Spherical Geometry Equilateral Pentagon

[GeometryIsHARD]

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?

 

[jedishrfu]

It probably refers to the fact that the angles must be greater than 108 degrees for the pentagon

http://euler.slu.edu/escher/index.php/Spherical_Geometry

 

[GeometryIsHARD]

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?

 

[jedishrfu]

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.