# Does there exist a limit for calculating pi?

## Main Question or Discussion Point

note that by limit I mean the calculus operation, as in limf(x) as x->a.

I was playing around with numbers earlier today and came up with a limit that gives an exact value for pi. I want to know if others have devised limits that equal to pi, because I am not sure if I am the first because my formula wasn't particularly complicated. If so, please post the formula. I apologize for not posting my limit here, but I hope you will understand why.

mgb_phys
Homework Helper
I was playing around with numbers earlier today and came up with a limit that gives an exact value for pi.
There are lots of series which calculate pi - given an infinite number of terms.
You can't have an exact value of pi - except in the sense of an infinite series

You most likely stumbled upon a derivation of one of the many infinite series that calculate out to Pi...

There quite interesting in many cases.

Pi is the number of times a diameter goes into its circles circumfrence... you can never have it perfectly accurate. I have a book which shows it to 10,000 digits. As I understant the most accurate super computer gives it to ~10,200. If you looked at a circle with radius 0.5 meters, the diameter would wrap around the circumfrence for 3 meters, 1 decimeter, 4 centimeters, 1 milimeter,... you can keep going and going and going. By deffinition its irrational, it seems like eventually you would get to a perfect spot where the diameter was exactly over the circumfrence without overlapping, alined atom by atom...

mgb_phys
Homework Helper
As I understant the most accurate super computer gives it to ~10,200.
Not quite, the record is something like 3 trillion digits

waste of a good computer & talent lol

I've found some limits for pi:
-limit for x→0 (360/x*tan(x/2))
-limit for x→∞ (x*sin(180/x))

Just found them with simple geometry to divide the circle into multiple triangles. The first limit brings the arc of a triangle to 0, so it'll be very small. The second limit brings the number of triangles to ∞.

Of course limits for pi exist, but as you can see, it's not possible to calculate it exactly. You can only approach the correct value, in this case by measuring/caculate the sin() or tan() of a very small arc.

edit: i've used degrees.

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HallsofIvy
Here's an obvious sequence whose limit is $\pi$: