# [OS X TeX] A little help needed (math formula problem)

Ross Moore ross at ics.mq.edu.au
Fri Dec 18 18:35:56 EST 2009

Hi Joe,

On 19/12/2009, at 3:58 AM, Joe Java wrote:

>>       B.  \frac{\rho^3}{3}  would look better as  (\tfrac13 \rho^3)
>>           which also reduces the size needed for the evaluation-bar.
>>
>     As a general rule numerators of value one are not shown.

That's not the kind of general rule that is always useful.

The expression here, as in most cases, has a physical factor
(\rho^3) multiplied by a coefficient (\frac13).
The form of the physical factor is usually deducible from
general considerations involving just the physical units.
Determining the exact numerical coefficient is what requires
a more detailed calculation, which is done quite separately
from any of the physical aspects.

Writing the expression as  \frac{\rho^3}{3} simply obfuscates
this understanding, besides requiring more vertical space
on the printed page.

Certainly when writing on a white-(or black-)board you would
probably put the \rho^3 factor down first, as this contains
the most physical meaning, then do the factor as a /3
--- with the slash as a fraction bar at whatever length or slant
comes easily, and with the 3 being under, below or behind it.
Furthermore, you'd be speaking something as you are writing it.

But you cannot capture this in print, nor should you be
wanting to. Instead the most meaningful, as well as aesthetic,
form is to pre-multiply by the simple fraction \tfrac13 as
a numerical coefficient --- with the \tfrac guaranteeing a small
text-style fraction, whether in a display or inline.

>>   line 4. Using just a space for implicit multiplication starts to
>>           look very cumbersome when if forces a need for lots of
>>           parentheses. Personally I'd write this line as:
>>
>>              2\pi \times 2 \times \tfrac13 R^3
>>
>>           which is both shorter and clearer in the source,
>>           as well as producing a cleaner, more readable rendering
>>           which saves on vertical space as a bonus.
>>
>
>     The 'x' for the times sign is rarely used except when teaching
> mathematics.

When you write out this many lines in a calculation,
you *are* teaching mathematics.

In a research article you would have lines 1 and 5 only,
placed as a single line of a display. Any decent editor
would impose this to help keep the page-count down.

>> To my mind, \tfrac{1}{3} is significantly less readable in the
>> LaTeX source. Furthermore, a translation to MathML might well
>> produce the single character at position U+2153 .
>> (I'm not advocating this, as I actually prefer the text-style
>> fraction form.  Is there an OT font that has small text-style
>> vertical fractions with bar, rather than using a slanted solidus?)
>>
>
>   Not that I could find with a few minutes of searching

Sure.
Ume Gothic  and Ume Mincho  are the closest to vertical
position of the numerator and denominator that I've seen.
But they use a long highly-slanted solidus.

>> Of course that is rather cumbersome to write, so I usually define
>> macros, as follows:
>>
>> \newcommand{\ddd}{\mathrm{d}}%  differential d  (upright)
>> \newcommand{\dd}{\,\ddd}% differential closing an integral
>> \newcommand{\Dd}[1]{\ddd#1}
>> \newcommand{\ddx}{\Dd{x}}
>> \newcommand{\ddt}{\Dd{t}}
>>   etc.
>>
>> Now derivatives look like:
>>     \dfrac{\ddx}{\ddt}  or  \dfrac{\Dd{}}{\ddt}
>> and integrals like:
>>     \int_0^{\pi} \sin\theta \dd\theta
>>
>>
>
>     Yes, but since there are so few instances on this page, doing
> it the
> long way is actually shorter.

Of course.

But people will learn from this email list too.
So it is best to proffer the most convenient solution
for more extensive situations as well.

>> Hope this helps,

If you are looking for more examples, try here:

http://db.uwaterloo.ca/mathretrieval/corpus.html

>   It does.  I will have your suggested changes done later today.
>
>   Thank you.

Cheers,

Ross

------------------------------------------------------------------------
Ross Moore                                       ross at maths.mq.edu.au
Mathematics Department                           office: E7A-419
Macquarie University                             tel: +61 (0)2 9850 8955
Sydney, Australia  2109                          fax: +61 (0)2 9850 8114
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