http://codex99.com/design/the-hp35.html
I found this site about the HP 35 history. I know that there are a lot of pages about the same matter and sorry if it was already posted here. I did not know how HP priced its products: the cost multiplied by a factor of "PI" or "e", that was curious to me. For those who do not know the page, it´s very cool.
This is an interesting blog. There are some most interesting claims. It would be helpful to have a list of annotated references - particularily from Hewlett, Packard, Cochran [etal] documents.
TomC
Great article!
I liked the company standard: selling price is (materials cost) * Pi !!!
Kevin
Thanks for that link @hibiki. I really enjoyed the read and it makes me think that I could learn a lot from reading HP history.
(06-17-2018 06:15 PM)mcquiggi Wrote: [ -> ]Great article!
I liked the company standard: selling price is (materials cost) * Pi !!!
Kevin
...or in competitive markets, list*
e...
Very interesting.
Thanks.
I found my HP 35 (serial # 1346A.....) at a flea market lost in a bunch of junk. It wanted I owned it because I never give a look to bunches of junk !
And it’s still alive !
(06-17-2018 06:15 PM)mcquiggi Wrote: [ -> ]Great article!
I liked the company standard: selling price is (materials cost) * Pi !!!
Kevin
If I took that phrase literally (Pi !!!), HP-50G calculates that to be 9.99999999999 E499. Somehow, I think even HP wouldn't be that crazy. Pi !! came to about 7380.55555766, and Pi! comes to 7.1881-ish, or so my HP-34C told me back in the day. That might be closer to the scale that HP was originally thinking of.
(Post 244)
(06-18-2018 12:02 AM)brickviking Wrote: [ -> ] (06-17-2018 06:15 PM)mcquiggi Wrote: [ -> ]Great article!
I liked the company standard: selling price is (materials cost) * Pi !!!
Kevin
If I took that phrase literally (Pi !!!), HP-50G calculates that to be 9.99999999999 E499. Somehow, I think even HP wouldn't be that crazy. Pi !! came to about 7380.55555766, and Pi! comes to 7.1881-ish, or so my HP-34C told me back in the day. That might be closer to the scale that HP was originally thinking of.
(Post 244)
Ha! I anticipated this interpretation so I put a space between Pi and the ‘!!!’ part!
Perhaps Pi!!! Was the government price!
Kevin
(06-18-2018 12:02 AM)brickviking Wrote: [ -> ] (06-17-2018 06:15 PM)mcquiggi Wrote: [ -> ]Great article!
I liked the company standard: selling price is (materials cost) * Pi !!!
Kevin
If I took that phrase literally (Pi !!!), HP-50G calculates that to be 9.99999999999 E499. Somehow, I think even HP wouldn't be that crazy. Pi !! came to about 7380.55555766, and Pi! comes to 7.1881-ish, or so my HP-34C told me back in the day. That might be closer to the scale that HP was originally thinking of.
(Post 244)
When did Pi become a natural number? Factorial is only defined for natural numbers.
(06-16-2018 10:58 PM)hibiki Wrote: [ -> ]http://codex99.com/design/the-hp35.html
I found this site about the HP 35 history. [...] For those who do not know the page, it´s very cool.
Indeed it is. Thank you very much, I've found it really interesting and an excellent read. Would love to find something similar about the HP-65.
V.
.
(06-18-2018 07:47 PM)Harald Wrote: [ -> ] (06-18-2018 12:02 AM)brickviking Wrote: [ -> ]If I took that phrase literally (Pi !!!), HP-50G calculates that to be 9.99999999999 E499. Somehow, I think even HP wouldn't be that crazy. Pi !! came to about 7380.55555766, and Pi! comes to 7.1881-ish, or so my HP-34C told me back in the day. That might be closer to the scale that HP was originally thinking of.
(Post 244)
When did Pi become a natural number? Factorial is only defined for natural numbers.
While that's true, certain factorial implementations (hp34c, HP48-series, HP-50G and others) interpolate non-integer results by using the Gamma function, as the factorial function is merely the integer-based special case of the Gamma function. Pretty much: \( n! = Γ(n+1) \), if I remember rightly, and I'm sorry if I can't get that Gamma to come out correctly. I had fun trying to generate the inverse... of course that's not defined anywhere mathematically, so I was told.
(Post 245)
@hibiki, thanks for the link. I knew about this site but this article has been updated in May 2018 with much more detailed information than previously.
Edit: here is the link to the
original article from 2012.
The middle section of
this video is about the HP-35 - "Death of the Slide Rule"
See also this archived site, presenting an article from 1972
Made in USA...finally!
(06-18-2018 11:05 PM)brickviking Wrote: [ -> ]Pretty much: \( n! = Γ(n+1) \), if I remember rightly, and I'm sorry if I can't get that Gamma to come out correctly. I had fun trying to generate the inverse... of course that's not defined anywhere mathematically, so I was told.
Do you mean something like
that?
I prefer Inverse Factorial, however:
120 XEQ InvFact -> 5
PI SQRT 3 * 4 / XEQ InvFact -> 1.5
163 ENTER ENTER + 1/x + ENTER * 5 * 18 / XEQ InvFact XEQ InvFact -> 3.14159265359
(On Free42)
00 { 89-Byte Prgm }
01▸LBL "InvFact"
02 ENTER
03 LN
04 SQRT
05 0.16
06 RCL× ST L
07 X<>Y
08 2.21
09 ×
10 +
11 0.194
12 +
13 2
14 X<Y?
15 X<>Y
16 X<> ST T
17▸LBL 00
18 R↓
19 R↓
20 STO ST Z
21 X<>Y
22 STO ST T
23 GAMMA
24 ÷
25 +/-
26 1
27 +
28 R↑
29 RCL+ ST T
30 1/X
31 RCL ST T
32 LN
33 STO- ST Y
34 X<> ST L
35 R↓
36 +/-
37 ÷
38 STO- ST Z
39 ABS
40 1ᴇ-30
41 X<Y?
42 GTO 00
43 R↑
44 1
45 -
46 END
(06-18-2018 12:02 AM)brickviking Wrote: [ -> ] (06-17-2018 06:15 PM)mcquiggi Wrote: [ -> ]Great article!
