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We consider “cos 123” an exact solution even though to numerically calculate it requires a power series approximation. So 3 body problem is just as “exact” as t
by zeroonetwothree 3y ago
We consider “cos 123” an exact solution even though to numerically calculate it requires a power series approximation. So 3 body problem is just as “exact” as that.
- cynicalkane 3y agoThis isn't why. You can always use a convenient Taylor series to approximate cosine anything to arbitrary precision. For the three-body problem, small changes to initial conditions diverge into incalculably chaotic behavior.
- rewmie 3y ago> We consider “cos 123” an exact solution even though to numerically calculate it requires a power series approximation. I think you're confusing what an exact solution is supposed to be with your own approximation of the exact solution. In your own example, cos(123) would represent a closed form solution to the problem. That solution doesn't cease to be exact if you decide to express it as a finite power series.