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Fooling the CASIO ClassWiz fx-991LA X
05-14-2017, 10:41 PM
Post: #1
Fooling the CASIO ClassWiz fx-991LA X
[Image: 34531773561_d7f18f5659_b.jpg]

\(\frac{\rm{e}^{\frac{23}{4}-{\left({\left(\frac{40}{211}\right)}^{2}+100\right)}^{-2}}}{100}\)


\[\rm{\pi}\]

;-)
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05-15-2017, 01:23 AM
Post: #2
RE: Fooling the CASIO ClassWiz fx-991LA X
Great approximation! Fooled my fx-991EX as well. My Prime shows the approximation departs from pi by <1 part in 10^-12.
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05-15-2017, 01:32 AM
Post: #3
RE: Fooling the CASIO ClassWiz fx-991LA X
In double precision mode, the approximation varies from pi by~8.21*10^-14 on my WP 34S
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05-15-2017, 01:33 AM (This post was last modified: 05-15-2017 01:35 AM by Paul Dale.)
Post: #4
RE: Fooling the CASIO ClassWiz fx-991LA X
Very nice approximation correct to fourteen digits!

Code:
3.1415926535897111461
3.1415926535897932384
               ^^^^^^

The second is π.


Pauli
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05-15-2017, 02:58 AM (This post was last modified: 05-15-2017 02:59 AM by Gerson W. Barbosa.)
Post: #5
RE: Fooling the CASIO ClassWiz fx-991LA X
(05-15-2017 01:23 AM)lrdheat Wrote:  Great approximation! Fooled my fx-991EX as well. My Prime shows the approximation departs from pi by <1 part in 10^-12.

This will almost fit the fx-991ES screen:


\(\frac{1501}{150115}\rm{e}^{\frac{23}{4}}\)

No fooling this time, though:

\(3.141592653\)

"http://wes.casio.com/math/index.php?q=I-273A+U-0005000CC3F8+M-C10000AD00+S-090410100000100E1210B00051DA+R-0314159265289162010000000000000000000000+E-C81D1A313530311B1A3135303131351B1E721AC81D1A32331B1A341B1E1B"
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05-15-2017, 04:14 AM (This post was last modified: 05-15-2017 12:23 PM by Gerson W. Barbosa.)
Post: #6
RE: Fooling the CASIO ClassWiz fx-991LA X
(05-15-2017 01:33 AM)Paul Dale Wrote:  Very nice approximation correct to fourteen digits!

Code:
3.1415926535897111461
3.1415926535897932384
               ^^^^^^

The second is π.


Pauli

Notice \(ln(100\pi)=5.749900072\) is close to 23/4 (but not close enough).

I like the following better, found with help of HP-32SII solver:

\(\ln\left(\frac{16\ln\left(878\right)}{\ln\left(16\ln\left(878\right)\right)}\r​ight)\)

"http://wes.casio.com/math/index.php?q=I-273A+U-0005000CC3F8+M-C10000AD00+S-090410100000100E1210B00051DA+R-0314159265376844010000000000000000000000+E-75C81D1A313675383738D01B1A75313675383738D0D01B1ED0"


[Image: 34504551052_f2a4143163_b.jpg]


Five digits reused once yielding 10 correct digits.

Gerson.

Edited. Trouble with LATEX here on Chrome, so I've added a picture. Also, I cannot link the CASIO WES website here, the address between quotes above.
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