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

Ross Moore ross at ics.mq.edu.au
Thu Dec 17 18:51:02 EST 2009

Hi Pete and Joe,

On 18/12/2009, at 8:17 AM, Peter Dyballa wrote:

> --
> Greetings
>
>   Pete
>
> There's something the technicians need to learn from the artists.
> If it isn't aesthetically pleasing, it's probably wrong.

You couldn't have said it better.
It especially applies to examples like on Joe's page,
which people may refer to and copy.
So let's get them right, both technically and aesthetically.

A glaring example is:   sphere_volume.tex
where there are aesthetic errors (to my mind) on every line.

line 1. the variable name  Volume  should be  \mathrm{Volume} .

line 2. the 'differential d' at the end of the integrals could be
The MathML rendering does it this way.
BTW, it's good to see that preceding thinspace.

line 3.
A.  the "evaluation-bars" after integration are far too large
instead of  \biggl|  use  \Bigr| .
(the 'l' is technically wrong, as this is a closing fence
around the integrated expression, and may result in too
little space before it)

B.  \frac{\rho^3}{3}  would look better as  (\tfrac13 \rho^3)
which also reduces the size needed for the evaluation-bar.

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.

line 5. the fraction 4/3 dominates the final result,
yet it is the least meaningful term in that expression
of a physical quantity.
Use:   \tfrac43 \pi R^3

The attached image allows you to see the difference
between your coding, and with these modifications.

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Note that expressions like  \tfrac13  are equivalent to \tfrac{1}{3}
which some LaTeX purists would say you should use.
I disagree, since within your source  \tfrac13  looks much more
like a single simple entity --- especially when you put a space
between quantities that are to be multiplied --- which it *is*
logically. That is, it is the fraction one-third, rather than
being primarily a representation of a division operation.

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?)

The use of text-style fractions for  d/dt  in the "Differentiable
Manifold (Tangent vector)" is another common (double) error.
These should be using:
\dfrac{\mathrm{d}}{\mathrm{d}t} .

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

These are primarily my opinions, but I know that many are
shared. Also, now that software can do much more, (much faster
than previously and the MathML standards/recommendations are
being implemented) then there is going to be a need to have
sets of examples that do everything in the best possible way.

Hope this helps,

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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