what does it mean when people say the universe is flat?
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Look at a piece of paper compared to a globe. The paper is flat, the globe is curved. While not exactly intuitive or easy to comprehend, there is an equivlance to this in 3D (whereas the paper and glove are 2D).
To tell the difference, we can use triangles. Triangles in flat space have angles that sum 180 whereas in curved space they can sum to different amounts (e.g. a triangle on a globe can have sums greater than 180).
By calculating the positions to and between distant celestial objects we can form triangles and measure their angles. Within a high degree of accuracy, these measurements imply we live in a flat, 3D universe.
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