Recent content by GeometryIsHARD

So i was reading my geometry textbook and it said "and obviously there can be no solid where every vertex has a (5,5,4) arrangement"; unfortunately, this is not an obvious fact to me. Can somebody explain to me what makes this so obvious? This statement was the end of a proof by contradiction so...

So it has come to my attention that 'different geometries' have different rules for the interior angles of a triangle... What are these different rules for Euclidean, elliptic and hyperbolic geometry? What I'm really wondering though is what knowing these rules about the interior angles tells us...

Homework Statement A spherical fruit has a radius of 1 inch. A slice has surface area of its peel equal to pi/8 . Determine the angle of cut for the slice. Homework Equations I'm sure there is a relevant equation here but I don't know it :-( The Attempt at a Solution So the radius is 1 inch...

a banana peel where each side can be modeled as a lune

So when you say follow the same procedure, you are saying that indeed a hyperbolic n-gon can be divided into n-2 triangles?

so the surface area of a spherical lune is given by 2*θ*R^2, and since there are five lunes would it just be this multiplied by 5?

Ahh i see. But can we relate a hyperbolic triangle to a hyperbolic n-gon the same way we do normal ones? Can a hyperbolic n-gon be divided into n-2 triangles such that the interior angles of the triangle coincide with the interior angles of the n-gon?

Ah, i suppose not very close, was just taking a shot in the dark. Is there a similar equation for this situation? It must be a bit more complicated because it would include angles and radius of the sphere I suppose.

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?

Hmm, I think I see what you are saying. But how can we relate the Euclid triangle to a hyperbolic n-gon? seems like a pretty far stretch

Homework Statement Given that the sum of interior angle measures of a triangle in hyperbolic geometry must be less than 180 degree's, what can we say about the sum of the interior angle measures of a hyperbolic n-gon? Homework EquationsThe Attempt at a Solution So in normal geometry an n-gon...

Homework Statement I'm trying to figure out the surface area on a 5 sided shape where the sides can all be modeled by "lunes". The shape will end up looking like a banana peel. We are modeling the sides of the shape as lunes with varying angles on a sphere of radius 3 inches. I'm trying to...

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?