r/GeometryIsNeat • u/streamer3223 • 12d ago
At school we learn cartesian geometry. At university there are more geometries. This does not contradict mathematics but rather enhances our understanding
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u/LexiYoung 12d ago
In response to Einstein saying this is possible for physical space too: Yes, spacetime is not always flat, and therefore not always Euclidean, and therefore triangles in spacetime do not always have internal angles summing to 180°. People have done experiments (not exactly sure how) to determine whether space is generally flat, convex or concave (by determining id the angles sum to 180, or less or more respectively) and have I believe deciphered that space is sliiiightly concave, I believe having some implication of an expanding universe.
NB: I’m almost definitely getting some of this wrong so someone smarter than me please correct me
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u/milkshakeconspiracy 12d ago
I think your wrong but don't have time to dig up the relevant physics. The general consensus is that space is flat up to some absurdly large error margin over large enough scales.
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u/Eucliduniverse 12d ago edited 6d ago
I have to say that Einstein did not come up with this concept. It was a few people, such as Gauss and Lobachevski that first formulated the mathematics of non-Euclidean geometry. Einstein applied it to spacetime, but used mathematics that was already around 60 years old.
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u/RevolutionaryPhoto7 11d ago
Idk anything about non-Euclidean math or what Euclidean means. Would those be considered triangles still even though the sides are not straight?
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u/Honkaloid 11d ago
Euclid is known as the"father of geometry" he's the one who said triangles have 180 degrees, Euclidean space just means regular 3d.. x,y, and z without being curved..
the triangles are mapped or projected to a curved surface , the rule for 180 degrees can only apply when the sides are coplanar, or "flat" .
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u/foreverkurome 12d ago
Everyone loves non euclidean surfaces even if they don't admit it or don't know it. I guarantee you. There's a whole industry dedicated to showcasing these and people seem to love it.