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The dangerous bend or caution symbol ☡ (U+2621 ☡ CAUTION SIGN) was created by the Nicolas Bourbaki group of mathematicians and appears in the margins of mathematics books written by the group. It resembles a road sign that indicates a "dangerous bend" in the road ahead, and is used to mark passages tricky on a first reading or with an especially difficult argument.^[1]

Certains passages sont destinés à prémunir le lecteur contre des erreurs graves, où il risquerait de tomber; ces passages sont signalés en marge par le signe ☡ (« tournant dangereux »)

Some passages are designed to forewarn the reader against serious errors, where he risks falling; these passages are indicated in the margin with the sign ☡ ("dangerous bend")

Nicolas Bourbaki's description of the symbol in several textbooks^[2]

Variations

Others have used variations of the symbol in their books. The computer scientist Donald Knuth introduced an American-style road sign depiction in his Metafont and TeX systems, with a pair of adjacent signs indicating doubly dangerous passages.^[3]^[4]^[5]^[6]

Typography

Knuth's "Dangerous Bend" sign, with yellow color added.

In the LaTeX typesetting system, Knuth's dangerous bend symbol can be produced by first loading the font manfnt (a font with extra symbols used in Knuth's TeX manual) with \usepackage{manfnt} and then typing \dbend

There are several variations given by \lhdbend, \reversedvideodbend, \textdbend, \textlhdbend, and \textreversedvideodbend.

In popular culture

The Twenty One Pilots song "Overcompensate", makes direct reference to the symbol. Since 2018, the Nicolas Bourbaki group has also been referenced in the conceptual narrative of the band.^[7]^[8]

References

^ Steven G. Krantz (2011), The Proof Is in the Pudding: The Changing Nature of Mathematical Proof, Springer, ISBN 0-387-48908-8, p. 92.
^ See, for example, Théorie des ensembles, p. I-8.
^ Donald Ervin Knuth (1986), The METAFONTbook, Addison-Wesley, ISBN 0-201-13445-4.
^ Donald Ervin Knuth (1984), The TeXbook, Addison-Wesley, ISBN 0-201-13448-9.
^ George J. Tourlakis (2003), Lectures in Logic and Set Theory, Volume 2: Set Theory, Cambridge University Press, ISBN 0-521-75374-0, p. xiv.
^ Gerard P. Michon (2012), Dangerous Bend Symbol, doubled and tripled, Numericana.
^ Kaufman, Gil (February 29, 2024). "Twenty One Pilots Announce 'Clancy' Album, Drop Video For Booming 'Overcompensate' Single". Billboard. Retrieved March 1, 2024.
^ "Map of Dema". dmaorg.info. Retrieved October 7, 2018.

External links

This article about a visual symbol is a stub. You can help Wikipedia by expanding it.

[1] Steven G. Krantz (2011), The Proof Is in the Pudding: The Changing Nature of Mathematical Proof, Springer, ISBN 0-387-48908-8, p. 92.

[2] See, for example, Théorie des ensembles, p. I-8.

[3] Donald Ervin Knuth (1986), The METAFONTbook, Addison-Wesley, ISBN 0-201-13445-4.

[4] Donald Ervin Knuth (1984), The TeXbook, Addison-Wesley, ISBN 0-201-13448-9.

[5] George J. Tourlakis (2003), Lectures in Logic and Set Theory, Volume 2: Set Theory, Cambridge University Press, ISBN 0-521-75374-0, p. xiv.

[6] Gerard P. Michon (2012), Dangerous Bend Symbol, doubled and tripled, Numericana.

[Billboard-7] Kaufman, Gil (February 29, 2024). "Twenty One Pilots Announce 'Clancy' Album, Drop Video For Booming 'Overcompensate' Single". Billboard. Retrieved March 1, 2024.

[8] "Map of Dema". dmaorg.info. Retrieved October 7, 2018.

