Every Possible Shape of the Universe, From Flat to Picard's Horn

If the universe is flat and infinite, somewhere out there an exact copy of you is watching this video. But flat is only one option among many. This video walks through the shape of the universe: the flat plane, the sphere, the Lobachevsky saddle, the donut-shaped torus, mirror gluings, the Poincaré dodecahedron and Picard's horn. From Gauss, Riemann and Friedmann to the cosmic microwave background, BOOMERanG and the Planck satellite, and why the shape of the universe may be impossible to see even in principle. #space #universe #cosmology