ring, and the Handcuffs

For some purposes…

The effect finds an intriguing—if somewhat isolated—appearance in the work of Somerville Gibney. His account, published in Boy’s Own, is notable for being the first known English-language description of the effect, and it stands apart from the seemingly interwoven French sources that preceded it. Gibney makes no reference to these earlier French accounts, and nothing in his writing suggests he was aware of them, despite their publication only six years prior.

The illustrations accompanying Gibney’s article differ markedly in style from the French originals. He briefly alludes to square roots in describing the proportions of the prepared strip, but ultimately opts for a simplified approximation in inches—presumably to suit the mathematical level of his youthful readership. This choice, along with the absence of any nod to popular French treatments, suggests that Gibney may have drawn from a mathematical source rather than from the more widely circulated French popular accounts.

His piece is divided into two distinct sections: one on coup de poing, and another on the so-called ‘Afghan’ paper ring trick, which he presents using just two cut rings.

Gibney appears to have been a magician or puzzle enthusiast of some kind, though he is not listed in Magicpedia. Across ten contributions to Boy’s Own, all under the banner “So Simple,” he offers tricks and puzzles with an emphasis on accessibility and ease.

It remains unclear how Gibney came upon coup de poing, but the evidence strongly suggests he was borrowing—perhaps liberally—from French publications, particularly the work of Tom Tit. The absence of citations or acknowledgements gives the impression, whether intentional or not, that Gibney is presenting the effect as his own. While the drawings differ and the language is tailored to a younger audience, the underlying mechanics and mathematical hints align closely with the French originals. In all likelihood, Gibney’s version is a repackaged derivation rather than an independent discovery.

Bio. Somerville Gibney was a popular playwright and novelist: he produced shows for the West End and the Spectator said of his 1891 novel, The Trial of Parson Finch: “It is certainly a well-told, healthy, and by no means uninteresting story.” Squashword
Source: Internet Archive 

1903 (5)
‘Figura Geométrica Hecha de un Puñetazo’. Caras y Caretas, 1903
Oddly, at first glance, the next appearance was in the Argentine Caras y Caretas = Faces and Masks, of August 1903, which then repeats the French text and illustration. This is explainable in that translations were readily made. For instance, La Science, by Tom Tit, was translated into English, Spanish, US, Scandinavian countries, and Russian! Undoubtedly, the Spanish translation made its way to Argentina.

Publication. At the beginning of the 20th century Caras y Caretas (Faces and Masks) was one of the most widely-read magazines in Buenos Aires. A collective venture, run mostly by exiles, it was dedicated to the Argentinian context as well to European traditions.…Caras y Caretas was founded by Eustaquio Pellicer in October 1898. 

Source: David Mitchell

Mansfield Daily Shield (US), November 28, 1903, pp. 9–12.
A MOST SURPRISING FEAT WITH MERELY A LITTLE STRIP OF PAPER

Do you know what a regular hexagon is? Don't be alarmed, for it is merely a six-sided figure with all its sides of the same length and all its six angles equal. Now if you are hoping that this is to be a lesson in geometry you will have to bear your disappointment as well as you can, for it is only going to be an easy but rather surprising trick.

You show your friends a long, narrow strip of paper and ask them to change it into a regular hexagon (which you can explain as I have done above or you can show a drawing of one) without using knife, scissors or paper or cutting or tearing the paper in any way.

It is reasonably certain that nobody who is not acquainted with the secret will guess it so that, to use the language of the day, it will be “up to you to make good”.

Then you perform the trick, as follows: Lay the strip of paper on the table and give it a half twist, that is to say, calling the two sides of the paper the front and the back, twist it so that the front is on top at one end and the back at the other. Paste the ends together, forming the twisted ring shown in the illustration, throw this carelessly on the table and smash it with your clenched fist.

To the surprise of everybody the paper ring will be changed by the blow into a six-sided figure or hexagon.

It may not be perfectly regular, and there may be a little hole in the middle. The regularity depends upon the way the ring happens to lie on the table and the way you hit it, and the shape may be improved by practice.

