[Tex/LaTex] How to best typeset “special” constants (complex unit i, Euler’s number e,…)

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I'm trying to come up with a typographically appealing way to express "special" numbers such as the complex unit i = sqrt(-1) or Euler's number e. It has to be such that it cannot be confused with regular numbers (such as the running index i, for example), and would ideally work for serif as well as sans-serif fonts.

I was briefly thinking of typesetting these numbers in bold, but found that bold face is often used to indicate vector quantities.

[Edit: Johannes Küster suggests to use upright for constants (about 14 minutes into his talk).]

I've seen double-stroked small letters too, and must say this isn't without appeal. I have no idea how to consistently typeset those, though. The (outdated?) bbm package seems to provide at least some basic functionality.

What do you use to represent special numbers, why do use it, and how to you typeset your solution?

Best Answer

Consistency is the primary goal. So the first task is to know what "special numbers" we need and define commands for them:

\newcommand{\euler}{e}
\newcommand{\ramuno}{i}

(ramuno was how some Italian mathematicians of the 16th century called the quantity that squared gives –1; then Euler started using i).

The mathematical typography tradition usually didn't have a special treatment of these symbols. See, for example, n. 359 in Gauss's Disquisitiones Arithmeticae, where the equivalent of

$\cos\frac{\lambda kP}{e} + i\sin\frac{\lambda kP}{e}$

is found (the edition I consulted is from the Werke by the Königlichen Gesellschaft der Wissenschaften in Göttingen, vol. 1, 1863, page 450). There's no doubt what this i is denoting.

enter image description here

http://gdz.sub.uni-goettingen.de/dms/load/img/?PPN=PPN235993352&IDDOC=137206

However, in recent times, under the influence of physics and applied mathematics, people started to denote "constants" with upright letters. There's even an ISO regulation about this, which is compulsory in some fields where uniformity among papers and books is very important.

In pure mathematics there's essentially no rule. Do as you like or how your field is used to. Using special names for the special numbers allow you to change the appearance of your document just by changing the definition.

If you feel that there may be confusion between the "imaginary unit" (no worse name could be chosen for it) and an index (for summations, for instance), you have three strategies:

  1. use a special denotation for the imaginary unit;

  2. don't use i as an index;

  3. forget about it and let the reader know from the context.

Strategy 2 is used by Graham, Knuth and Patashnik in their "Concrete Mathematics". Strategy 3 is very common in math textbooks.

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