"RG" <rnospa...@flownet.com> wrote in message
news:rnospamon-ee76e8.18291912102...@news.albasani.net...
In article <i930ek$uv...@news.eternal-september.org>,
"BartC" <b...@freeuk.com> wrote:
"RG" <rnospa...@flownet.com> wrote in message
> Likewise, all of the following are the same number written in different
> notations:
>
> pi/2
> pi/2 radians
> 90 degrees
> 100 gradians
> 1/4 circle
> 0.25 circle
> 25% of a circle
> 25% of 2pi
>
> See?
But what exactly *is* this number? Is it 0.25, 1.57 or 90?
It's an irrational number, so it cannot be written out exactly. But
it's approximately 1.57.
My money would have been on 0.25, based on using 1.0 for a 360° circular
angle. It seems far more attractive than using the arbitrary-looking 6.28...
(I understand that when 2 pi is used, this works more naturally in certain
mathematical formulae.)
I can also write 12 inches, 1 foot, 1/3 yards, 1/5280 miles, 304.8 mm and
so
on. They are all the same number, roughly 1/131000000 of the polar
circumference of the Earth.
These aren't numbers, these are lengths. They correspond to a physical
thing out there in the real world. Numbers don't.
This does depend on the actual size of an arbitrary circle, but that
seems
little different from the choice of 0.25, 1.57 or 90 for your quarter
circle.
Why does it seem "little different"? That is exactly the difference.
What you're doing in your "1/131000000 of the polar circumference of the
Earth" is taking the number 1/131000000 and using it to describe a
length.
My example was based on the fact that a metre was once defined as 1/10000000
of the equator-pole distance. They were taking the number 1/10000000 and
using it to describe a length (of a unit called a metre).
Above, you're using 1/(two pi), and using it to describe an angle (of a unit
called a radian).
The only difference is that on a different planet, they would almost
certainly use a different unit for length, but would quite possibly still
use radians for angles, amongst others units.
--
Bartc
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