Mathematics Behind Distances

We all know the properties of simple geometrical figures, such as squares, triangles, circles etc. If I say I gave a talk on the sum of angles in a triangle, you will think I was doing 6th class stuff. However, it is surprising that these simple properties of figures breakdown when we set out to understand the universe. For example, if we try to draw an infinite straight line on the surface of earth, we would come back to the same point! Moreover, is the sum of angles of a triangle drawn on a sphere equal to zero? No.

In this talk, I presented an overview of the geometrical aspects of spacetime, the concept of distance and time on a given geometry and the definition of inertial frames. We also briefly discussed the variational principle. Then, we used these geometrical ideas to describe spacetime and separate events based on their causal relationship. In fact, we tried to construct the surface of constant t slices of a wormhole.

The talk ended with a brief discussion on the various terminologies of planetary motion such as perihelion, aphelion, synodic period and eccentricity of a planet's orbit.