Expert: Jack Cheng - 12/29/2006

Question
Hi, I am trying to help a co-worker with some math problems that her 9th grade daughter did not understand, but I am having some trouble with it.  The questions relate to spherical geometry and how it is different from euclidean geometry.  Here is the one I am having the most trouble with:  1. In a sphere, you can draw two equiangular triangles such that they have different angle measures.  (This does not make sense to me, I thought if a triangle was equiangular the angle measures are the same, how can they be different?)  

Answer
Hi Kelly,

I am really impressed the your co-worker's daughter is learning spherical geometry in 9th grade. Anyway, the key to this question is understanding that in spherical geometry, the sum of interior angles can exceed 180 degrees; you are dealing with a spherical surface with lines replaced by great circles.  The sum of the angles is not constant like in Euclidean geometry.

Check out this page for more information:
http://en.wikipedia.org/wiki/Spherical_trigonometry

I hope this helps,
Jack