Sude Dursun - Interior Angles of a Triangle

In this talk, we will show some topological and metric properties that allow us to calculate the interior angles of a triangle on any surface. The talk will consist of four parts: In the first part, we will use manifold theory for construct the metric space and we call this space as Riemannian manifold. Then second part,the curve and its curvature are defined on this manifold. In the next part these curves will be limited to geodesic ones and polygons will be constructed with geodesic curves. And finally the interior angles of this polygon will be calculated using the Gauss-Bonnet theorem. As a result, we will see that the sum of the interior angles of triangles on surfaces with different curvatures can be different than 180 degree.

Видео Sude Dursun - Interior Angles of a Triangle канала DRP Türkiye