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Noneudlidean geometry

  • #1
1,197
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I need to draw a triangle on a surface of a sphere for which the sum of the interior angles is slightly greather than pi and also the sum of angles is equal to 2pi.

I think i have an idea of what to draw for the sum of interior angles slightly greater than pi (http://www.math.hmc.edu/funfacts/ffiles/20001.2.shtml) [Broken], but not quite sure how to get the angles greater than 2pi

any ideas?
 
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Answers and Replies

  • #2
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well if you want slightly larger than pi, any non-zero area triangle on the surface of the sphere will work. For exactly 2pi, try going from north pole to equator, then around on the equator to direct opposite side, then back up to the north pole. Go farther than direct opposite side if you want more than 2pi. Hope this helps and you can visualize what i'm saying.
 
  • #3
1,197
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it is a bit difficult, could you give another explanation?

what do you mean by "from north pole to equator"?

thanks
 
  • #4
quasar987
Science Advisor
Homework Helper
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4,773
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it means you dessend along a meridian.

The "triangle" dimachka is talking about is 1/4th of the surface of the sphere.

It has half the equator as one of its side and its other side passes through the north pole.
 
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