I don't like to think there are magics in the aritmetic, but...

[Psychophanta]

I don't like to think there are magics in the aritmetic, just like the old and new pitagorics school think, but...
Pitagoric old school believed universe is made by numbers, and new people who continues that thinking, believes Universe is arimetic (mathematic).

This is just a curious example, the so called "Wallis product":

Code: Select all

a.q=2
b.q=1
r.d=1
n.q=10000000
For i=1 To n
  r.d*a*a:a+2
  r.d/b/b:b+2
Next
r/n
Debug r
debug #PI

[Cyllceaux]

[BarryG]

The output:

Code: Select all

3.1415927321308840802771556
3.1415926535897931159979635

[Quin]

The output:

Code: Select all

3.1415927321308840802771556
3.1415926535897931159979635

So...pi. Okay?
I've seen way weirder things in my life that have made me believe in higher powers than some code producing the result of pi. I'm not dissing you, just to be clear, but I'm just not seeing the significance here, would you mind explaining a bit more?

[Psychophanta]

https://en.wikipedia.org/wiki/Wallis_product

[Piero]

[Piero]

I've seen way weirder things in my life that have made me believe in higher powers than some code producing the result of pi.

Amazing grace! how sweet the sound,
That saved a wretch; like me!
I once was lost, but now am found,
Was blind, but now I see.

[Olli]

Pi has been discovered in the Indiana (US) since only 150 years. Since more than 30 years, the universe has forced me to believe the Pi was discovered at the Greek's, since 2000 years. I am disgusted, near... depressed...

Source

[Piero]

This is just a curious example, the so called "Wallis product"

Is yours an improved Wallis?
I'm curious because it should be smaller than π (https://upload.wikimedia.org/wikipedia/ ... series.svg)

Code: Select all

n=100000000
n2=n*2
Debug #PI

r.d=3 ; π=3+4/(2·3·4)-4/(4·5·6)+4/(6·7·8)-4/(8·9·10)… Nilakantha Somayaji
a=2:b=1
; StartTime.q = ElapsedMilliseconds()
For i=1 To n
   r+4/(a*(a+1)*(a+2))*b
   b*-1:a+2
Next
; Debug ElapsedMilliseconds() - StartTime
Debug r

r.d=1 ; Wallis
; StartTime.q = ElapsedMilliseconds()
For i=1 To n
   s.d=4*i*i
   r*s/(s-1)
Next
; Debug ElapsedMilliseconds() - StartTime
r*2
Debug r

r.d=1 ; Psychophanta Modified (Test)
; StartTime.q = ElapsedMilliseconds()
For i=1 To n2 step 2
   r*(i+1)*(i+1)/i/i
Next
; Debug ElapsedMilliseconds() - StartTime
r/n2*2
Debug r

r.d=1 ; Psychophanta
a=2:b=1
; StartTime.q = ElapsedMilliseconds()
For i=1 To n
  r.d*a*a:a+2
  r.d/b/b:b+2
Next
; Debug ElapsedMilliseconds() - StartTime
r/n
Debug r

[tj1010]

I'm no genius, I stopped at differential equations and abstract algebra ~12 years ago, but I'm fairly certain you can't 'figure out' large dynamical systems you don't even have a whole map of using obvious patterns in small states of it.. Which was what was being worked on when this was found by Wallis in the seventeenth century AD..

By the way there are at least three ways to do this more efficiently in calculus that were discovered within a quarter-century of Wallis