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
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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.
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Curves make a non-Euclidean object.
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