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Hyperbolic Geometry (Rectangles)

  • #1

Homework Statement


  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.

Homework Equations




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.
 

Answers and Replies

  • #2
Buzz Bloom
Gold Member
2,211
365
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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