My Math Forum Calculate the arc length between 2 points over a hypersphere
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 December 13th, 2012, 02:30 AM #1 Newbie   Joined: Dec 2012 Posts: 1 Thanks: 0 Calculate the arc length between 2 points over a hypersphere Good morning, I'm trying to compute the arclength (geodesic distance) between two n-dimensional points over a n-dimensional sphere (hypersphere). Do you know if it is possible? If yes, please, I'd be very pleased if you, as experts, provide me this knowledge. Thank you very much Best,
 December 23rd, 2012, 09:00 AM #2 Senior Member   Joined: Dec 2012 Posts: 372 Thanks: 2 Re: Calculate the arc length between 2 points over a hypersp Get the 2 vectors connecting the respective hypershperical points to its center, say A and B. Compute the angle (^) between A and B with Cos(^) = A.B / |A|.|B| . The geodesic arclength between the points is (^) times r where r is the radius of the hypersphere and (^) is given in radian measure.

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