HP-35 origin

[hibiki]

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.

[TomC]

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

[mcquiggi]

Great article!

I liked the company standard: selling price is (materials cost) * Pi !!!

Kevin

[drdbthompson]

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...

[badaze]

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 !

[brickviking]

(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)

[mcquiggi]

(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

[Harald]

(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.

[Valentin Albillo]

(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.
.

[brickviking]

(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)

[Steve Simpkin]

(06-18-2018 10:27 PM)Valentin Albillo Wrote:  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.

A few more links:
http://www.hpl.hp.com/hpjournal/pdfs/Iss...974-05.pdf
http://hpmemoryproject.org/wb_pages/wall_b_page_11b.htm
http://hpmemoryproject.org/wb_pages/j_minck_01.htm
https://www.hpe.com/us/en/insights/artic...-1709.html

[Didier Lachieze]

@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.

[EdS2]

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!

[Gerson W. Barbosa]

(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

[StephenG1CMZ]

(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)

[Thomas Okken]

(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?

[brickviking]

(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)

[KimH]

(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

[Gerson W. Barbosa]

(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

[ttw]

(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.