Which Unicode characters can you depend on?

Unicode is supported everywhere, but font support for Unicode characters is sparse. When you use any slightly uncommon character, you have no guarantee someone else will be able to see it.

I’m starting a Twitter account @MusicTheoryTip and so I wanted to know whether I could count on followers seeing music symbols. I asked whether people could see ♭ (flat, U+266D), ♮ (natural, U+266E), and ♯ (sharp, U+266F). Most people could see all three symbols, from desktop or phone, browser or Twitter app. However, several were unable to see the natural sign from an Android phone, whether using a browser or a Twitter app. One person said none of the symbols show up on his Blackberry.

I also asked @diff_eq followers whether they could see the math symbols ∂ (partial, U+2202), Δ (Delta, U+0394), and ∇ (gradient, U+2207). One person said he couldn’t see the gradient symbol, but the rest of the feedback was positive.

So what characters can you count on nearly everyone being able to see? To answer this question, I looked at the characters in the intersection of several common fonts: Verdana, Georgia, Times New Roman, Arial, Courier New, and Droid Sans. My thought was that this would make a very conservative set of characters.

There are 585 characters supported by all the fonts listed above. Most of the characters with code points up to U+01FF are included. This range includes the code blocks for Basic Latin, Latin-1 Supplement, Latin Extended-A, and some of Latin Extended-B.

The rest of the characters in the intersection are Greek and Cyrillic letters and a few scattered symbols. Flat, natural, sharp, and gradient didn’t make the cut.

There are a dozen math symbols included:

0x2202 ∂
0x2206 ∆
0x220F ∏
0x2211 ∑
0x2212 −
0x221A √
0x221E ∞
0x222B ∫
0x2248 ≈
0x2260 ≠
0x2264 ≤
0x2265 ≥

Interestingly, even in such a conservative set of characters, there are a three characters included for semantic distinction: the minus sign (i.e. not a hyphen), the difference operator (i.e. not the Greek letter Delta), and the summation operator (i.e. not the Greek letter Sigma).

And in case you’re interested, here’s the complete list of the Unicode characters in the intersection of the fonts listed here. (Update: Added notes to indicate the start of a new code block and listed some of the isolated characters.)

0x0009           Basic Latin
0x0020 - 0x007e 
0x00a0 - 0x017f  Latin-1 supplement
0x01fa - 0x01ff
0x0218 - 0x0219  
0x02c6 - 0x02c7  
0x02d8 - 0x02dd 
0x0300 - 0x0301 
0x0384 - 0x038a  Greek and Coptic
0x038e - 0x03a1
0x03a3 - 0x03ce
0x0401 - 0x040c 
0x040e - 0x044f  Cyrillic
0x0451 - 0x045c
0x045e - 0x045f
0x0490 - 0x0491
0x1e80 - 0x1e85  Latin extended additional
0x1ef2 - 0x1ef3
0x200c - 0x200f  General punctuation
0x2013 - 0x2015
0x2017 - 0x201e
0x2020 - 0x2022
0x2028 - 0x202e
0x2032 - 0x2033
0x2039 - 0x203a
0x206a - 0x206f  
0x20a3 - 0x20a4  Currency symbols ₣ ₤
0x20a7           ₧
0x20ac           €
0x2105           Letterlike symbols ℅
0x2116           №
0x2122           ™
0x2126           Ω
0x212e           ℮
0x215b - 0x215e  ⅛ ⅜ ⅝ ⅞
0x2202 	         Mathematical operators ∂
0x2206           ∆
0x220f           ∏
0x2211 - 0x2212  ∑ −
0x221a           √
0x221e           ∞
0x222b           ∫
0x2248           ≈
0x2260           ≠
0x2264 - 0x2265  ≤ ≥
0x25ca           Box drawing ◊
0xfb01 - 0xfb02  Alphabetic presentation forms fi fl

A web built on LaTeX

The other day on TeXtip, I threw this out:

Imagine if the web had been built on LaTeX instead of HTML …

Here are some of the responses I got:

  • It would have been more pretty looking.
  • Frightening.
  • Single tear down the cheek.
  • No crap amateurish content because of the steep learning curve, and beautiful rendering … What a dream!
  • Shiny math, crappy picture placement: glad it did not!
  • Overfull hboxes EVERYWHERE.
  • LaTeX would have become bloated, and people would be tweeting about HTML being so much better.
  • Noooo! LaTeX would have been “standardised”, “extended” and would by now be a useless pile of complexity.

