Question

Would the sum of the interior angles of a triangle in this type of geometry be different from those of triangle in Euclidean geometry? Explain.

Answer 1

Answer: Yes

Explanation:

If a triangle was inscribed onto the surface of a sphere, the sum of its interior angles will not add up 180 degrees. This is actually a method in differential geometry to see if a surface is flat or curved; see if the angles up to 180 degrees. Now, it depends on how large the triangle is. If we were to draw a triangle on the surface of the earth with lets say a piece of chalk, the angles will appear to add up to 180 degrees. The larger amount of surface that the triangle covers, the larger deviation you will get from 180 degrees.