Fractions may be your friends, but they won't pick you up at the airport!

by Michael S. Kaplan, published on 2007/07/14 15:01 -04:00, original URI: http://blogs.msdn.com/b/michkap/archive/2007/07/14/3869052.aspx


To me, fractions will always have a special place. The teacher pointed out we all knew what ½ was, and we all knew what 0.5 was, and we all knew about division. Then he blew my mind when he pointed out they were not connected because they were multiple things to memorize, but because they really were the same thing.

Fractions are the first time I saw math operations as all being connected. And it mostly because that one teacher was the first one to teach it that way (and the book didn't, it was him). I hope the books are better now, since I think my old teacher is retired....

He also was the first person I remember telling me that fractions were our friends. I think I almost believed it at the time, as it got me realizing that math had the potential to be cool.

Thanks, Mr. Snodgrass!

Anyway, back to fractions.

In Unicode, there are a whole bunch of fractions encoded. Here they are in numeric order (something not even Shell number sorting will do for you!):

 Code Point   Character    Character Name  1.0 Character Name
 U+215b  ⅛  VULGAR FRACTION ONE EIGHTH  FRACTION ONE EIGHTH
 U+2159  ⅙  VULGAR FRACTION ONE SIXTH  FRACTION ONE SIXTH
 U+2155  ⅕  VULGAR FRACTION ONE FIFTH  FRACTION ONE FIFTH
 U+00bc  ¼  VULGAR FRACTION ONE QUARTER  FRACTION ONE QUARTER
 U+2153  ⅓  VULGAR FRACTION ONE THIRD  FRACTION ONE THIRD
 U+215c  ⅜  VULGAR FRACTION THREE EIGHTHS  FRACTION THREE EIGHTHS
 U+2156  ⅖  VULGAR FRACTION TWO FIFTHS  FRACTION TWO FIFTHS
 U+00bd  ½  VULGAR FRACTION ONE HALF  FRACTION ONE HALF
 U+2157  ⅗  VULGAR FRACTION THREE FIFTHS  FRACTION THREE FIFTHS
 U+215d  ⅝  VULGAR FRACTION FIVE EIGHTHS  FRACTION FIVE EIGHTHS
 U+2154  ⅔  VULGAR FRACTION TWO THIRDS  FRACTION TWO THIRDS
 U+00be  ¾  VULGAR FRACTION THREE QUARTERS   FRACTION THREE QUARTERS 
 U+2158  ⅘  VULGAR FRACTION FOUR FIFTHS  FRACTION FOUR FIFTHS
 U+215a  ⅚  VULGAR FRACTION FIVE SIXTHS  FRACTION FIVE SIXTHS
 U+215e  ⅞  VULGAR FRACTION SEVEN EIGHTHS  FRACTION SEVEN EIGHTHS

That last column is really interesting -- it is the name of the character in Unicode 1.0, prior to the merger with ISO 10646. Name changes were done to go along with particular preferences in 10646, which in most cases related to compatibility with other ISO standards that involved names nad inother cases involved particular conventions.

Though I have to wonder how we are going to get the next generation of kids interested in considering fractions to be their friends if we spend all of our time telling them that fractions are vulgar!

Now all of these characters are really thought to be compatibility characters -- the "right" way to do fractions is to use regular numbers and U+2044 (FRACTION SLASH) between them...

Which would perhaps explain why they are vulgar? :-)

Actually, the reason they are called vulgar is apparently that the reference glyphs use diagonal slashes rather than horizontal bars. Though the two different ways to write fractions are considered glyph variants of each other (as they should be, since they are). Which means that a font developer can use either way to show them.

There are other standards that actually do try to distinguish between them and encode both -- for example the ones in the DPRK (which caused for some interesting discussions in WG2 and UTC when the DPRK additions to Unicode were being discussed back in 2001, with interesting conversations about variations selectors, if memory serves. I do remember that no one from UTC wanted to encode that extra set of fractions.

In any case, I guess the moral of the story using the principles of logic is that your friends are vulgar (which actually was an alternate title I considered for this post)....

 

This post brought to you by    (U+2044, a.k.a. FRACTION SLASH)


# John Cowan on 14 Jul 2007 6:37 PM:

In fact, *vulgaris* is the Latin word meaning 'common, ordinary', and was originally used that way in English too.  It was only about 200 years ago that the word got its current meaning because of aristocratic snobbery that said the common people were "ill-bred, uncultured, coarse."

So vulgar fractions are common, ordinary fractions, as opposed to newfangled decimal fractions.  It has nothing to do with the use of slashes rather than bars.

# Michael S. Kaplan on 14 Jul 2007 8:38 PM:

Ah, that is interesting. I definitely was not 100% sure of the source here (which caused me to put the word "apparently" in the description!) but I am perfectly happy to consider myself mistaken here.

I had another reader suggest that teenagers would perhaps be more interested in learning about fractions due to them being "vulgar" though I wonder how many teenagers pay enough attention in math to care. :-)

# Johannes Roessel on 4 Aug 2007 10:40 AM:

In fact, we learnt those fractions as "gemeine Brüche" at school, which directly translates to vulgar/ordinary fraction. Also I liked vulgar fractions more than decimal ones because of their expressiveness when it comes to infinitely repeating series of numbers. One third looks much better than 0.333... or even 0.3̅ (should be a 3 with a combining overline).


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