Re: Right-to-left mathematics

From: James E. Agenbroad (
Date: Tue Jan 11 2000 - 09:45:17 EST

On Tue, 11 Jan 2000 wrote:

> Hallo.
> Some Unicode character have the "mirrored" property. This means that, when
> they occur in a right-to-left context, they should be displayed with an
> alternative reversed glyph. For example, an open parenthesis looks like "("
> in LTR, but like ")" in RTL.
> a) This applies to all opening/closing punctuation, e.g.:
> U+0028 / U+0029 (LEFT ... / RIGHT PARENTHESIS)
> b) The same applies with some pairs of mathematical operators, that are the
> opposite of each other, both in shape as in meaning; e.g.:
> U+003C / U+003E (LESS-... / GREATER-THAN SIGN)
> c) But also some unpaired mathematical operators have the "mirrored"
> property, e.g.:
> I guess that, in cases (a) and (b), fonts actually just contain one pair of
> glyphs, and "swap" their encoding as needed by the bidi context. But, for
> case (c), ad-hoc reversed glyphs must be designed separately.
> Are the mirrored glyphs for case (c) operators actually used in
> right-to-left languages?
> What do mathematical formulas look like in Hebrew, Arabic, Urdu, Pashto,
> Thaana, etc.? Are they always RTL or is sometimes LTR used (as is the case
> for Hebrew music)?
> What is the attitude of font designers? Are you providing "reversed" maths
> glyphs for RTL scripts?
> Anyone knows examples of mathematical applications that implement bidi? How
> do they work?
> Thanks.
> Marco
                                              Tuesday, January 11, 2000
No answer, but an extension of your question: In 2.0, Solidus, 002F, and
Reverse solidus 005C are not mirrored pairs, but, I think (p.4-22)
Division slash, 2215 and Set minus, 2216 are. I gather those who write in
RTL scripts write fractions the same way we do: "1/2" is one half.
In a RTL context would this mean those writing fractions who use a slash
will see "1/2" but those who use the divison slash will see "1\2"? If the
answer is in the bidi algorithm just tell me so. I'm geting ready for a
meeting in San Antonio and may not reply real soon.

  In passing, in Hebrew in lieu of a plus sign (which looks like a
cross) one sometimes sees a character similar to 2245 but with a shorter
ascender. Perhaps this can be considered as a font issue and ignored.
          Jim Agenbroad ( )
     The above are purely personal opinions, not necessarily the official
views of any government or any agency of any.
Phone: 202 707-9612; Fax: 202 707-0955; US mail: I.T.S. Dev.Gp.4, Library
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