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For daily tips on LaTeX and typography, follow @TeXtip on Twitter.

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Use typewriter font for code inside prose

There’s a useful tradition of using a typewriter font, or more generally some monospaced font, for bits of code sprinkled in prose. The practice is analogous to using italic to mark, for example, a French mot dropped into an English paragraph. In HTML, the code tag marks content as software code, which a browser typically will render in a typewriter font.

Here’s a sentence from a new article on Python at Netflix that could benefit a few code tags.

These features (and more) have led to increasingly pervasive use of Python in everything from small tools using boto to talk to AWS, to storing information with python-memcached and pycassa, managing processes with Envoy, polling restful APIs to large applications with requests, providing web interfaces with CherryPy and Bottle, and crunching data with scipy.

Here’s the same sentence with some code tags.

These features (and more) have led to increasingly pervasive use of Python in everything from small tools using boto to talk to AWS, to storing information with python-memcached and pycassa, managing processes with Envoy, polling restful APIs to large applications with requests, providing web interfaces with CherryPy and Bottle, and crunching data with scipy.

It’s especially helpful to let the reader know that packages like requests are indeed packages. It helps to clarify, for example, whether Wes McKinney has been stress testing pandas or pandas. That way we know whether to inform animal protection authorities or to download a new version of a library.

Unicode to LaTeX

I’ve run across a couple web sites that let you enter a LaTeX symbol and get back its Unicode value. But I didn’t find a site that does the reverse, going from Unicode to LaTeX, so I wrote my own.

Unicode / LaTeX Conversion

If you enter Unicode, it will return LaTeX. If you enter LaTeX, it will return Unicode. It interprets a string starting with “U+” as a Unicode code point, and a string starting with a backslash as a LaTeX command.

screenshot of www.johndcook.com/unicode_latex.png

For example, the screenshot above shows what happens if you enter U+221E and click “convert.” You could also enter infty and get back U+221E.

However, if you go from Unicode to LaTeX to Unicode, you won’t always end up where you started. There may be multiple Unicode values that map to a single LaTeX symbol. This is because Unicode is semantic and LaTeX is not. For example, Unicode distinguishes between the Greek letter Ω and the symbol Ω for ohms, the unit of electrical resistance, but LaTeX does not.

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For daily tips on LaTeX and typography, follow @TeXtip on Twitter.

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Letters that fell out of the alphabet

Mental Floss had an interesting article called 12 letters that didn’t make the alphabet. A more accurate title might be 12 letters that fell out of the modern English alphabet.

I thought it would have been better if the article had included the Unicode values of the letters, so I did a little research and created the following table.

Insular gU+A77DU+1D79
Thorn with strokeU+A764U+A765
Tironian ondU+204A
Long sU+017F


Once you know the Unicode code point for a symbol, you can find out more about it, for example, here.

Related posts:

Entering Unicode characters in Windows and Linux.

To enter a Unicode character in Emacs, you can type C-x 8 <return>, then enter the value.

The paper is too big

In response to the question “Why are default LaTeX margins so big?” Paul Stanley answers

It’s not that the margins are too wide. It’s that the paper is too big!

This sounds flippant, but he gives a compelling argument that paper really is too big for how it is now used.

As is surely by now well-known, the real question is the size of the text block. That is a really important factor in legibility. As others have noted, the optimum line length is broadly somewhere between 60 characters and 75 characters.

Given reasonable sizes of font which are comfortable for reading at the distance we want to read at (roughly 9 to 12 point), there are only so many line lengths that make sense. If you take a book off your shelf, especially a book that you would actually read for a prolonged period of time, and compare it to a LaTeX document in one of the standard classes, you’ll probably notice that the line length is pretty similar.

The real problem is with paper size. As it happens, we have ended up with paper sizes that were never designed or adapted for printing with 10-12 point proportionally spaced type. They were designed for handwriting (which is usually much bigger) or for typewriters. Typewriters produced 10 or 12 characters per inch: so on (say) 8.5 inch wide paper, with 1 inch margins, you had 6.5 inches of type, giving … around 65 to 78 characters: in other words something pretty close to ideal. But if you type in a standard proportionally spaced font (worse, in Times — which is rather condensed because it was designed to be used in narrow columns) at 12 point, you will get about 90 to 100 characters in the line.

