Re: OT: Math symbols conventions

En réponse à Gustavo Eulalio <guga@...>:

>         Hi all,
>
>         Anyone knows where I can find about math conventions? I'm
> specially
> interested in the trigonometrical symbols (like cos, sin, ...).
>         I'm asking because most programs I've been using will print
> 'sin'
> for Sine. But we use 'sen' or 'Sen' for that (from Seno) in
> Portuguese.
> I was wondering whether there's some international convention defining
> if it's 'sin', or 'sen', or whatever.
>         I've also seen variants for Tangent: tan, tg, Tg
>
AFAIK, unlike for names and abbreviations of physical units, there's no
international convention for mathematical symbols. On the other hand, there are
*recommendations* on what symbols should be used and how. But in many cases
those symbols differ depending on the country or even the university you're in.
And mathematical books often define their own standards ;)) . Still, for most
common symbols there is something like an unofficial agreement. For instance, I
doubt your 'sen/Sen' would be understood anywere else than in Portugal and
Brasil. There is quite a strong international agreement to use 'sin' or 'Sin'
(normally mathematical symbols are case-sensitive, but this one isn't. You
could very well decide to use 'SIN' ;)) ). Also, even among the accepted forms
of symbols there can be a lot of variation. You showed the case of 'tan, tg,
Tg'. Indeed, all three are commonly accepted ('tan' is considered more modern
and more 'correct', because it parallels better with 'sin' and 'cos'. Also,
forms with a small initial are considered more 'modern' and are supposed to be
preferred instead of capitalised forms). Another example is the hyperbolic
functions. Forms like 'cosh' and 'ch' cohabit freely, although recommendations
say that the shorter and newer form 'ch' should prevail. Inertia seems
extremely strong in the mathematical world ;))) . And in some cases even
nonsense symbols are still being used, although they break rules which are well
accepted in the mathematical world. For instance, look at the reciprocal
trigonometric functions (arc cosine, arc sine, etc...). The forms recommended
are 'Arccos', 'Arcsin', 'Arctan' (with or without capital is not important
here). Yet you still see about everywhere (especially on calculators) the older
symbols 'cos-1' (it's supposed to be an exponent), 'sin-1' and 'tan-1'. Yet
according to a convention that every mathematician uses, those symbols refer to
something completely different! Indeed, there is this convention that you can
simplify a formula like '(cos x)^2' to 'cos2 x' (with the 2 being an exponent
on 'cos'). This is something that you can do with any real exponent, and thus
also with -1! But according to this convention 'cos-1 x' should really mean '1/
(cos x)'!!! So the force of habit goes so far as driving mathematicians to use
symbols which don't make sense if read according to accepted rules of writing
mathematics ;))) .

It's just to insist on the fact that mathematical symbols are far from being
regulated ;)) .

Christophe.

http://rainbow.conlang.free.fr

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