The hole indicates that the strip of paper was not exactly of the right shape. 

The circumference of the ring should be (very nearly) five and a quarter times its width.

The simplest way of getting these proportions and at the same time making a figure of convenient size is to cut the strip two inches wide and eleven inches long and lap the ends just half an inch.

Of note as the first newspaper reference, worldwide, and was syndicated five times between 1903–1904. All the syndications were in US newspapers. Newspaper appearances are at a premium, with the only other, unrelated, from Australia, much later, in 1941. No reference is made to coup de poing, despite the drawing being a simplified take from Tom Tit. This omission suggests the anonymous author was familiar with La Science Amusante, yet chose not to acknowledge its source or the mathematical context. Nor was mention made to Möbius.

Syndicated, 1/5. 1903 (4), 1904 (1)

Google Newspapers

The Clinton Morning Age (US), November 29, 1903, p. 6.

A MOST SURPRISING FEAT WITH MERELY A LITTLE STRIP OF PAPER

Do you know what a regular hexagon is? Don't be alarmed, for it is merely a six-sided figure with all… 

As detailed above.

Syndicated, 2/5. 1903 (4), 1904 (1)

Google Newspapers

The Coalville Times (US), December 4, 1903, not paginated. 

A MOST SURPRISING FEAT WITH MERELY A LITTLE STRIP OF PAPER

Do you know what a regular hexagon is? Don't be alarmed, for it is merely a six-sided figure with all…

As detailed above.

Syndicated, 3/5. 1903 (4), 1904 (1)

Chronicling America

The Goodland Republic (US), December 11, 1903, not paginated.

A MOST SURPRISING FEAT WITH MERELY A LITTLE STRIP OF PAPER

Do you know what a regular hexagon is? Don't be alarmed, for it is merely a six-sided figure with all…

As detailed above.

Syndicated, 4/5. 1903 (4), 1904 (1)

Chronicling America

1904 (1)

The Afro-American-Ledger (US), January 16, 1904, p. 3.

A MOST SURPRISING FEAT WITH MERELY A LITTLE STRIP OF PAPER

Do you know what a regular hexagon is? Don't be alarmed, for it is merely a six-sided figure with all…

As detailed above.

Syndicated, 5/5. 1903 (4), 1904 (1)

Google Newspapers

1918 (1)
Tom Tit. Scientific Amusements. Translated into English by C. G. Knott. Thomas Nelson and Sons Ltd, London, 1918, pp. 49–51.
Take a strip of paper about five and a-half times longer than its width, give the one end half a turn and then gum it to the other end. You will obtain a bracelet of the form shown in Fig. 1. If this curious twisted strip is pressed flat to the table, a hexagon, more or less irregular, will be produced. A regular hexagon will be obtained if the length to the width is properly adjusted…
An English translation of Tom Tit’s La Science Amusante (1893), albeit with a simplified line drawing. 

1941 (1)
The Age (Australia), Saturday, August 9, 1941, p. 16.
A Simple Trick

Given a long, narrow rectangle of paper, could you transform it into a neat hexagon without cutting it in any way? At first sight this might seem impossible but a glance at the accompanying diagram will show that it can be done quite simply. First make a half twist in the paper, and paste the ends together to form the ring shown ln Fig.1. Pressing the ring flat on the table, the shape shown ln Fig. 2 will be formed, and with a little manoeuvring of the folds the intersections at A, B and D can be closed together to complete the hexagon.

Of note is the appearance in an Australian newspaper, the first from that country. In light of the newspaper finding, I also investigated possible syndications, but none (surprisingly) were found (Trove, BNA, Google Newspapers were examined). 

Coup de poing in style, if not substance; a generic strip is used, rather than one of the exact mathematics.

This account is also surprising regarding its isolation in time, with the preceding account 22 years earlier! Also, the text and diagrams have no predecessor. This also marks the end of any further reports.

