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General Science / Re: Is There A Pattern In The Number Pi?
« on: 30/09/2024 06:28:47 »
Pi can be represented by a very simple pattern:
π/4 = 1 - 1/3 + 1/5 - 1/7 + etc
This series is very slow to converge, so it's not of any practical use to calculate π
But it does illustrate some important aspects:
- 1/1000001 is zero in the first 6 decimal places
- So any pattern that you might detect in the first 6 decimal places will be destroyed by adding in this factor which does not affect the first 6 decimal places.
- The series continues forever, so it will destroy any other pattern you detect in the decimal expansion
It is necessary that the digits of π (or any transcendental number) do not form a repeating pattern
- But it is not sufficient
If you want to represent π, you could use the infinite series, or adopt the standard mathematical shorthand, and just write "π".
https://www.forbes.com/sites/kevinknudson/2016/04/18/everything-you-wanted-to-know-about-pi-part-4-infinite-series/
π/4 = 1 - 1/3 + 1/5 - 1/7 + etc
This series is very slow to converge, so it's not of any practical use to calculate π
But it does illustrate some important aspects:
- 1/1000001 is zero in the first 6 decimal places
- So any pattern that you might detect in the first 6 decimal places will be destroyed by adding in this factor which does not affect the first 6 decimal places.
- The series continues forever, so it will destroy any other pattern you detect in the decimal expansion
It is necessary that the digits of π (or any transcendental number) do not form a repeating pattern
- But it is not sufficient
If you want to represent π, you could use the infinite series, or adopt the standard mathematical shorthand, and just write "π".
https://www.forbes.com/sites/kevinknudson/2016/04/18/everything-you-wanted-to-know-about-pi-part-4-infinite-series/