Thread: 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?

According to the Girard's theorem, 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 - . And, as I remember, curvature is the inverse of the radius.

Originally Posted by emakarov

According to the Girard's theorem, 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 - .

which means that the angles must be given in radians here.

And, as I remember, curvature is the inverse of the radius.