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Nov 22, 2020 at 0:56 history edited Tim Carson CC BY-SA 4.0
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Nov 22, 2020 at 0:52 comment added Tim Carson That's a good way of phrasing the connection between the intuition and the concrete math.
Nov 21, 2020 at 9:10 vote accept Andrea Marino
Nov 21, 2020 at 9:10 comment added Andrea Marino Thanks. The second example is conceptually cristalline: if we were on the circle (embedded in R^2), the acceleration along the curve would be calculated by the ordinary second derivative and then *projecting * to the tangent space to $S^1$. The latter makes the acceleration zero. If, instead, you inflate the circle, you don't project anymore, and you get a big acceleration, no matter what you do.
Nov 20, 2020 at 16:58 history edited Tim Carson CC BY-SA 4.0
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Nov 20, 2020 at 16:46 history answered Tim Carson CC BY-SA 4.0