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Suppose🚶♂️&🚶♀️Start at point A.
🚶♂️walks A→C pointing North the whole time
🚶♀️walks A→B→C pointing North the whole time
👉When they both arrive at the North pole they will be pointing different directions.
🚶♂️walks A→C pointing North the whole time
🚶♀️walks A→B→C pointing North the whole time
👉When they both arrive at the North pole they will be pointing different directions.
Indeed, this is how🚶♂️&🚶♀️could tell they are living on a curved surface.
👉In Physics & Mathematics, this way of moving a vector along a curved surface is known as 𝒑𝒂𝒓𝒂𝒍𝒍𝒆𝒍 𝒕𝒓𝒂𝒏𝒔𝒑𝒐𝒓𝒕.
👉In Physics & Mathematics, this way of moving a vector along a curved surface is known as 𝒑𝒂𝒓𝒂𝒍𝒍𝒆𝒍 𝒕𝒓𝒂𝒏𝒔𝒑𝒐𝒓𝒕.
A nice demonstration of parallel transport.
Note☝️: The animation keeps the vector facing East (as opposed to North, in my previous example)
source:naturelovesmath.com/en/mathematica…
Note☝️: The animation keeps the vector facing East (as opposed to North, in my previous example)
source:naturelovesmath.com/en/mathematica…
