1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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.

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Threads - Hyperbolic Geometry Rectangles Date
N-gon hyperbolic geometry May 6, 2016
Hyperbolic Geometry: Parameterization of Curves for Hyperbolic Distance Oct 11, 2012
What is a line in hyperbolic geometry? Jun 25, 2011
Hyperbolic geometry Apr 2, 2010
Hyperbolic Geometry Question Oct 5, 2008