Trove

Undated Trade Card

L’hexagone construit d’un coup de poing

Prenez une bande de papier de 5 centimètres de largeur sur 26 centimètres de longueur, plus 1 centimètre pour le recouvrement de la partie que vous enduisez de colle. Vous le collez à l'autre bout de la bande, mais en donnant une demi-torsion à l'un des bouts, de façon que l'envers du paper soit collé contre l’endroit. Posez le papier ainsi préparé sur la table; donnez-y un coup de poing et vous aurez formé l'hexagone régulier.

Translated

The hexagon built with one punch

Take a strip of paper 5 centimetres wide by 26 centimetres long, plus 1 centimetre to cover the part you are coating with glue. You stick it to the other end of the strip, but give one end a half twist, so that the back of the paper is stuck against the right side. Place the paper thus prepared on the table; punch it and you will have formed the regular hexagon.

TOM TIT

An undated trade card by Tom Tit, possibly from L’Ilustration. This more accurately (and notably, with two boys) shows the act of coup de poing, which the others don't. The text is different from that of La Amusante.

The same image appeared on trade cards of various French brands, namely Chocolat Félix Potin (a famous grocery store brand), Chocolat Géurin-Boutron (a luxury brand from Paris), and Grands magasins de nouveautes. Other images (non-related, popular scientific) by Tom Tit were also used in the series.

 Unfortunately, the cards are not dated. A rough date of ‘around 1890’ is given (Album Online). David Mitchell gives …undated but probably from the early years of the 20th Century.

State Library Australia gives 1857/1903, with the earliest year obviously in error.

Summary

Despite its formal introduction in 1892, coup de poing remains strikingly infrequent. Just eleven references have surfaced to date—some duplicated across languages, others syndicated—leaving a surprisingly low count of unique sources. Its most active period spans 1892 to 1918, with only a single additional mention appearing in 1941. Given its historical footprint, the term arguably merits formal recognition, which this investigation aims to outline.

Tracking down references has proven difficult. The phrase coup de poing is more commonly associated with physical confrontation, which tends to mask its rare usage in mathematical or topological contexts. In fact, the few newspaper citations I uncovered emerged serendipitously while researching idiomatic expressions linked to the Möbius strip and not by the term itself.

A deeper dive into French archival material would be ideal. Unfortunately, limited fluency and the archives’ navigational challenges have made this impractical for now. What’s truly needed is a dedicated French researcher willing to take up the baton.
Nonetheless, meaningful progress has been made—first through David Mitchell’s foundational work, and more recently through my own contributions in 2024 and 2025. Who’s to say what further insights a future revisit might yield? 

References

Newspapers

Mansfield Daily Shield (US), November 28, 1903, pp. 9–12. 

https://books.google.co.uk/books?id=EWpZAAAAIBAJ&pg=PA61&dq=%22half+twist%22+paper&article_id=7570,1482248&hl=en&sa=X&ved=2ahUKEwijtPq4p5COAxUEWEEAHfR9DrsQ6AF6BAgNEAM#v=onepage&q=%22half%20twist%22%20paper&f=false

The Clinton Morning Age (US), November 29, 1903, p. 6.

https://books.google.co.uk/books?id=tOUyAAAAIBAJ&pg=PA6&dq=Do+you+know+what+a+regular+hexagon+is?&article_id=6438,5721483&hl=en&sa=X&ved=2ahUKEwiywrn83_OOAxWqZkEAHTV8CIUQ6AF6BAgMEAM#v=onepage&q=Do%20you%20know%20what%20a%20regular%20hexagon%20is%3F&f=false

The Coalville Times (US), December 4, 1903, not paginated.

https://www.loc.gov/resource/sn85058217/1903-12-04/ed-1/?sp=3&q=a+most+surprising+feat+with

The Goodland Republic (US), December 11, 1903, not paginated.

https://www.loc.gov/resource/sn85030821/1903-12-11/ed-1/?sp=2&q=a+most+surprising+feat+with

The Afro-American-Ledger (US), January 16, 1904, p. 3.

