Spherical Geometry Equilateral Pentagon

  • #1
Hey PF! I'm going through a textbook right now and it just said "obviously, you can't have an equilateral pentagon with 4 right angles in spherical geometry (Lambert quadrilaterals).

However, I am not able to make the connection. can somebody help me understand why this is?
 

Answers and Replies

  • #3
So every angle must be greater than 108 degrees and therefore it's quite obvious you can't have four of them being 90 degree's. Is that what you are saying?
 
  • #4
12,693
6,558
So every angle must be greater than 108 degrees and therefore it's quite obvious you can't have four of them being 90 degree's. Is that what you are saying?

Yes.
 

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