Quick challenge- novel coding for value of Pi

[tenochtitlanuk]

   '   Nilakantha series
   '   pi     = 3 + 4/(2*3*4) - 4/(4*5*6) + 4/(6*7*8) - 4/(8*9*10) + 4/(10*11*12) - 4/(12*13*14)


I hadn't seen this series before- you can code it in a handful of lines and a few minutes and it converges very quickly.

How long did you take to code it?

Bit of an antidote to my ten-dimension hypersphere method..

[Brandon Parker]

I did this a while ago ... like April 2013 while ago ...

Print calcPI(1114)

Function calcPI(stepsToCalc)
   For i = 2 To (stepsToCalc + 2) Step 2
       If (i Mod 4) Then
           calcPI = calcPI + 4/ (i * (i + 1) * (i + 2))
       Else
           calcPI = calcPI - 4/ (i * (i + 1) * (i + 2))
       End If
   Next i
   calcPI = (3 + calcPI)
End Function


{:0)

Brandon Parker

[sarossell]

Pi = ASN(1)*2

[tenochtitlanuk]

Brandon- nice series method isn't it! Your comment makes me feel like a necroposter..

sarossell- the point of the OP was to use this method.

I memorised 10 digits of Pi as a teenager and don't need to use ANY calculation when coding.
I thought I'd collected most methods of calculating Pi to varying numbers of digits ( as on my web pages) but Nilakantha had escaped me, even if he operated 500 years ago. So before my teenage years, but not widely known 'back then'. The Wikipedia pages on Pi give lots of methods that are fun to program. However it goes way beyond my maths level- gamma functions etc. and more -at Ramanujan's level.



This was my code..

   '   Nilakantha series

   '   pi     = 3 + 4/(2*3*4) - 4/(4*5*6) + 4/(6*7*8) - 4/(8*9*10) + 4/(10*11*12) - 4/(12*13*14)

   '   199 terms     3.1415926219  error -0.0000000317
   '   200 terms     3.1415926848  error  0.0000000312 and decreasing.


   LBpi    =4 *atn( 1)
   start   =2
   pi      =3

   for i =1 to 200
       print i, using( "#.##########", pi), using( "##.##########", pi -LBpi)
       if ( i mod 2) =0 then sgn =-1 else sgn =1
       denom   =start *( start +1) *( start +2)
       pi      =pi +4 /denom *sgn
       start   =start +2
   next i

   end


[timur77]

I would like to share my experience in finding the number Pi.

I wrote the first program for finding the Pi number on another 286 PCs. Here is the code.

p=0
s=0
p1=0
p2=0
p3=0
p4=0
p5=0
for i=1 to 50000
p1=p
b=10^15*(-1)^(i+1)
p=p+(b-(b mod (i*2-1)))/(i*2-1)
p3=p2
p2=((p1+p)-((p1+p) mod 2))/2
p4=p3
p3=((p2+p3)-((p2+p3) mod 2))/2
p5=((p3+p4)-((p3+p4) mod 2))/2

s=4*p5
locate 0,0
print s
scan
next i
wait


Then I searched for faster methods for finding more PI digits.

p=2
a=0
for i=1 to 500
a=sqr(2+a)
p=p*2/a
locate 0,0
print p
next i


But the best result I got in the next program. The calculation is made in whole numbers, the number of digits you need can be set in a cycle, more digits are longer the calculation, for example, 200 digits of the number of PIs I find in 4 minutes, and 400 digits in 8 minutes and 20 seconds

ms=10^600
s=0
for i=0 to 400
   ii=8*i
   s=s+del(1*ms, 16^i)*(del(4*ms, (ii+1))-_
                        del(2*ms, (ii+4))-_
                        del(1*ms, (ii+5))-_
                        del(1*ms, (ii+6)))
   locate 0,0
   print s
   scan
next i
print "Все"
end
function del(a, b)
   del=(a-(a mod b))/b
end function


[tenochtitlanuk]

Neat! I don't think I've ever thought of coding a line involving 10^600 to avoid the decimal...

It is fun to see if your date of birth ( in your local way of expressing it) comes in the first 10000 digits- eg 09042020 in UK standard way. Or check if all digits are equally represented...

[timur77]

In your example, really, the dimension of the dates, month and year is different, but I did not come up with the method itself, I just implemented it in the algorithm
Bailey–Borwein–Plouffe formula

and naturally I checked the result with the real value

3,1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 4428810975 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 4543266482 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 9171536436 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 5759591953 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 8912279381 8301194912 9833673362 4406566430 8602139494 6395224737 1907021798 6094370277 0539217176 2931767523 8467481846 7669405132 0005681271 4526356082 7785771342 7577896091 7363717872 1468440901 2249534301 4654958537 1050792279 6892589235 4201995611 2129021960 8640344181 5981362977 4771309960 5187072113 4999999837 2978049951 0597317328 1609631859 5024459455 3469083026 4252230825 3344685035 2619311881 7101000313 7838752886 5875332083 8142061717 7669147303 5982534904 2875546873 1159562863 8823537875 9375195778 1857780532 1712268066 1300192787 6611195909 2164201989 ...


You can check it yourself

[tenochtitlanuk]

Thanks for that reference... looking forward to more contributions from you!

(and I did do the checks..)

[bluatigro]

my genetic programing code trys to find a alteritive formula for PI
it often finds sqr( 10 ) and than does not go on