[whatwg] Vulgar fractions

Øistein E. Andersen liszt at coq.no
Thu Apr 16 13:46:05 PDT 2009

Currently, only a limited set of vulgar fractions can be expressed in  
HTML, viz, those that exist as pre-composed characters in Unicode.   
(For example, 16ths and 32nds, which are often used with imperial  
units, are not included.)  This can be solved in several ways:

1) According to Unicode (<http://unicode.org/book/ch06.pdf>, p. 154),  
`any sequence of one or more decimal digits, followed by the fraction  
slash [U+2044], followed by any sequence of one or more decimal  
digits ... should be displayed as a unit, such as ¾'.  Furthermore,  
Unicode Technical Report No. 20, `Unicode in XML and other Markup  
Languages', says that the fraction slash is suitable for use with mark- 
up.  Unfortunately, no browser seems to transform a sequence like  
3⁄16 into a proper vulgar fraction.  If, however, browsers are  
willing to implement this, no changes to HTML are needed.

2) Unicode Technical Report No. 20 also suggests that specific mark- 
up, MathML in particular, may be used instead.  MathML mark-up is a  
bit more verbose:
	<math xmlns="http://www.w3.org/1998/Math/MathML">
Unfortunately, this corresponds to a mathematical fraction rather than  
a vulgar fraction, which means that it has a horizontal fraction bar  
and that it takes up too much vertical space.  (Admittedly, vulgar  
fractions may have horizontal fraction bars as well, but this is not  
suitable for on-screen viewing since the numbers get tiny, whereas a  
diagonal fraction bar only requires the numbers to be scaled to 60%  
vertically and 65% horizontally, as suggested in the PostScript  
Language Cookbook.)

2') There is a MathML attribute called `bevelled' which is indicates  
that at diagonal line should be used to separate numerator from  
	<math xmlns="http://www.w3.org/1998/Math/MathML">
	    <mfrac bevelled="true">
However, Firefox and Opera both display this as <small>3 / 16</small>,  
and the example given in the MathML specification <http://www.w3.org/TR/MathML3/image/f3008.gif 
 > suggests that this is not really meant for vulgar fractions at  
all.  This could still be a solution if <mfrac bevelled="true"/> is  
defined to correspond to a vulgar fraction if both numerator and  
denominator are <mn/> elements consisting of digits 0--9.

2'') Alternatively, a new attribute (e.g., `vulgar') could be added to  
cover this case.

3) If neither special handling of the fraction slash nor a MathML  
solution for vulgar/non-mathematical fractions is possible, the only  
remaining solution would be to add specific mark-up to HTML directly.

(I am aware that fractions have been proposed earlier in the context  
of mathematical formulae, but I have not been able to find any  
previous discussion regarding vulgar fractions.)

Øistein E. Andersen

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