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Pandigital RPL algebraic pi approximation - Gerson W. Barbosa - 10-16-2024 03:41 AM
'2*√LN(ALOG(1)+LN(6)+3*SQ(9-0!)/(ALOG(8)-SQ(75/4)))'
RE: Pandigital RPL algebraic pi approximation - Gerson W. Barbosa - 10-16-2024 11:43 AM
Or, in an expression WolframAlpha can understand:
2*√ln(alog(1)+ln(6)+3*sq(9-0!)/(alog(8)-sq(75/4)))
RE: Pandigital RPL algebraic pi approximation - EdS2 - 10-16-2024 01:51 PM
wow that's a lot of digits of correct approximation! well done!
RE: Pandigital RPL algebraic pi approximation - naddy - 10-16-2024 02:20 PM
What's "alog"?
I thought anti-logarithm to base 10, so 10^, but that doesn't make sense.
Edit: Never mind, it works out with alog as 10^. I was lost among the parentheses.
RE: Pandigital RPL algebraic pi approximation - Maximilian Hohmann - 10-16-2024 02:32 PM
Hello!
(10-16-2024 02:20 PM)naddy Wrote: What's "alog"?
I thought anti-logarithm to base 10, so 10^, but that doesn't make sense.
Wolfram Alpha interprets it as natural logarithm. But like you, I have never seen that written as "alog". And why square root of nine minus factorial of zero?
Regards
Max
RE: Pandigital RPL algebraic pi approximation - klesl - 10-16-2024 03:51 PM
if alog is natural logarithm, what is ln in the expression?
RE: Pandigital RPL algebraic pi approximation - AnnoyedOne - 10-16-2024 04:12 PM
(10-16-2024 02:32 PM)Maximilian Hohmann Wrote: I have never seen that written as "alog". And why square root of nine minus factorial of zero?
Yeah. I'd write "alog" as "e^x" and "9-0!" as "8" (9-1) but that's just me.
Ln is fine (natural log = log base e where e = 2.718 approx).
A1
RE: Pandigital RPL algebraic pi approximation - Gerson W. Barbosa - 10-16-2024 04:14 PM
(10-16-2024 02:32 PM)Maximilian Hohmann Wrote: Hello!
(10-16-2024 02:20 PM)naddy Wrote: What's "alog"?
I thought anti-logarithm to base 10, so 10^, but that doesn't make sense.
Wolfram Alpha interprets it as natural logarithm. But like you, I have never seen that written as "alog". And why square root of nine minus factorial of zero?
ALOG is RPL for 10^x, likewise SQ stands for x squared (x^2). WolframAlpha interprets ALOG as log, but gets alog in lowercase right.
I used (9 - 0!)^2 instead of simply 8^2 because 8 had already been used elsewhere. Pandigital expressions use all ten decimal digits only once. They are somewhat difficult to write. Resorting to SQ and ALOG instead of x^2 and 10^x is kind of cheating, but that makes the task a bit easier.
Best,
Gerson.
RE: Pandigital RPL algebraic pi approximation - Gerson W. Barbosa - 10-18-2024 05:17 PM
(10-16-2024 01:51 PM)EdS2 Wrote: wow that's a lot of digits of correct approximation! well done!
Thanks, Ed!
Yes, nineteen correct digits from the nine significant digits in this more conventional equivalent expression:
\(2\sqrt{\ln\left({10+\frac{3\times32^2}{200^4-75^2}+\ln\left({6}\right)}\right)}\)
RE: Pandigital RPL algebraic pi approximation - KeithB - 10-18-2024 05:39 PM
8 digits if you go for pi/2. 8^)