He then gives six suggestions for what to do about this. You can see his answer for a full explanation. Here I’ll just summarize his points.

  1. Use smaller paper.
  2. Use long lines of text but extra space between lines.
  3. Use wide margins.
  4. Use margins for notes and illustrations.
  5. Use a two column format.
  6. Use large type.

Given these options, wide margins (as in #3 and #4) sound reasonable.

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For daily tips on LaTeX and typography, follow @TeXtip on Twitter.

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The Readability bookmarklet lets you reformat any web to make it easier to read. It strips out flashing ads and other distractions. It uses black text on a white background, wide margins, a moderate-sized font, etc. I use Readability fairly often. (Instapaper is a similar service. I discuss it at the end of this post.)

Yesterday I used it to reformat an article on literate programming. For some inexplicable reason, the author chose to use a lemon yellow background. It’s ironic that the article is about making source code easier to read. The content of the article is easy to read, but the format is not.

Readability to the rescue! Here are before and after screen shots.



I recommend the article, Example of Literate Programming in HTML, and I also recommend using reformatting the page unless you enjoy reading black text on a yellow background.

Readability did a good job until about half way through the article. The article has C and HTML code examples, and perhaps these confused Readability. (Readability usually handles code samples well. It correctly formats the first few code samples in this article.) The last half of the article renders like source code, and the font gets smaller and smaller.

I ran the page through an HTML validator to see whether some malformed HTML could be the source of the problem. The validator found numerous problems, so perhaps that was the issue.

I haven’t seen Readability fail like this before. I’ve been surprised how well it has handled some pages I thought might trip it up.

I ended up saving the article and editing its source, changing the bgcolor value to white. It’s a nice article on literate programming once you get past the formatting. The best part of the article is the first section, and that much Readability formats correctly.


Instapaper reformats web pages similarly. It produces a narrower column of text, but otherwise the output looks quite similar.

Instapaper did not discover the title of the literate programming article. (The title of the article was not in an <h1> tag as software might expect but was only in a <title> tag in the page header.) However, it did format the entire body of the article correctly.

I find it slightly more convenient to use the Readability bookmarklet than to submit a link to Instapaper. I imagine there are browser plug-ins that make Instapaper just as easy to use, though I haven’t looked into this because I’m usually satisfied with Readability.

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Draw a symbol, look it up

LaTeX users may know about Detexify, a web site that lets you draw a character then looks up its TeX command. Now there’s a new site Shapecatcher that does the same thing for Unicode. According to the site, “Currently, there are 10,007 Unicode character glyphs in the database.” It does not yet support Chinese, Japanese, or Korean.

For example, I drew a treble clef on the page:

The site came back with a list of possible matches, and the first one was what I was hoping for:

Interestingly, the sixth possible match on the list was a symbol for contour integration:

Notice the treble clef response has a funny little box on the right side. That’s because my browser did not have a glyph to display that Unicode character. The browser did have a glyph for the contour integration symbol and displayed it.

Another Unicode resource I recommend is this Unicode Codepoint Chart. It is organized by code point value, in blocks of 256. If you were looking for the contour integration symbol above, for example, you could click on a link “U+2200 to U+22FF: Mathematical Operators” and see a grid of 256 symbols and click on the one you’re looking for. This site gives more detail about each character than does Shapecatcher. So you might use Shapecatcher to find where to start looking, then go to the Unicode Codepoint Chart to find related symbols or more details.

Other posts on Unicode:

For daily tips on LaTeX and typography, follow @TeXtip on Twitter.

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Typesetting “C#” in LaTeX

How do you refer to the C# programming language in LaTeX? Simply typing C# doesn’t work because # is a special character in LaTeX. You could type C#. That works, but it looks a little odd. The number sign is too big and too low.

What about using a musical sharp sign, i.e. C$\sharp$? That also looks a little odd. Even though the language is pronounced “C sharp,” it’s usually written with a number sign, not a sharp.

