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Hyperbolic Geometry (Rectangles)

  1. Jun 30, 2017 #1
    1. The problem statement, all variables and given/known data
    1. Recall that in hyperbolic geometry the interior angle sum for any triangle is less than 180◦. Using this fact prove that it is impossible to have a rectangle in hyperbolic geometry.
    2. Relevant equations


    3. The attempt at a solution
    - I wanted to use the idea that rectangles are 4 right angles meaning they would add up to 360 to help with the proof. I am not sure if that is useful, or even how I would write that in a proof.
     
  2. jcsd
  3. Jun 30, 2017 #2
    Hi SportsLover:

    Here is hint. Think about a four sided figure that you might want to test to see if it is a rectangle. Think about a diagonal line connecting two corners. You now have two triangles.

    Hope this helps.

    Regards,
    Buzz
     
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