Another Ramanujan Trick

[Valentin Albillo]

(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.

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.

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.

If something as immensely complicated as a function capable of finding the real part of one root of a 34th degree polynomial with 32 zero coefficients and 3 real-valued coefficients is to be counted as just one function applied to 3 parameters then you can go the whole hog and simply use:

               4*arctan(1) = 3,1415926535897932384626433832795+

which uses just 2 digits and one function, which is many orders of magnitude simpler than your function which gives the root of the 34th-degree polynomial, and further agrees with infinitely many correct digits of Pi.

Anyway, quite ingenious on your part, but hopelessly useless as a simple approximate formula.

Best regards.
V.
.