I liked the company standard: selling price is (materials cost) * Pi !!!
Kevin
If I took that phrase literally (Pi !!!), HP-50G calculates that to be 9.99999999999 E499. Somehow, I think even HP wouldn't be that crazy. Pi !! came to about 7380.55555766, and Pi! comes to 7.1881-ish, or so my HP-34C told me back in the day. That might be closer to the scale that HP was originally thinking of.
(Post 244)
I am curious - How did you parse that expression?
X!! Is not the same as (X!)! If you have heard of double-factorials, although of course it is if you haven't, ! Being an ambiguous mathematical symbol.
Is that x!!! (A triple factorial?)
(X!!)! (Factorial of a double factorial)
(X!)!! (Double factorial of a factorial)
((X!)!)! (Factorial of a factorial of a factorial)
(06-19-2018 10:22 AM)StephenG1CMZ Wrote: [ -> ] (06-18-2018 12:02 AM)brickviking Wrote: [ -> ]Pi !!!
I am curious - How did you parse that expression?
X!! Is not the same as (X!)! If you have heard of double-factorials, although of course it is if you haven't, ! Being an ambiguous mathematical symbol.
Is that x!!! (A triple factorial?)
(X!!)! (Factorial of a double factorial)
(X!)!! (Double factorial of a factorial)
((X!)!)! (Factorial of a factorial of a factorial)
I'd vote for the
triple factorial interpretation. Although I noticed that Wolfram Alpha interprets it as (Pi !!)! instead, so it recognizes the double factorial but not higher-order multifactorials. Also interesting is that it appears to have an
analytic continuation of the double factorial; I wonder if such continuations exist for higher-order multifactorials as well?
(06-19-2018 10:22 AM)StephenG1CMZ Wrote: [ -> ] (06-18-2018 12:02 AM)brickviking Wrote: [ -> ]If I took that phrase literally (Pi !!!), HP-50G calculates that to be 9.99999999999 E499. Somehow, I think even HP wouldn't be that crazy. Pi !! came to about 7380.55555766, and Pi! comes to 7.1881-ish, or so my HP-34C told me back in the day. That might be closer to the scale that HP was originally thinking of.
(Post 244)
I am curious - How did you parse that expression?
X!! Is not the same as (X!)! If you have heard of double-factorials, although of course it is if you haven't, ! Being an ambiguous mathematical symbol.
Is that x!!! (A triple factorial?)
(X!!)! (Factorial of a double factorial)
(X!)!! (Double factorial of a factorial)
((X!)!)! (Factorial of a factorial of a factorial)
I parsed that as the following procedure would indicate:
\((((\pi!)!)!)\), therefore would have approximately been:
\(\pi! = 7.18808272898\)
\(7.18808272898! = 7380.55555766 \)
\(7380.55555766! = OVERFLOW \)(at least for my 50G)
And I'd have to check what on earth are double-factorials or triple-factorials. I haven't heard of such a beast.
(Later) Oh, so that's what those are. Interesting.
(Post 246)
(06-16-2018 10:58 PM)hibiki Wrote: [ -> ]http://codex99.com/design/the-hp35.html
I found this site about the HP 35 history. I know that there are a lot of pages about the same matter and sorry if it was already posted here. I did not know how HP priced its products: the cost multiplied by a factor of "PI" or "e", that was curious to me. For those who do not know the page, it´s very cool.
On a journey to get the story about HP35 and forward until the TITAN with the SATURN, i noticed your links in this stream.
The PI was once explained to me like this
1/3 for Components and MFG
1/3 for Cost of Sales / Admin
1/3 for Profits
(06-20-2018 07:31 PM)brickviking Wrote: [ -> ]I parsed that as the following procedure would indicate:
\((((\pi!)!)!)\), therefore would have approximately been:
\(\pi! = 7.18808272898\)
\(7.18808272898! = 7380.55555766 \)
\(7380.55555766! = OVERFLOW \)(at least for my 50G)
That’s a job for super-wp34s:
pi ! ! 1 + LNgamma 10 LN / IP RCL L FP 10^x —> 4.41316713166
x<>y —> 25345
=> ((pi!)!)! = 4.41316713166*10^25345
or, approximately,
490347/111110*10^25345
Notice that
(pi!)! ~ 66425/9 is much nicer.
PS: LOGGAMMA on the HP 50g gives a less accurate mantissa:
4.4131694182
(06-18-2018 07:47 PM)Harald Wrote: [ -> ] (06-18-2018 12:02 AM)brickviking Wrote: [ -> ]If I took that phrase literally (Pi !!!), HP-50G calculates that to be 9.99999999999 E499. Somehow, I think even HP wouldn't be that crazy. Pi !! came to about 7380.55555766, and Pi! comes to 7.1881-ish, or so my HP-34C told me back in the day. That might be closer to the scale that HP was originally thinking of.
(Post 244)
When did Pi become a natural number? Factorial is only defined for natural numbers.
The Gamma function is defined for reals (and complex numbers). It agrees with the factorial on the positive integers.