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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/