A not so useful HP-16C program

[Gerson W. Barbosa]

(04-22-2018 01:08 PM)Dieter Wrote:  

(04-22-2018 02:11 AM)Gerson W. Barbosa Wrote:  P.S.: BTW, the perimeter of the circumscribed 96-gon, Archimedes’ second bound, is about 21.9990021999/7 (well, actually 22.9990021975, but the former is nicer). This is also the place to discuss near integers like 2*(e - atan(e)) = 2.9999978 (that ‘s gonna be our 3 in that nerd’s clock!).

This reminds me of e^pi – pi.

I've tried to "fix" that at least a couple of times :-)

\({e}^{\pi }-\pi +\frac{9^{2}}{89998-{10}^{5}\cdot \left ( {\frac{9^{2}}{89998}} \right )^{2}}=19.99999999999999295470\)

\({e}^{\pi }-\pi+\left(\frac{3}{10^{2}}\right)^{2}+\frac{1}{\left ( \ln (2)\cdot 10^{4}+\frac{\sqrt{10}}{6} \right )^{2}}=20.00000000000000072951\)

(04-22-2018 01:08 PM)Dieter Wrote:  And you should also read the caption. ;-)

"Also, I hear the 4th root of (9^2 + 19^2/22) is pi."

Only slightly better, but many 2's and too many 9's, although not so much at 6's and 7's:

\(\frac{2\left ( 16\sqrt{2}+1 \right )}{15+\frac{1}{24-\frac{9999}{2^{20+\frac{22552}{99999}}}}}=3.1415926535876\)

Gerson.