From: spike66 (spike66@attglobal.net)
Date: Sat Mar 09 2002 - 10:31:11 MST
Damien Broderick wrote:
>>Since arctan x = x - x**3/3 + x**5/5 - x**7/7 - ...
>>
>> pi/4 = 1 - 1/3 + 1/5 - 1/7 ...
>>
>
>In our world. But if 2 pi radians is defined = 360 degrees, what happens
>when a circle has more or fewer than 360 degrees, due to space curvature? I have the feeling that by invoking the arctan function you're being, as it were, circular here.
>
>Damien Broderick
>[not any kind of mathematician]
>
I disagree sir. In any universe with any curvature, a circle would still
have 360 degrees, for the circle defines the degree, as well as the radian.
The expansion given would work even in a different space curvature,
and they would derive the same value for pi. Nowthen, if they were to
actually attempt to measure the ratio of the circumference to the diameter,
Im not exactly sure what would happen. spike
>
>
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