For the sum of the interior angles of triangles in Spherical geometry the sum must be greater than 180°
What is Spherical geometry?
- Spherical geometry is the geometry of the two-dimensional surface of a sphere.
- In this context the word "sphere" refers only to the 2-dimensional surface and other terms like "ball" or "solid sphere" are used for the surface together with its 3-dimensional interior.
- In spherical geometry, straight lines are great circles, so any two lines meet in two points.
How to solve this problem?
The steps are as follow:
- Think about a sphere, like the Earth. A very small triangle, say ,one with sides less than a meter, is very close to a similar triangle in Euclidean space. The sum of the angles is very close to 180 degrees.
- But a very large triangle, with two of its vertices on the equator and the third at the north pole has the right angles at the vertices on the equator, and the other can be anything between zero and 360 degrees.
So, for the sum of the interior angles of triangles in Spherical geometry the sum must be greater than 180°
Learn about Spherical geometry here:
https://brainly.com/question/10171109
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