An experiement -- Would it work?

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The discussion revolves around the relationship between a perfect sphere, its circumference, and the mathematical constant pi. It asserts that if a sphere's diameter is set to 1, then its circumference naturally equals pi, emphasizing that the choice of unit systems is arbitrary. Participants question the concept of growth in this context, clarifying that a sphere defined in this way does not grow. The conversation also touches on common confusions between radius and diameter. Ultimately, the discussion highlights the simplicity of mathematical definitions in geometry.
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If you had a perfect sphere, and pi was it's circumference, what would happen? Would it be complete? Would it grow forever? How fast would it grow?
 
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Shain said:
what would happen?
It's diameter would be 1 in the same units you used for circumference. Otherwise nothing at all.
 
Shain said:
If you had a perfect sphere, and pi was it's circumference, what would happen? Would it be complete?
All spheres have Pi as the circumference if you arbitrarliy declare a unit system where r=1. That's what Pi means. The units we use (meters, feet) are abitrary and unnecessary and mathematically it is simpler to just use a unit of D=1, so C=Pi.
http://en.wikipedia.org/wiki/Unit_circle
Would it grow forever? How fast would it grow?
Grow? Why would it grow? And how is this an experiment?
 
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russ_watters said:
r=1, so C=Pi.
I'm glad I'm not the only one who keeps confusing radius and diameter. :wink:
 
Bandersnatch said:
I'm glad I'm not the only one who keeps confusing radius and diameter. :wink:
Oops. Corrected.
 

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