.infinity);
1.002008392826082214417852769232412060485605851394888756548596615
9097850533902583989503930691271695861574086047658470602614253739
7072243015306913249876425109092948687676545396979415407826022964
1544836250668629056707364521601531424421326337598815558052591454
0848901539527747456133451028740613274660692763390016294270864220
1123162209241265753326205462293215454665179945038662778223564776
1660330281492364570399301119383985017167926002064923069795850945
8457966548540026945118759481561430375776154443343398399851419383
-----------------------------------------------------------------------------
This number, the Product[Cos[Pi/n], {n,3,infinity}]
is the limit of an interesting figure in geometry.:
If we take a circle, inscribe a triangle, then incribe another circle
inside the triangle, then inscribe a square inside the inner circle,
then inscribe another circle inside the square, then inscribe a pentagon...
The radius of this figure (the number of sides of the polygon increase
with every step:triangle 3, square 4, pentagon 5, ...) approaches a
limit: Product[Cos[Pi/n], {n,3,infinity}]
Is there any way to get an analytic solution to this? Like this
would be the square root of Pi or some combination of radicals
and irrational numbers? Anyway, Thanks,
Mounitra Chatterji
mounitra@seas.
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