Lars Kristan wrote:
> 3.14... is to a circle what 4 is to a square. It is the relationship between
> the diameter and the circumference.
No it is NOT, mathematically. The square whose Perimeter is 4 has
diameter \sqrt 2. What is the "side" of a circle?
It shows that the problem is so ingrained that it is almost invisible
and that many people cannot imagine that \pi is not perfect.
(Note however that the inscribed hexagon, six equilateral triangles of
side 1, gives an immediate estimate that \newpi is greater than, and
close to 6. (Thanks to Prof. Cherkaev)
If the discussion must persist, I will wait to respond to such attempts
to argue the mathematical point (which don't belong here.
Observing your discussions, I do wonder if the participants recognize
the responsibility of their influence upon ideas, through symbols
(but it seems some may enjoy it too much.) Speaking of adding words
to the dictionary, it did bring to mind the word "eumemics" which is
to "memes" as eugenics is to genes. Anyway, the point being while
a symbol such as "f" may not have a specific concept associated with
it, \pi and \newpi do, important enough that broadcast of \pi to
the heavens was supposed to prove our intelligence. They'll get a laugh.
Yes, Pi IS the ratio of circumference to diameter, but that was
the last time anyone ever saw or used diameter,
\newpi is the circumference of the unit (radius) circle, which is used
exclusively in mathematics. Hence all the MEANINGLESS 2s. My point was
not that formulas involving 2 \pi are incorrect, but that they, and
formulas derived by then separating the 2 and the \pi are not economical
of meaning. To me it is like writing 2+2 instead of 4 everywhere, or
changing the value of "Euler's other number" e. Lots of meaningless
factors would follow.
The fact that the number 2 appears in
> many formulas does not make it bad. I even welcome it, because 2 pi is
> something that stands out and immediately suggests circles and angles. You
> can call it inertia, but you have to agree that "2x" is more special than
> "Y". Well, it is to me anyway.
>
>
> Anyway, good luck with the newpi efforts, and .... may the best pi win! ;)
>
>
> Lars
>
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