Let’s look at recommended ways of typesetting C++ to see whether that helps. The top answer to this question on TeX Stack Exchange is to define a new command as follows:

\newcommand{\CC}{C\nolinebreak\hspace{-.05em}\raisebox{.4ex}{\tiny\bf +}\nolinebreak\hspace{-.10em}\raisebox{.4ex}{\tiny\bf +}}

This does several things. First, it prevents line breaks between the constituent characters. It also does several things to the plus signs:

  • Draws them in closer
  • Makes them smaller
  • Raises them
  • Makes them bold

The result is what we’re subconsciously accustomed to seeing in print.

Here’s an analogous command for C#.

\newcommand{\CS}{C\nolinebreak\hspace{-.05em}\raisebox{.6ex}{\tiny\bf #}}

And here’s the output. The number sign is a little too small.

To make a little larger number sign, replace \tiny with \scriptsize.

Related posts:

For daily tips on LaTeX and typography, follow @TeXtip on Twitter.

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Typesetting chemistry in LaTeX

Yesterday I gave the following tip on TeXtip:

Set chemical formulas with math Roman. Example: sulfate is $mathrm{SO_4^{2-}}$

TorbjoernT and scmbradley let me know there’s a better way: use Martin Hansel’s package mhchem. The package is simpler to use and it correctly handles subtle typographical details.

Using the mhchem package, sulfate would be written ce{SO4^2-}. In addition to chemical compounds, mhchem has support for bonds, arrows, and related chemical notation.







\ce{CO2 + C -> 2CO}

\ce{SO4^2- + Ba^2+ -> BaSO4 v}



For more information, see the mhchem package documentation.

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For daily tips on LaTeX and typography, follow @TeXtip on Twitter.

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Google Docs OCR

Google Docs now offers OCR (optical character recognition), but I’ve had little success getting  it to work.

The link to upload files was flaky under Firefox 3.6.4. The underlined text that says “Select files to upload” is not clickable, but you can click the white space a few millimeters above or below what looks like a link. However, the clickable white space didn’t do anything when I clicked it. The link worked just fine in IE 8 and Safari 5.0.

screen shot of page to upload documents for OCR

I clicked the check box that says “Convert text from PDF or image files to Google Docs documents” and uploaded a PDF file. The file was a decent quality scan of a paper document.

section of text from a scanned article

I got a message back saying “Unable to convert document.”

So I tried again with a PDF file that had been created from a LaTeX file using pdflatex. The optical quality of the document was perfect since the document it wasn’t a scan but rather an electronic document printed directly to PDF. Moreover, the PDF file contains the plain text.  Google indexes such PDFs created with pdflatex just as easily as HTML files. However, I still got the message “Unable to convert document.”

My experience with Google OCR wasn’t a total failure. I created a Microsoft Word document with text in 12-point Times New Roman — I figured this was as commonplace as I could get — and printed it to PDF. Google Docs did successfully convert that document to text.

I imagine Google’s OCR feature will be useful once they debug it. But it doesn’t yet seem ready for prime time based on my limited experience.

The disappointing state of Unicode fonts

Modern operating systems understand Unicode internally, but font support for Unicode is spotty. For an example of the problems this can cause, take a look at these screen shots of how the same Twitter message appears differently depending on what program is used to read it.

No font can display all Unicode characters. According to Wikipedia

… it would be impossible to create such a font in any common font format, as Unicode includes over 100,000 characters, while no widely-used font format supports more than 65,535 glyphs.

However, the biggest problem isn’t the number of characters a font can display. Most Unicode characters are quite rare. About 30,000 characters are enough to display the vast majority of characters in use in all the world’s languages as well as a generous selection of symbols. However Unicode fonts vary greatly in their support even for the more commonly used ranges of characters. See this comparison chart. The only range completely covered by all Unicode fonts in the chart is the 128 characters of Latin Extended-A.

Unifont supports all printable characters in the basic multilingual plane, characters U+0000 through U+FFFF. This includes the 30,000 characters mentioned above plus many more. Unifont isn’t pretty, but it’s complete. As far as I know, it’s the only font that covers the characters below U+FFFF.

Related posts:

Free alternative to Consolas font

Consolas is my favorite monospace font. It’s a good programmer’s font because it exaggerates the differences between some characters that may easily be confused. It ships with Visual Studio and with many other Microsoft products. See this post for examples.

