Re: mathematical formulae-punctuation

Subject: Re: mathematical formulae-punctuation
From: Dick Margulis <margulis -at- fiam -dot- net>
To: "TECHWR-L" <techwr-l -at- lists -dot- raycomm -dot- com>
Date: Mon, 24 Nov 2003 23:39:54 -0500


Robert Kidd wrote:


Usually, I assume that sentences containing mathematical formulae use normal punctuation but the format of the present book I am working on has all formulae inserted as images with a paragraph break before and after each one.

Here is an example in .gif format: http://www.editfast.com/assets/graphics/mathpunctuation.gif

Should I be treating these differently? Does anyone know of a good on-line source for mathematical paper punctuation or punctuation of sentences containing mathematical formulae? I did a search on Google but most of what I could find were general references telling me to go buy a book. It may come to that, so if you have any recommendations they are welcome.

Robert Kidd
Director, EditFast



Robert,

My math books are all at least 35 yeaers old, so it's possible styles have changed radically. However, the ones I just grabbed confirm your suspicion. Eequations are displayed, for the most part, but they fall within punctuated sentences. If a comma should, grammatically, follow the equation, it does so. If a period should follow, it does so. If the equation follows a colon, there is no following punctuation.

Detailed considerations:

1. The equation numbers in parens are always set flush right, no matter what else is going on. This is a long-standing convention and I've never seen it violated. So your sample page just looks very odd.

2. If the equation is a single line (e.g., a = b + c), then the following punctuation comes immediately after the last character, as if the equation were set in line within a paragraph. On the other hand, if the equation is built up so that the rightmost element is a 2-line or larger character or a built-up fraction, then there is a thin space (4/m) between the last term of the equation and the punctuation.

3. If it is not too late to do so, you should choose a font in which the comma and period are big enough that they won't be mistaken for random spots. If it is too late to pick a different font, you could cheat a little by using a slightly larger point size for these marks.

4. Multiple equations that are short in their horizontal dimension can be combined on one line, with intervening conjunction or punctuation, rather than stacked.

5. Pay attention to the alignment of multiple related equations or overlong equations that need to be split into two lines (happens a lot in a narrow measure engineering journal column). The general rule is that equals signs are aligned vertically, and the individual equations are not centered on the page, but the overall block is. So you look at the longest left side and the longest right side (even if they are in different equations within the set) and center on that measure. For broken (overlong) equations, the left side is on the first line and the equals sign begins the second line; position the second line so that there is at least an em space between the end of the equation and the left paren of the equation number (two ems is better); position the first line so that it is indented from the left as much as the second line is indented from the right. If the equation is too long for two lines, the third and succeeding lines begin with an operator that is aligned not with the equals sign but with the term following the equals sign. Occasionally odd situations arise where this strategy doesn't work and you have to just make a decision on the fly to accommodate what's in front of you.

Looking at your sample gif, aside from the misaligned equation numbers, here are the errors I can see immediately, without bothering to think about the math:

a. The binary (but not unary) operators and relations are all set too tight. They should have at least a thin on either side. This would, for example, solve the problem with 2.108, where it looks like the plus is not centered (illusion caused by the subscript on the left and the hook on the last J).

b. The equation font is bigger than the text font. Looks stupid. Don't do it. The convention is that they're the same size or, if not, the equations are smaller.

c. There is something amiss with the sub- and superscripts. You should be using an expert font with true sub- and superscript glyphs. These are out of proportion in a strange way. Basically, they're too large (numerals and uppercase); but the x-height of the regular font is so short that the lowercase subs and supers look too tiny.

d. 2.82 should have regular parens, not two-line parens. There is nothing in the equation that requires the greater height.

Overall, I'd say you need to find someone who knows how to set equations properly rather than relying on the default settings in some desktop equation editor. If you don't have that option, please at least talk to the author about these points.

HTH,

Dick



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References:
mathematical formulae-punctuation: From: Robert Kidd

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