https://books.google.co.uk/books?id=YR4mAAAAIBAJ&pg=PA3&dq=Do+you+know+what+a+regular+hexagon+is?&article_id=6245,1431588&hl=en&sa=X&ved=2ahUKEwj68vDUvJGOAxUkQEEAHf1YOWUQ6AF6BAgIEAM#v=onepage&q=Do%20you%20know%20what%20a%20regular%20hexagon%20is%3F&f=false

The Age (Australia). Saturday, August 9, 1941, p. 16.

https://trove.nla.gov.au/newspaper/article/205174737/19386374

French Sources

Album Online

'L'hexagone construit d'un coup de poing'. Chromo vers 1890, serie Tom Tit.

https://www.album-online.com/detail/en/ZmMwYmEwMA/hexagone-construit-coup-poing-chromo-189

https://www.album-online.com/fr/search?iSF=3&sT=TOM+TIT&iSp=4187&sGs=mosaic&iPP=2

L’Illustration

The home page of L’Illustration. Paywalled, but with a limited preview. 

https://www.lillustration.com/

Books

Somerville Gibney. ‘So simple! The hexagon, the enlarged ring, and the handcuffs’. The Boy's Own Paper 20 (No. 1012), 4 June, 1898, pp. 573–574.
https://babel.hathitrust.org/cgi/pt?id=uc1.c2723989&seq=602&q1=gibney

(Bio) https://www.squashword.com/?p=176632388

Tom Tit. Tom Tit's Experiment. Scientific distractions. First Swedish edition, 1897. Translated from the French by G. C. Foreword by A. E. Hellgren. With 300 illustrations. Alf. Samuelsson's, Stockholm, 1898. 287 richly illustrated pages.

ps://auctionet.com/en/2157151-tom-tit-s-experiment-in-first-swedish-edition-1897-with-300-illustrations

Not seen in full. Documented as ‘seen and noted’, with a rare Sweden edition.

Tom Tit. Tom Tit száz kisérlete és produkciója I-III. Kötet, Year unknown.

Translated Tom Tit's hundred experiments and productions I-III. volume

Not seen in full. Documented as ‘seen and noted’, with a rare Hungarian edition.

https://antikva.hu/fizika/totm-tit-szaz-kiserlete-es-produkcioja-i-iii-kotet/good-arthor

Tom Tit. Scientific Amusements. Translated into English by C. G. Knott. Thomas Nelson and Sons Ltd, London, 1918, pp. 49–51.

https://archive.org/details/in.ernet.dli.2015.219115/page/n51/mode/2up?q=%22strip+of+paper+ABCD%22

Web

David Mitchell. ‘How to Flatten a Mobius Band into a Regular Hexagon with a 'Coup de Poing'. 

Gives a general survey (in line with the site), with each entry of a picture, with basic background details, of two or three lines.

https://www.origamiheaven.com/historyhowtoflattenamobiusband.htm

Australia

State Library Australia

https://find.slv.vic.gov.au/discovery/fulldisplay?vid=61SLV_INST:SLV&search_scope=slv_local&tab=searchProfile&docid=alma9939668830607636&context=L

Biographies

Arthur Good (Tom Tit)

Gives good background detail on Arthur Good (Tom Tit). Relatively little detail elsewhere is available on him.

https://en.wikipedia.org/wiki/Arthur_Good

Appendix

Translations and Original Text in La Science Amusante and the Trade Card

Below, I present both the original French and an English translation of the La Science Amusante text, followed by the version found on the trade card. As expected, the publication provides a more expansive and mathematically exact description, while the trade card opts for brevity and accessibility.
Central to understanding its origins is the French publication L'Illustration (1892), which, beyond reasonable doubt, appears to be the earliest source. Unfortunately, the original article remains elusive and is not readily accessible, posing a challenge to thorough research.
Yet all is not lost. Strong indications suggest that the same text was reproduced in La Science Amusante (1893), and in the absence of the original, I will proceed on the assumption that this later version faithfully reflects the earlier publication. This text spans over three pages and includes a single illustration. It offers a rigorous treatment of the phenomenon, detailing its geometric construction with notable precision—including the use of square roots and a calculated approximation.
In contrast, a contemporary trade card presents a more concise account. Understandably limited by space, it simplifies the construction, offering only approximate measurements (5 and 26 centimetres) without delving into the underlying mathematics.

