Understanding wiki math image

[Soulkeeper]

I asked somewhere else, but got no response.
Maybe someone here can help me understand this image.

When solving for a particular value of i
where i == digit, am I correct in converting that image to this ?

answer = 1/16^digit * (4/8*digit+1 - 2/8*digit+4 - 1/8*digit+5 - 1/8*digit+6)

is a multiplication implied with number(number) in that image ?


thanks

 

[Vectronic]

Minor correction (should be):
(1/(16^i)) * (4/(8*i+1) - 2/(8*i+4) - 1/(8*i+5) - 1/(8*i+6))

Otherwise you would be doing (4/8) * (i+1)... which would be wrong.

And yes, excluding the first those appear to be multiplications rather than exponents.

 

[Soulkeeper]

Thanks, but even with the extra parenthesis and correct order of precedence, i'm still getting a wrong result.

ie: for i = 5

answer = 9.5367431640625e-07 * (0.097561 - 0.045455 - 0.022222 - 0.021739)
insanely small number.

As this formula is supposed to calculate a digit (i) of pi, the 5th digit should be 9.
Unless i'm understanding this wrong ?

url to formula explanation

 

[serpretetsky]

http://www.math.hmc.edu/funfacts/ffiles/20010.5.shtml

not familiar with this equation, but it looks like it should work just like you want.... except it's in hexadecimal (hence the reason you see 1/16th at the front, and not 1/10th).

 

[Soulkeeper]

base 16 ... that explains the confusions

 

[Vectronic]

Ahh yeah, the Wiki you were reading kind of separates the Hexidecimal part... I thought you were looking at this which says

This formula, unlike others before it, can produce any individual hexadecimal digit of π without calculating all the preceding digits

 

[Soulkeeper]

thanks guys