Results 1 to 3 of 3

Math Help - non-euclidean

  1. #1
    Member
    Joined
    Oct 2007
    Posts
    89

    non-euclidean

    A bug named Fred lives in a 2 dimensional universe on constant curvature. He draws a ΔABC of area 108 km2 and finds that μ (∠A) = 100, μ (∠B )= 90 and μ(∠C)= 10, What kind of universe does he live in? What is its curvature and radius?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,539
    Thanks
    778
    According to the Girard's theorem, A = R^2 \cdot E where A is the triangle area, R is the radius of the sphere (it's the sphere because the sum of the angles is greater than 180) and E = ∠A + ∠B + ∠C - \pi. And, as I remember, curvature is the inverse of the radius.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,725
    Thanks
    1478
    Quote Originally Posted by emakarov View Post
    According to the Girard's theorem, A = R^2 \cdot E where A is the triangle area, R is the radius of the sphere (it's the sphere because the sum of the angles is greater than 180) and E = ∠A + ∠B + ∠C - \pi.
    which means that the angles must be given in radians here.

    And, as I remember, curvature is the inverse of the radius.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Euclidean Algorithm
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: September 30th 2010, 10:46 AM
  2. Euclidean Isometries - Help Please!
    Posted in the Geometry Forum
    Replies: 3
    Last Post: December 13th 2009, 07:55 PM
  3. Euclidean Norm
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: October 4th 2009, 07:03 AM
  4. Euclidean algorithm
    Posted in the Number Theory Forum
    Replies: 4
    Last Post: August 8th 2009, 08:28 AM
  5. Euclidean help
    Posted in the Geometry Forum
    Replies: 1
    Last Post: July 22nd 2009, 09:42 AM

Search Tags


/mathhelpforum @mathhelpforum