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Bourbaki dangerous bend symbol

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Title: Bourbaki dangerous bend symbol  
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Subject: Nicolas Bourbaki, Mathematical symbols, Hazard symbol, Miscellaneous Symbols, Readability
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Bourbaki dangerous bend symbol

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 signposted in the margin with the sign ☡ ("dangerous bend")

— Nicolas Bourbaki's description of the symbol in several textbooks[1]
French "virages dangereux" road sign, before 1949.

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.[2]

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.[3][4][5][6]


Knuth's "Dangerous Bend" sign

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


and then typing


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

See also


  1. ^ See, for example, Théorie des ensembles, p. I-8.
  2. ^ Steven G. Krantz (2011), The Proof Is in the Pudding: The Changing Nature of Mathematical Proof, Springer, ISBN 0-387-48908-8, p. 92.
  3. ^ Donald Ervin Knuth (1984), The TeXbook, Addison-Wesley, ISBN 0-201-13448-9.
  4. ^ Donald Ervin Knuth (1986), The METAFONTbook, Addison-Wesley, ISBN 0-201-13445-4.
  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

External links

  • Knuth's use of the dangerous bend sign. Public domain GIF files.
  • Latex style file to provide a "danger" environment marked by a dangerous bend sign, based on Knuth's book.
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