And another 12c minichallenge (phi)  Printable Version + HP Forums (https://archived.hpcalc.org/museumforum) + Forum: HP Museum Forums (https://archived.hpcalc.org/museumforum/forum1.html) + Forum: Old HP Forum Archives (https://archived.hpcalc.org/museumforum/forum2.html) + Thread: And another 12c minichallenge (phi) (/thread145811.html) 
And another 12c minichallenge (phi)  Paul Dale  01152009 After the rather difficult pi challenge, I thought I'd propose another (hopefully) easier challenge. This time we're after the golden ratio, phi, which is approximately 1.6180339887... Now, the obvious six command / seven keystroke sequence on the 12c is:
5 gsqrt 1 + 2 / This results in 1.618033989 on the display (assume FIX 9 is already set). I think it would be difficult to better this but I would be very interested in a shorter sequence if such is found. However, let us presume for some unknown reason that we want the resulting digits correct and unrounded. That is, we want 1.618033988 on the display. Now clearly this can be done in four additional steps/keystrokes with
5 sqrt 1 + 2 / EEX 9 CHS  However, it can be done with fewer. Specifically, it can be done in at most the same number of operations and keystrokes as the correctly rounded version I gave initially. That is, six operations maximum and seven keystrokes maximum. Is anybody up to this challenge?
Re: And another 12c minichallenge (phi)  Namir  01152009 How about [3] [6] [cos] [2] [x] You get phi. I assume the angle mode is degrees.
Namir
Re: And another 12c minichallenge (phi)  Paul Dale  01152009 Nice solution, which for some reason I didn't remember. Still it would save a key stroke on a 15c. However, we're on a 12c which doesn't have COS and I asked for phi unrounded which is (phi  10^9).  Pauli edit: got the keystroke count wrong edit: and then realised I hadn't
Edited: 15 Jan 2009, 11:18 p.m. after one or more responses were posted
Re: And another 12c minichallenge (phi)  Namir  01152009 You are right. There is no cos in the 12c. However, one who needs to work with phi will most likely use an 11c, 15c, 41c, 42s, and so on. So why not use the more appropriate tool?
Namir
Re: And another 12c minichallenge (phi)  Paul Dale  01152009 This is a challenge and for scientific things the 12c is often not the best suited which makes it more interesting...
 Pauli
Re: And another 12c minichallenge (phi)  Namir  01152009 So how is it best suited for trig functions (for example)? It takes pretty much a long set of keystrokes to emulate predefined trig functions in the scientific calculators. I learned that it is better to work smarter than harder.
Re: And another 12c minichallenge (phi)  Anthony L. Mach  01152009 It looks like replacing EEX 9 CHS  with 1  1/x seems to do the trick as well. Interesting...
Tony
Re: And another 12c minichallenge (phi)  Paul Dale  01152009 Yes, one of the many self referential formulas involving phi rounds the other way. Unfortunately, 9 commands / 10 keystrokes.
Re: And another 12c minichallenge (phi)  Chris Dean  01162009 How about the ratio of two consecutive Fibonacci numbers? 196418 enter 121393 / = 1.6180339887... (displayed as 1.618033989) Regards
Chris Dean
Re: And another 12c minichallenge (phi)  Namir  01162009 Chris, That requires "beaucoup" keystrokes!!!
Namir
Re: And another 12c minichallenge (phi)  Namir  01162009 I forgot to mention that MY Hp12C has a COS key!!! Minor detail! Sorry!
Edited: 16 Jan 2009, 9:54 a.m.
Re: And another 12c minichallenge (phi)  Chris Dean  01162009 Ah but so simple
Re: And another 12c minichallenge (phi)  Namir  01162009 I think Paul is counting keystrokes. The one that is even simpler is to simply type they value of phi. :)
Namir
Re: And another 12c minichallenge (phi)  Paul Dale  01162009 Time for a hint. Skip this post if you want to try the challenge unaided.
The formula I used for phi (sqrt(5) + 1)/2 is still used, however you'll have to juggle the percentages to obtain the answer.
Re: And another 12c minichallenge (phi)  Gerson W. Barbosa  01162009 Obviously this is not a solution, just a different way to get phi on the 12C:
01 1 After 19 or so iterations it will display the unrounded value of phi. However the next ones will show the properly rounded answer. There is another 9step solution around but it will take too long before the answer briefly appears :) Gerson.
Re: And another 12c minichallenge (phi)  Namir  01162009 Here is an approximation for phi that has a 5decimal accuracy: [5] [LN] [9] [EEX] [CHS] [3] [+] Seven steps. Namir
Edited: 16 Jan 2009, 9:13 p.m.
Re: And another 12c minichallenge (phi)  Paul Dale  01182009 Even with the hint, no success :( I was seeking this solution:
5 SQRT 5 delta% 2 %T  Pauli
Edited: 18 Jan 2009, 3:58 p.m.
