Recent content by GeometryIsHARD

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    I Why can't a (5,5,4) solid exist?

    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...
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    I Triangles in different geometries

    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...
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    Finding the Angle of Cut for a Spherical Fruit Slice

    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...
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    Determining the surface area on a 5 sided lunar esque shape

    a banana peel where each side can be modeled as a lune
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    What is the sum of interior angles in a hyperbolic n-gon?

    So when you say follow the same procedure, you are saying that indeed a hyperbolic n-gon can be divided into n-2 triangles?
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    Determining the surface area on a 5 sided lunar esque shape

    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?
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    What is the sum of interior angles in a hyperbolic n-gon?

    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?
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    Determining the surface area on a 5 sided lunar esque shape

    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.
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    I Spherical Geometry Equilateral Pentagon

    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?
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    What is the sum of interior angles in a hyperbolic n-gon?

    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
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    What is the sum of interior angles in a hyperbolic n-gon?

    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...
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    Determining the surface area on a 5 sided lunar esque shape

    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...
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    I Spherical Geometry Equilateral Pentagon

    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?
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