Journey into Maths Country
Season 2 Episode 3 - Non-Euclidean Geometries
For centuries, geometry was based on Euclid's postulates, which seemed eternal and irrevocable. However, one of the postulates (the fifth) has always seemed "a little less natural" than the others, and hundreds of mathematicians have tried in vain to do without it by deducing it from the other postulates. In the mid-19th century, Bernhard Riemann came up with a novel idea: let's imagine it's false! This was the birth of "non-Euclidean geometries", which would later have major applications in physics.
Episodes in Season 2
The Monty Hall Problem
10 min
Simpson's Paradox
10 min
Non-Euclidean Geometries
10 min
Planar Tessellations
10 min
Graph Theory
10 min
Alicia Boole in the Land of Polytopes
10 min
The Kepler Conjecture, or How to Store Your Cannonballs
10 min
Chaos Theory or Order in Disorder
10 min
Kovaleskaya's Spinning Top or The Best Way to Spin
10 min
Entscheidungsproblem: The End of Mathematics?
10 min