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@@ Line 1: / Line 1: @@
+{{Short description|Typological symbol representing difficulty}}
-__NOTOC__
+[[File:Borne_Michelin_Virages.JPG|thumb|French "{{lang|fr|virages dangereux}}" road sign, before 1949]]
+The '''dangerous bend''' or '''caution''' symbol '''☡''' ({{unichar|2621|CAUTION SIGN}}) was created by the [[Nicolas Bourbaki]] group of mathematicians and  appears in the margins of [[mathematics]] books written by the group.  It resembles a [[Traffic sign|road sign]] that indicates a "dangerous bend" in the road ahead, and is used to mark passages tricky on a first reading or with an especially difficult argument.<ref>Steven G. Krantz (2011), ''[https://books.google.com/books?id=mMZBtxVZiQoC&pg=PA92 The Proof Is in the Pudding: The Changing Nature of Mathematical Proof]'', Springer, {{ISBN |0-387-48908-8}}, p. 92.</ref>
 {{quote box
 |align=right
-|width=33%
+|width=40%
-|quote={{lang|fr|Certains passages sont destinés à prémunir le lecteur contre des erreurs graves, où il risquerait de tomber ; ces passages sont signalés en marge par le signe ☡ (« tournant dangereux »)}}
+|quote={{lang|fr|Certains passages sont destinés à prémunir le lecteur contre des erreurs graves, où il risquerait de tomber; ces passages sont signalés en marge par le signe ☡ (« tournant dangereux »)}}
 <p>
 Some passages are designed to forewarn the reader against serious errors, where he risks falling; these passages are indicated in the margin with the sign ☡ ("dangerous bend")
@@ Line 9: / Line 12: @@
 |source=Nicolas Bourbaki's description of the symbol in several textbooks<ref>See, for example, ''[https://books.google.com/books?id=VDGifaOQogcC&pg=SA1-PA5  Théorie des ensembles]'', p. I-8.</ref>
 }}
-[[File:Borne_Michelin_Virages.JPG|thumb|left|French "{{lang|fr|virages dangereux}}" road sign, before 1949]]
+==Variations==
-The '''dangerous bend''' or '''caution''' symbol '''☡''' ({{unichar|2621|CAUTION SIGN}}) was created by the [[Nicolas Bourbaki]] group of mathematicians and  appears in the margins of [[mathematics]] books written by the group.  It resembles a [[Traffic sign|road sign]] that indicates a "dangerous bend" in the road ahead, and is used to mark passages tricky on a first reading or with an especially difficult argument.<ref>Steven G. Krantz (2011), ''[https://books.google.com/books?id=mMZBtxVZiQoC&pg=PA92 The Proof Is in the Pudding: The Changing Nature of Mathematical Proof]'', Springer, {{ISBN |0-387-48908-8}}, p. 92.</ref>
+Others have used variations of the symbol in their books. The computer scientist [[Donald Knuth]] introduced an American-style road sign depiction in his [[Metafont]] and [[TeX]] systems, with a pair of adjacent signs indicating doubly dangerous passages.<ref>Donald Ervin Knuth (1986), ''[https://books.google.com/books?id=GghUAAAAMAAJ The METAFONTbook]'', Addison-Wesley, {{ISBN |0-201-13445-4}}.</ref><ref>Donald Ervin Knuth (1984), ''[https://books.google.com/books?id=hEYuAQAAIAAJ The TeXbook]'', Addison-Wesley, {{ISBN |0-201-13448-9}}.</ref><ref>George J. Tourlakis (2003), ''[https://books.google.com/books?id=nparMXao59QC&pg=PR14 Lectures in Logic and Set Theory, Volume 2: Set Theory]'', Cambridge University Press, {{ISBN |0-521-75374-0}}, p. xiv.</ref><ref>Gerard P. Michon (2012), ''[http://www.numericana.com/answer/symbol.htm#db Dangerous Bend Symbol, doubled and tripled]'', Numericana.</ref>
-Others have used variations of the symbol in their textbooks, and computer scientist [[Donald Knuth]] introduced an American-style road-sign depiction in his [[Metafont]] and [[TeX]] systems, with a pair of adjacent signs indicating doubly dangerous passages.<ref>Donald Ervin Knuth (1986), ''[https://books.google.com/books?id=GghUAAAAMAAJ The METAFONTbook]'', Addison-Wesley, {{ISBN |0-201-13445-4}}.</ref><ref>Donald Ervin Knuth (1984), ''[https://books.google.com/books?id=hEYuAQAAIAAJ The TeXbook]'', Addison-Wesley, {{ISBN |0-201-13448-9}}.</ref><ref>George J. Tourlakis (2003), ''[https://books.google.com/books?id=nparMXao59QC&pg=PR14 Lectures in Logic and Set Theory, Volume 2: Set Theory]'', Cambridge University Press, {{ISBN |0-521-75374-0}}, p. xiv.</ref><ref>Gerard P. Michon (2012), ''[http://www.numericana.com/answer/symbol.htm#db Dangerous Bend Symbol, doubled and tripled]'', Numericana.</ref>
 {{clear}}
 ==Typography==
-[[File:Knuth's dangerous bend symbol.svg|thumb|60px|right|Knuth's "Dangerous Bend" sign]]
+[[File:Knuth's dangerous bend symbol.svg|thumb|60px|right|Knuth's "Dangerous Bend" sign, with yellow color added.]]
 In the [[LaTeX]] typesetting system, Knuth's dangerous bend symbol  can be produced by
-first loading the font manfnt (a font with extra symbols used in Knuth's TeX manual) with
+first loading the font manfnt (a font with extra symbols used in Knuth's TeX manual) with <code>
+\usepackage{manfnt}</code> and then typing <code>\dbend</code>
+There are several variations given by <code>\lhdbend</code>, <code>\reversedvideodbend</code>, <code>\textdbend</code>, <code>\textlhdbend</code>, and <code>\textreversedvideodbend</code>.
-<pre>
-\usepackage{manfnt}
-</pre>
+==In popular culture==
-and then typing
+The [[Twenty One Pilots]] song "[[Overcompensate (song)|Overcompensate]]", makes direct reference to the symbol. Since 2018, the Nicolas Bourbaki group has also been referenced in the conceptual narrative of the band.<ref name=Billboard>{{Cite magazine |last=Kaufman |first=Gil |date=February 29, 2024 |title=Twenty One Pilots Announce 'Clancy' Album, Drop Video For Booming 'Overcompensate' Single |url=https://www.billboard.com/music/rock/twenty-one-pilots-clancy-album-overcompensate-single-1235618630/ |access-date=March 1, 2024 |magazine=Billboard}}</ref><ref>{{Cite web|url=http://dmaorg.info/found/15398642_14/img/6629097cc6e3/_ti_su_p.png|title=Map of Dema|website=dmaorg.info|access-date=October 7, 2018}}</ref>
-<pre>
-\dbend
-</pre>
-There are several variations given by <tt>\lhdbend</tt>, <tt>\reversedvideodbend</tt>, <tt>\textdbend</tt>, <tt>\textlhdbend</tt>,
-and <tt>\textreversedvideodbend</tt>.
 ==See also==
@@ Line 47: / Line 42: @@
 [[Category:Mathematical symbols]]
 [[Category:Nicolas Bourbaki|*]]
+{{Visual-symbol-stub}}