What is circumference of a circle of radius r drawn on hyperbolic plane?

360 ants sit on the rim of merry-go-round at equal angular separations 1 degree from each other.



The merry-go-round is set in rapid rotation, each ant moving at speed v=0.8 speed of light.



Then there is a circle of radius r = artanh(v) drawn on hyperbolic plane of unit negative curvature.



What is lenght of circumference of the circle of radius r?What is circumference of a circle of radius r drawn on hyperbolic plane?Where is your younger brother Alexander when we need him? Or maybe your first cousin Zo Maar?



There are some interesting relativistic aspects to this problem -- but you put it in math and I don't know how to do hyperbolic planes.



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But if this relates to relativity, I'll bet the answer is either 1.2 pi or 3.333 pi.