Fooling the CASIO ClassWiz fx-991LA X
05-14-2017, 10:41 PM
Post: #1
 Gerson W. Barbosa Senior Member Posts: 1,419 Joined: Dec 2013
Fooling the CASIO ClassWiz fx-991LA X

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

$\rm{\pi}$

;-)
05-15-2017, 01:23 AM
Post: #2
 lrdheat Senior Member Posts: 664 Joined: Feb 2014
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.
05-15-2017, 01:32 AM
Post: #3
 lrdheat Senior Member Posts: 664 Joined: Feb 2014
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
05-15-2017, 01:33 AM (This post was last modified: 05-15-2017 01:35 AM by Paul Dale.)
Post: #4
 Paul Dale Senior Member Posts: 1,725 Joined: Dec 2013
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
05-15-2017, 02:58 AM (This post was last modified: 05-15-2017 02:59 AM by Gerson W. Barbosa.)
Post: #5
 Gerson W. Barbosa Senior Member Posts: 1,419 Joined: Dec 2013
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:

$$3.141592653$$

05-15-2017, 04:14 AM (This post was last modified: 05-15-2017 12:23 PM by Gerson W. Barbosa.)
Post: #6
 Gerson W. Barbosa Senior Member Posts: 1,419 Joined: Dec 2013
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:

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

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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