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Full Version: Fooling the CASIO ClassWiz fx-991LA X
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$$\frac{\rm{e}^{\frac{23}{4}-{\left({\left(\frac{40}{211}\right)}^{2}+100\right)}^{-2}}}{100}$$

$\rm{\pi}$

;-)
Great approximation! Fooled my fx-991EX as well. My Prime shows the approximation departs from pi by <1 part in 10^-12.
In double precision mode, the approximation varies from pi by~8.21*10^-14 on my WP 34S
Very nice approximation correct to fourteen digits!

Code:
3.1415926535897111461 3.1415926535897932384                ^^^^^^

The second is π.

Pauli
(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"
(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"

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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