1. Translation of La Science Amusante. Although strictly irrelevant, to better put the book into context, I have also translated the introduction. Of note is the geometry reference.

Introduction

As in the previous volumes, the amateur will find in this one experiments in physics and mechanics that are easy to perform, without expense and without danger, using everyday objects. I have added a special chapter on soap bubbles, as well as some recreations on geometry.

A large part has been reserved for small manual works, several of which, performed in the patronage meetings of the "Dons Jeudis", can be recommended for youth meetings and family evenings.

I express here my deepest gratitude to the many friends, known or unknown, of Science Amusante, as well as to the Maison Larousse, for the care taken by it in the publication of the three volumes; this one, the last of the series, will, I hope, be received with the same favour as its two elders.

ARTHUR GOOD (TOM TIT)

Paris, January 1, 1906

II – POLYGONS

Build a regular hexagon with a punch.

Glue together the ends of a strip of paper, so as to obtain an endless strip, but by giving one of the ends, before glueing it, a half-twist; you thus obtain a paper bracelet having the appearance of figure 1 of our drawing. If you press this paper flat on the table, you will instantly form a more or less regular hexagon (fig. 2). With this very simple process, you will be able, by calculating in advance the length of the strip, to obtain

Page 160

the regular hexagon, in which the points a b c of figure 2 will coincide so as to no longer have a gap in the middle of the polygon. To do this, simply take a strip of paper 5 centimeters wide by 26 centimetres long, plus 1 centimetre, for example, for covering the glued part. Give one of your friends the strip ready prepared, asking him to flatten it on the table with a blow of his fist; he will be quite surprised to see that he has, in a single blow, constructed a rigorously geometric figure.

Note. — It is obvious that you can operate with any width of paper, provided that the length is proportional; it is enough to remember that the circumference of the regular hexagon is equal to the width of the strip multiplied by the number 3 √3. As 3 √3 is equal to 1.7321, it is therefore by 5.1963 that the width of the side must be multiplied. — You can, moreover, operate without any calculation, and by simply folding the strip of paper, by making the construction represented at the top of our drawing.

Let the strip ABCD. Let us fold it along the line CE, then along EF. We have the square ACEF, in which CE is equal to √2, assuming the width of the strip to be 1. Let us carry the fold CE on EB; the point C arrives at a. Let us mark this point, and fold the paper according to Fa. By virtue of the theorem of the square of the hypotenuse, we have: Fa = √2. We therefore only have to carry 3 times this length on the line a B, at a b, b c and c x;

Page 161

the length a x is equal to the circumference of the hexagon, because it is equal to AC x √3. Let us fold the strip according to a x, b y, c z and x’ a’, leaving the small rectangle x’ B a’ D to receive the glue; cut the paper according to a x, glue the two ends by giving a half-turn to one of them, so that x’ coincides with x, and a’ with a; and here is our strip ready to provide us, by its crushing, with the regular hexagon represented in no. 3 of the figure.

Original French

Comme dans les précédents volumes, l’amateur trouvera dans celui-ci des expériences de physique et de mécanique faciles à exécuter, sans dépenses et sans danger, à l’aide d'objets usuels. J’y ai joint un chapitre spécial sur les bulles de savon, ainsi que quelques récréations sur ia géométrie.

Une partie importante a été réservée aux petits travaux manuels dont plusieurs, exécutés dans les réunions de patronage des « Dons Jeudis », peuvent être recommandés pour les réunions de jeunesse et les soirées de famille,

J’exprime ici ma plus vive reconnaissance aux nombreux amis, connus ou inconnus, de la Science Amusante, ainsi qu'à la Maison Larousse, pour le soin apporté par elle à la publication des trois volumes; celui-ci, le dernier de la série, sera, je l’espère, accueilli avec la même faveur que ses deux aînés.

