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4.6 The Shape of the Universe
Discussion
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Einstein showed with General Relativity that the universe doesn’t necessarily need to be a “flat” geometry. But when you hear the word “flat,” you might think of a sort of pancake shape. Is that what Professor Guth means about the shape of our universe? What does it mean to be “flat,” geometrically? How can we know for sure if our universe is “flat”? How would we know if it were some other non-Euclidean geometry?
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Hello Ladies and Gentlemen,
Most cosmological evidence points to the universe’s density as being just right — the equivalent of around six protons per 1.3 cubic yards — and that it expands in every direction without curving positively or negatively. In other words, the universe is flat, and has
flatness
It expands in every direction without curving positively or negatively. This is Euclidean- it has no curves.
Prof. Guth`s proof of flatness allows for flatness on a sphere or a torus.
Euclidean geometry exists over two dimensions.
The surface of a sphere is no loner flat. Hyperbolic and elliptical shapes are non-euclidean.
Curves make a non-Euclidean object.
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