Does there exist a limit for calculating pi?

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Discussion Overview

The discussion revolves around the existence of limits that can be used to calculate the value of pi. Participants explore various mathematical approaches, including limits and infinite series, while expressing uncertainty about the exactness of pi and the methods used to derive it.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant suggests they have discovered a limit that yields an exact value for pi and invites others to share their findings.
  • Another participant notes that while there are many series that can calculate pi, an exact value can only be approached through infinite series.
  • A different participant proposes that the original claim may be a derivation of existing infinite series that calculate pi.
  • One participant emphasizes that pi is irrational, suggesting that it can never be perfectly accurate, regardless of the number of digits calculated.
  • Another participant corrects a claim about the number of digits of pi calculated by supercomputers, asserting that the record is around 3 trillion digits.
  • One participant shares limits they found for calculating pi, specifically as x approaches 0 and as x approaches infinity, while noting that these limits can only approximate pi rather than provide an exact value.
  • A participant humorously presents a sequence of increasingly precise decimal approximations of pi as a limit.

Areas of Agreement / Disagreement

Participants express differing views on the nature of limits and their ability to yield exact values for pi. There is no consensus on whether any limit can provide an exact value, as some argue that only approximations are possible.

Contextual Notes

Participants reference various mathematical concepts, including limits, infinite series, and the irrationality of pi, without resolving the complexities involved in these discussions.

polaris12
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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.
 
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polaris12 said:
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...
 
Coriolis314 said:
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
 
  • #10
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.
 
Last edited:
  • #11
Here's an obvious sequence whose limit is \pi:
3, 3.1, 3.14, 3.141, 3.1415, 3.14159, 3.141592, ... !
 

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