I recently found out about Inconsolata, a free font similar to Consolas. Inconsolata is part of the OFL font collection from SIL International.

Another interesting font from SIL is Andika, mentioned previously here. The Andika home page describes this font as follows.

Andika is a sans serif, Unicode-compliant font designed especially for literacy use, taking into account the needs of beginning readers. The focus is on clear, easy-to-perceive letterforms that will not be readily confused with one another.

Related posts:

For daily tips on LaTeX and typography, follow @TeXtip on Twitter.

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Adding fonts to the PowerShell and cmd.exe consoles

The default font options for the PowerShell console are limited: raster fonts and Lucida Console. Raster fonts are the default, though Lucida Console is an improvement. In my opinion, Consolas is even better, but it’s not on the list of options.

Mastering PowerShell by Tobias Weltner explains how to expand the list of font options for the PowerShell console. The same trick increases the list of font options in the Windows command prompt cmd.exe as well. The book is free for download. See page 16 for details. However, I have two comments about the instructions it gives.

First, the book says “The name must be exactly the same as the official font name, just the way it’s stated under [registry key].” However, the Consolas font is listed in the registry as “Consolas (True Type)”. You should enter “Consolas” and leave out the parenthetical description.

Second, the book says “the new font will work only after you either log off at least once or restart your computer.” When I tried it, logging off was not sufficient; I had to reboot my computer before the font change would work.

Update: In order to make this post self-contained, I’ve added below the necessary information from Mastering PowerShell.

Run regedit.exe and navigate to HKEY_LOCAL_MACHINESOFTWAREMicrosoftWindows NTCurrentVersionConsoleTrueTypeFont.

Right-click in the panel on the right side and create a new string value. Name that value “0” or “00” or however many zeros you need to create a new key. That string’s value is the name of the font to add.

Update: See Necessary criteria for fonts to be available in a command window

Related posts:

Improved PowerShell prompt
A couple thoughts on typography
Better R console fonts

I owe Microsoft Word an apology

I tried to use the Equation Editor in Microsoft Word years ago and hated it. It was hard to use and produced ugly output. I tried it again recently and was pleasantly surprised. I’m using Word 2007. I don’t remember what version I’d tried before.

I’ve long said that math written in Word is ugly, and it usually is. But the fault lies with users, like myself, not with Word. I realize now that the problem is that most people writing math in Word are not using the Equation Editor. LaTeX produces ugly math too when people do not use it correctly, though this happens less often.

Math typography is subtle. For example, mathematical symbols are set in an italic font that is not quite the same as the italic font used in prose. Also, word-like symbols such as “log” or “cos” are not set in italics. I imagine most people do not consciously notice these conventions — I never noticed until I learned to use LaTeX — but subconsciously notice when the conventions are violated. The conventions of math typography give clues that help readers distinguish, for example, the English indefinite article “a” from a variable named “a” and to distinguish the symbol for maximum from the product of variables “m”, “a”, and “x.”

Microsoft’s Equation Editor typesets math correctly. Word documents usually do not, but only because folks usually do not use the Equation Editor. In the following example, I set the same equation three times: using ordinary text, using ordinary italic for the “x”, and finally using the Equation Editor.

screen shot of trig identity using MS Word

Note that the “x” in the third version is not the same as the italic “x” in the second version. The prose in this example is set in Calibri font and the Equation Editor uses Cambria Math font. Also, I did not tell Word to format “sin” and “cos” one way and “x” another or tell it what font to use; I simply typed sin^2 x + cos^2 x = 1 into the Equation Editor and it formatted the result as above. I haven’t used it much, but the Equation Editor seems to be more capable and easier to use than I thought.

Here are a few more examples of Equation Editor output.

examples of math using Word: Gaussian integral, Fourier series, quadratic equation

I still prefer using LaTeX for documents containing math symbols. I’ve used LaTeX for many years and I can typeset equations very quickly using it. But I’m glad to know that Word can typeset equations well and that the process is easier than I thought.

I tried out the Equation Editor because Bob Matthews suggested I try MathType, a third-party equation editor add-on for Microsoft Word. I haven’t tried MathType yet but from what I hear it produces even better output.

Related post: Contrasting Microsoft Word and LaTeX

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