>From: Robert Palais <[EMAIL PROTECTED]>
>To: Lars Kristan <[EMAIL PROTECTED]>
>CC: [EMAIL PROTECTED]
>Subject: RE: The benefit of a symbol for 2 pi
>Date: Thu, 17 Jan 2002 10:11:37 -0700 (MST)
>
>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.
>
As for all this about radian measure:
1. Design a machine to indicate the number of revolutions through which a
wheel has turned. Easy.
2. Design a machine to indicate the number of RADIANS through which a wheel
has turned. Can it be done?? (Using a 355:113 gear ratio is cheating.)
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