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

[Joe Java]

> -------- Original Message --------
> Subject: Re: [OS X TeX] A little help needed (math formula problem)
> From: Ross Moore <ross at ics.mq.edu.au>
> Date: Thu, December 17, 2009 4:51 pm
> To: TeX on Mac OS X Mailing List <macosx-tex at email.esm.psu.edu>
> 
> 
> 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.
> 

    Very good observation.

> 
> 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} .
> 
> 
    OK

>   line 2. the 'differential d' at the end of the integrals could be
>           made upright (e.g. \,\phi\mathrm{d}\phi )
>           The MathML rendering does it this way.
>           BTW, it's good to see that preceding thinspace.
> 
> 

    OK

>   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)
> 

    OK

>       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.

> 
>   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.

> 
>   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
> 

    OK

> The attached image allows you to see the difference
> between your coding, and with these modifications.<hr>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?)
> 

  Not that I could find with a few minutes of searching

> 
> 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} .
> 

    OK

> 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.

> 
> 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.
> 
> 

   I agree.

> Hope this helps,
> 

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

  Thank you.