Another Ramanujan Trick

[Gerson W. Barbosa]

(10-02-2019 11:14 PM)Valentin Albillo Wrote:  

(10-02-2019 04:03 AM)Gerson W. Barbosa Wrote:  I would consider one 4 and the two instances of -6 as functions (fourth root and the reciprocals of sixth roots).

The fourth root would be the function nthroot(4,x) so the nthroot would be one function and the 4 would be one digit.

Two nested square roots woudn't help, so I'll leave it as is.

(10-02-2019 11:14 PM)Valentin Albillo Wrote:  Same with the various -6, they would be power(-6,x), i.e: one function, power, and one-digit argument, -6. And that 's being generous and not counting the "-" as one unary operation.

Else, you could have 2^1,651496129472 = 3,141592653589+ and claim that the underlined power is just one function. Nope.

You do have a point here.

(10-02-2019 11:14 PM)Valentin Albillo Wrote:  

Quote:But I have yet another trick up my sleeve:

10 DESTROY ALL
20 OPTION BASE 1 @ DIM A(35) @ COMPLEX B(34)
30 A(1)=3 @ A(34)=-1.E+12 @ A(35)=-2.4E+17
40 MAT B=PROOT(A)
50 DISP REPT(B(2))

The four significant digits in line 30 of the HP-71B program above yield 10 correct digits of pi.

You forgot to include the <justjoking> ... </justjoking> tags.

No need to. I knew I could count on your sense of humor.

(10-02-2019 11:14 PM)Valentin Albillo Wrote:  Anyway, quite ingenious on your part, but hopelessly useless as a simple approximate formula.

Yes, I am aware of its uselessness as an approximation to pi, but I thought the associated polynomial is interesting just the same. It arises from noticing that the 34th power of pi is 8.00010471505E16, whose underlined digits match the first digits of pi/3.

Best regards,

Gerson.

P.S.:

I forgot to mention that it take more than 3 minutes for the HP-71B to show the result. The HP-50g is faster, still it takes 38 seconds which certainly most of you will find too much time.

« { 1 35 } 0 CON 1 3 PUT 34 -1.E12 PUT 35 -2.4E17 PUT PROOT 6 GET RE
»

EVAL -> 3.14159265364