Pi

[Neil Fernandez]

In message <3D68628B.C9314911 at math.wvu.edu>, Henry Gould
<gould at math.wvu.edu> writes

>The most important constant in the entire known Universe is the number 1
>(one).

[snip]

>Why don't we admit that pi is  1? . . .  of course then the
>circumference of the circle gets a bit complicated.

We'd lose something, because pi (or, which relates to Franklin's point,
2*pi) expresses oneness in the specific case of circleness :-) We'd lose
the relations between stuff, and the specific essence thereof.

Taking the angle subtending an arc of UNIT length on the circumference
of a UNIT circle to be a UNIT angle, the magnitude of an angle that
subtends the entire unit circle (or all of 2D space) is 2*pi units of
angle. The constant 2*pi expresses the relation between straight-line
length and 2D-space/circularity.

Similarly, 4*pi expresses oneness in the specific case of sphereness.

...because, taking the angle subtending an area of UNIT magnitude on the
surface of a UNIT sphere to be a UNIT of solid angle, the magnitude of a
solid angle that subtends the entire unit sphere (or all of 3D space) is
4*pi units of solid angle. The constant 4*pi expresses the relation
between straight-line length and 3D-space/sphericality.

Best regards,

Neil

[snip]

>Jud McCranie wrote:
>
>> At 10:15 PM 8/23/2002 -0400, Franklin T. Adams-Watters wrote:
>> >Actually, there's good reason to think pi is not the MOST FAMOUS
>> >TRANSCEDENTAL CONSTANT OF *THE WHOLE COSMOS*.  It's only a historical
>> >accident that we wound up with the ratio of the circumference to the
>> >diameter.  It could just as easily have been 2*pi: the ratio of the
>> >circumference to the radius.  And while the relationship is obviously
>> >trivial, 2*pi is slightly more fundamental mathematically: it is the
>> >period for sin and cos, among other things.
>>
>> Once I tried to make a similar point on sci.math, and people didn't
>> understand what I was saying.  Most constants are "fixed", but we could use
>> 2pi or pi/2 as the basic constant.  Some things would be easier with one of
>> them, but they are fundamentally the same.

-- 
Neil Fernandez