1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Triangle on a Sphere Question Interpretation

  1. Sep 17, 2012 #1
    1. The problem statement, all variables and given/known data
    Consider a tiling of the unit sphere in ##\mathbb R^3## by equilateral triangles so that the triangles
    meet full edge to full edge (and vertex to vertex). Suppose n such triangles meet an one
    vertex. Show that the only possibilities for n are
    ## n=3 ##, ##n = 4##, or ##n=5##


    2. Relevant equations



    3. The attempt at a solution
    I guess the main thing I need help with is interpretation of the question.

    Thank you
     
  2. jcsd
  3. Sep 17, 2012 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    A (flat) triangle won't fit on the surface of a sphere. Do you mean spherical triangles?
     
  4. Sep 17, 2012 #3

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Hint: there's a relation between the angles of a triangle and it's area. Figure out the area of a triangle if n of them share a vertex. How many will fit on a sphere? If you think about there is also a easy correspondence between these and some of the platonic solids.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Triangle on a Sphere Question Interpretation
  1. Triangle question (Replies: 7)

Loading...