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")

— Nicholas Bourbaki's description of the symbol in several textbooks^[1]

French "virages dangereux" road sign, before 1949.

The dangerous bend or caution symbol ☡ (unicode 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 a more realistic road-sign depiction in his Metafont and TeX systems, with a pair of adjacent signs indicating doubly dangerous passages.^[3][4][5]

Typography

Knuth's "Dangerous Bend" sign

In HTML the unicode dangerous bend symbol ☡ can be produced by:

☡

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.

References

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 0387489088, p. 92.
3. ^ Donald Ervin Knuth (1984), The TeXbook, Addison-Wesley, ISBN 0201134489.
4. ^ Donald Ervin Knuth (1986), The METAFONTbook, Addison-Wesley, ISBN 0201134454.
5. ^ George J. Tourlakis (2003), Lectures in Logic and Set Theory, Volume 2: Set Theory, Cambridge University Press, ISBN 0521753740, p. xiv.

See also

• Halmos box

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.