# Jakob Ekstedt: The angle sum of a triangle: From Euclid to Einstein

**Time: **
Fri 2021-08-27 14.00 - 15.00

**Location: **
Zoom, meeting ID: 697 4204 2109 (password required, contact arias@math.su.se)

**Respondent: **
Jakob Ekstedt

**Abstract:** Einstein’s general relativity theory changed our understanding of gravity. First defined by Newton as an attractive force between matter, general relativity connects it to the geometry of the space-time and particularly to its curvature.

This thesis focuses on the historical role of the triangle’s angle sum in defining and deriving curvature and developing non-Euclidean geometry. This was needed for Einstein to be able to formulate the relation between the curvature and the energy and momentum. The curvature of a surface is shown to be an intrinsic property of the space, calculable by the angle sum of a triangle. From the results of an experiment testing general relativity in 1919, the angle sum of a triangle is shown to exceed 180 degrees verifying that space is curved. The thesis also deals with Einstein’s special relativity theory, proving that time and distances are relative to the frame of reference.