traditional German sans-serif (and serif) blackboard-bold symbols

Question

What I have always been looking for in LaTeX were traditional German sans-serif blackboard-bold letters, mainly for: N (natural numbers), Z (integers), Q (rational numbers), R (reals), C (complex numbers).

These five symbols are used widely in German secondary-school math textbooks and in a type of book called "Formelsammlung" (a book that functions as a collection of formulas; usually secondary school students will use one for math and physics each). The most widely used Formelsammlung was (for a long time at least) "Mathematische Formeln / Erweiterte Ausgabe E" by Sieber/Klett.

The standard array of German textbook publishers (such as Cornelsen and Klett; I'm afraid I don't remember which math textbook my school used) always styled the blackboard-bold letters in a particular, uniform way: for sans-serif letters this was with the doublestroke having equal strength as the one that it is doubling, and also without a connection to the original stroke (for vertical-ish doubled strokes). The symbols look very similar (and are I think homotopy-equivalent (a notion from topology)) to the ones of dsfont's sans option (\(\mathds{N},\mathds{Z},\mathds{Q},\mathds{R},\mathds{C}\)), except I see that the vertical stroke for "Q" is rendered imperfectly in my viewer (the vertical stroke is not perfectly connected at the bottom) but not all viewers it seems; also for "A" we'd expect the doubled stroke to be on the left (though technically German secondary school math has no precedent here, since "A" is not commonly used to denote a specific set).

Important: After initially posting my question, I do believe to remember that there are both sans-serif and serif styles in standard German schoolbooks and (at least lower-division) math textbooks. As for serif letters, the \varmathbb symbols of the txfonts package look very close to what I remember. (I initially thought that the doubled stroke for at least Z was too thin there, but now I don't remember whether this perhaps applied only to the German sans-serif style.)

Is anyone aware of a DIN standard defining the proper symbols? I suspect there might be one.

Much more importantly, is anyone aware of a font for (La)TeX that provides the type of blackboard bold symbols that are commonly used in German school literature for both (a) sans-serif and (b) serif styles?

(I can not find online scans of this literature and do not have easy access to it right now. If someone else can help out here that would be much appreciated.)

Answer 1

I suggest you take a look at Michael Sharpe's mathalfa (the spelling "mathalpha" works too) package. In the package's user guide, the author lists five "hollowed-out" and fourteen [!] "geometric" variants of blackboard-bold fonts. (Note that not all of the underlying fonts are free.) I trust that one or more of the math blackboard board fonts listed and/or made available through the mathalfa package will meet your needs. (I'm afraid I don't have access to German-language math textbooks.)

A big plus of using the mathalfa package is that you can "mix and match" various math alphabets (blackboard bold, caligraphic, curly, script, fraktur, etc) with ease. Excerpting from the README file that comes with the mathalfa package:

This package provides a standard means of setting math alphabets associated with the macros \mathcal, \mathbb, \mathfrak and \mathscr and, where available, their bold counterparts \mathbcal, \mathbbb, \mathbfrak and \mathbscr.

It mostly bypasses the usual fd and sty files used to load these alphabets in order to allow each to be scaled independently and without silently quantizing the sizes.

Answer 2

The definitive answer turns out to be quite distributed (found through collaborative discussion). Credit goes to multiple people (see the entire discussion). Awarding bounties would have been infeasible in this case as they would have to be distributed over a few people.

Sans-serif: Package mathds with option sans (\usepackage[sans]{dsfont}), except for doublestroke-"A" one needs to use \mathds{a} instead of \mathds{A} to get the doubled stroke on the "correct" (as per expectation) side (i.e., on the left).

Serif: The following fonts mentioned in mathalfa's documentation would "pass" to the eye of a German user used to the traditional lettershapes of German blackboard bold: pazo (Mathpazo bb), tx (tx bb), px (px bb). "tx bb" looks closest to my memories, though I like the "S" of Mathpazo bb as being more consistent with the implicit design. The mathds package also yields letters whose shapes "pass" for "traditional German" appearance, except for the doublestroke-"A", one needs to remember to use the lowercase option (\mathds{aBCDEFGHIJKLMNOPQRSTUVWXYZ}), just like I mentioned above in the sans-serif paragraph.

Answer 3

In the modern toolchain, with unicode-math, you can load the \mathbb (or \symbb) alphabets from any other font with the range= option of \setmathfont. I’m not sure exactly what you want (Is it similar to this?), but here is an example:

\documentclass{article}
\usepackage{unicode-math}

\setmathfont{Latin Modern Math}
\setmathfont{TeX Gyre Pagella Math}[range={bb,bbit}, Scale=MatchUppercase]

\begin{document}
\[ \mathbb{CDHNRQSZ} \]
\end{document}

Here is the same sample with the font changed to:

\setmathfont{TeX Gyre DejaVu Math}[range={bb,bbit}, Scale=MatchUppercase]

You might also try Microsoft’s Cambria Math, if you have it on your system.

Or for a sans-serif version, you might change the relevant line to:

\setmathfont{STIX Two Math}[range={bb,bbit}, Scale=MatchUppercase]

Beware: As of 2019, range= and version= do not mix.

You can see the list of symbols from unicode-math for font samples of the double-struck letters from a half-dozen fonts, and look for specimens of the rest. (Note that all the most common double-struck letters, including ℂ, ℕ, ℝ and ℤ, are printed in section 13.3 instead.)

If you find a display font that is not a math font, but you like better, you can use a similar command, e.g \setmathfont{FoglihtenNo3}[range=bb, Scale=MatchUppercase].

Follow-up to earlier answers

The mathalfa package changed its name to mathalpha in 2019, and some of the alphabet names have changed. The older names should continue to work.

Answer 4

(Note: I overlooked, that the OP already wrote about this package. But according to the comments my answer seems still to be useful.)

There is also the package doublestroke (Texlive)/dstroke (MiKTeX), which provides a serif font (and a sans-serif version), that

is useful for typesetting the mathematical symbols for the natural numbers …, whole numbers …, rational numbers …, real numbers …, complex numbers …, and a couple of others which are sometimes needed.

To use it, one has despite the package name to add first \usepackage{dsfont} and later a \mathds{<symbol>}. There are glyphs for all capital letters A…Z, for 1, h, k and for the letter a (i.e. the small letter!). The latter gives a different A with the doubled line in the upstroke.

_{(The source for the following example is the manual.)}

\documentclass{article}
\usepackage{dsfont}
\begin{document}
\[\mathds{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\]
\[\mathds{a}\]
\[\mathds{1}\;\mathds{h}\;\mathds{k}\]
\end{document}

To get the sans-serif version, one has to set the package option ‘sans’:

\documentclass{article}
\usepackage[sans]{dsfont}
\begin{document}
\[\mathds{ABCDEFGHIJKLMNOPQRSTUVWXYZ}\]
\[\mathds{a}\]
\[\mathds{1}\;\mathds{h}\;\mathds{k}\]
\end{document}

_{BTW: Found by searching with Detexify LaTeX handwritten symbol recognition and then looking for dsfont on my computer.}