ARTHUR GOOD (TOM TIT)

Paris, le 1er janvier 1906

II – POLYGONES

Construire d’un coup de poing un l’hexagone régulier.

Collez ensemble les extrémités d’une bande de papier, de façon, à obtenir une bande sans fin, mais en donnant à l’un des bouts, avant de le coller, une demi-torsion; vous obtenez ainsi un bracelet de papier ayant l’aspect de la figure 1 de notre dessin. Si vous pressez ce papier à plat sur la table, vous formerez instantanément un hexagone plus ou moins régulier (fig. 2). Avec ce procédé si simple, vous pourrez, en calculant d’avance la longueur de la bande, obtenir

Page 160

l’hexagone régulier, dans lequel les points a b c de la figure 2 coïncideront de façon à ne plus avoir de vide au milieu du polygone. Il suffit, pour cela, de prendre une bande de papier de 5 centimètres de largeur sur 26 centimètres de longueur, plus 1 centimètre, par exemple, pour le recouvrement de la partie collée. Donnez à un de vos amis la bande toute préparée, en le priant de l'aplatir sur la fable d’un coup de poing; il sera tout surpris de voir qu’il a, d’un seul coup, construit une figure rigoureusement géométrique.

Nota. — Il est évident que vous pouvez opérer avec une largeur de papier quelconque, pourvu que la longueur soit proportionnelle; il suffit de se rappeler que le pourtour de l’hexagone régulier est égal à la largeur de la bande multipliée par le nombre 3 √3. Comme 3 √3 est égal à 1,7321, c’est donc par 5,1963 qu’il faut multiplier la largeur du côté. — Vous pouvez, du reste, opérer sans aucun calcul, et par le simple pliage de la bande de papier, en faisant la construction représentée en haut de notre dessin.

Soit la bande ABCD. Plions-la suivant la ligne CE, puis suivant EF. Nous avons le carré ACEF, dans lequel CE est égale, à √2 en supposant la largeur de la bande égale à 1. Portons le pli CE sur EB; le point C arrive en a. Marquons ce point, et plions le papier suivant Fa. En vertu du tiiéorème du carré de l’hypoténuse, on a: Fa = √2. Nous n’avons donc qu’à porter 3 fois cette longueur sur la ligne a B, en a b, b c et c x; 

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la longueur a x est égale au pourtour de l’hexagone, car elle est égale à AC x √3. Plions la bande suivant a x, b y, c z et x’ a’ en laissant le petit rectangle x’ B a’ D pour recevoir la colle; coupons le papier suivant a x, colIons les deux bouts en donnant un demi-tour à l’un d’eux, de façon que x' coïncide avec x, et a’ avec a; et voilà notre bande prête à nous fournir, par son écrase ment, I’ hexagone régulier représenté au n° 3 de la figure.

2. Translation of the Trade Card

Translation

The hexagon built with one punch

Take a strip of paper 5 centimetres wide by 26 centimetres long, plus 1 centimetre to cover the part you are coating with glue. You stick it to the other end of the strip, but give one end a half twist, so that the back of the paper is stuck against the right side. Place the paper thus prepared on the table; punch it and you will have formed the regular hexagon.

TOM TIT

Original French

L’hexagone construit d’un coup de poing

Prenez une bande de papier de 5 centimètres de largeur sur 26 centimètres de longueur, plus 1 centimètre pour le recouvrement de la partie que vous enduisez de colle. Vous le collez à l'autre bout de la bande, mais en donnant une demi-torsion à l'un des bouts, de façon que l'envers du paper soit collé contre l’endroit. Posez le papier ainsi préparé sur la table; donnez-y un coup de poing et vous aurez formé l'hexagone régulier. 

TOM TIT

4 February 2026 Text. Installed from the essay 6–9, 12–14 August, 7 October 2024 (Version 1); 5–8 August 2025 (Version 2).