The Fundamentals of Geometry

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Euclidean geometry is flat with no curvature, while non-Euclidean geometry has curvature
Curvature of space-time is related to gravity
Bernard Riemann developed the foundations of geometry and introduced the concept of living inside a space
The metric, which measures the length of curves, provides a complete description of a space's geometry
The concept of calculus is essential in determining the lengths of curves

My little pandemic-lockdown contribution to the world was a series of videos called The Biggest Ideas in the Universe. The idea was to explain physics in a pedagogical way, concentrating on established ideas rather than speculations, with the twist that I tried to include and explain any equations that seemed useful, even though no prior mathematical knowledge was presumed. I’m in the process of writing a series of three books inspired by those videos, and the first one is coming out now: The Biggest Ideas In The Universe: Space, Time, and Motion. For this solo episode I go through one of the highlights from the book: explaining the mathematical and physical basis of Einstein’s equation of general relativity, relating mass and energy to the curvature of spacetime. Hope it works!

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