HP35s Revisited Trig Quandary Bug # 2
02-17-2015, 09:23 PM
Post: #21
 Massimo Gnerucci Senior Member Posts: 1,752 Joined: Dec 2013
RE: HP35s Revisited Trig Quandary Bug # 2
(02-17-2015 09:18 PM)MarkHaysHarris777 Wrote:  PSS its also the same internal value either way... 174532925000

What's a PSS?
Maybe a PPS would be better.

Greetings,
Massimo

-+×÷ ↔ left is right and right is wrong
02-17-2015, 09:31 PM
Post: #22
 MarkHaysHarris777 Senior Member Posts: 333 Joined: Jan 2015
RE: HP35s Revisited Trig Quandary Bug # 2
(02-17-2015 09:01 PM)Paul Dale Wrote:
Quote:'nobody' (at least not engineers, nor scientists) runs their calculator in 'all' mode

I pretty much always run my calculator in ALL mode and I'm in that nobody group

I rest my case.

But seriously, what is intended is that (whether you run your calculator 'physically' to show all digits, in your intellect you are certain that all of those digits don't MEAN anything. We like to see many digits of PI strung out because they're beautiful, right, but what do they MEAN. With 13-15 digits of PI I can calculate the circumference of the visible universe to within the width of a hadron... what do I need with 30 digits or more? When most of the time normal people can't measure further than 3-4 significant figures why in the world do we need our calculators set in 'all' mode so that every one of those digits shows?

Here's an example 0.142857142857142857142857 blah blah blah we all recognize 1/7 th immediately, but some of us 'need' to see all those repeating digits (I don't know why).

The pretty print of the FX115es Plus only shows five of them... and draws a line over it-! BUT, if you were going to measure 1/7 0.142857 how far would you really be able to measure it on a cm scale for instance?? Accurately?? You might squeak out the '2' but you'd not even get the '8'.

Cheers,
marcus

Kind regards,
marcus
02-17-2015, 09:45 PM
Post: #23
 Jlouis Senior Member Posts: 623 Joined: Nov 2014
RE: HP35s Revisited Trig Quandary Bug # 2
C'mon guys, lets be reasonable.

There are two diferents situations here:

1- the 35s does not have the alleged precision, or at least does not equal the precision of the 42s, 15c, 48, etc.
If one could not live with that, ok. The 35s is not for you.

2- The 35s has enough precision for day to day work, maybe as an engineer, or scientist, etc, using, lets say, fix 4 (I do too). For these guys, the 35s is a very good calculator, very pretty, with a big enter key, full of functions, good keyboard, etc.

So, lets not bury it in the grave. If the original 35 is not as precise than the 35s, and I believe there's no known case of buildings falling, aircraft dissaster and so on, due the use of the original 35, I supose we can use the 35s without much worry.

Just my 0,0002 cents. (fix 4 always).

Health and Peace
02-17-2015, 09:51 PM
Post: #24
 Thomas Klemm Senior Member Posts: 1,448 Joined: Dec 2013
RE: HP35s Revisited Trig Quandary Bug # 2
(02-17-2015 09:01 PM)Paul Dale Wrote:  I'm in that nobody group

Quote: 'Who did you pass on the road?' the King went on, holding out his hand to the Messenger for some more hay.

'Nobody,' said the Messenger.

'Quite right,' said the King: 'this young lady saw him too. So of course Nobody walks slower than you.'

'I do my best,' the Messenger said in a sulky tone. 'I'm sure nobody walks much faster than I do!'

'He can't do that,' said the King, 'or else he'd have been here first.

-- Through the Looking-Glass by Lewis Carroll
02-17-2015, 09:56 PM (This post was last modified: 02-17-2015 10:19 PM by MarkHaysHarris777.)
Post: #25
 MarkHaysHarris777 Senior Member Posts: 333 Joined: Jan 2015
RE: HP35s Revisited Trig Quandary Bug # 2
(02-17-2015 09:45 PM)Jlouis Wrote:  So, lets not bury it in the grave. If the original 35 is not as precise than the 35s, and I believe there's no known case of buildings falling, aircraft disaster and so on, due to the use of the original 35, I suppose we can use the 35s without much worry.

Just my 0,0002 cents. (fix 4 always).

Yes. Jlouis, its even more profound than that... engineers at NASA (most of them no older than 21) put people on the moon; with slide rules.*

I honestly believe that every engineer should be forced to work their entire freshman and sophomore year with a slide rule, and pad of paper, and logarithms; before they EVER get to touch a calculator... would teach humility, and would give them an appreciation for the instrument that most of our engineers take for granted today.

* -unless you're one of those who think we didn't land on the moon... in which case, NASA engineers (most of them no older than 21) FAKED the moon landing; with slide rules-!

Cheers,
marcus

Kind regards,
marcus
02-17-2015, 10:57 PM
Post: #26
 Thomas Klemm Senior Member Posts: 1,448 Joined: Dec 2013
RE: HP35s Revisited Trig Quandary Bug # 2
(02-17-2015 09:31 PM)MarkHaysHarris777 Wrote:  Here's an example 0.142857142857142857142857 blah blah blah we all recognize 1/7 th immediately, but some of us 'need' to see all those repeating digits (I don't know why).

Others might rather see:
$\frac{3288636824430133867996269763537699932860894482908342665}{10638735892371652​4807713475752456393740167855629859291136}$

Cheers
Thomas

PS: Use both [Hide block form] and [More digits].
06-27-2015, 05:36 AM
Post: #27
 Marcio Senior Member Posts: 438 Joined: Feb 2015
RE: HP35s Revisited Trig Quandary Bug # 2
(02-17-2015 07:52 PM)Thomas Klemm Wrote:
(02-16-2015 11:53 PM)MarkHaysHarris777 Wrote:  Conclusion: Bug # 2 is not a bug... its a petty annoyance.

You may try this simple program with 0, 1, 2, 3, ... as input. Just make sure to use DEG mode.
Code:
0001 10^x 0002 ENTER 0003 1/x 0004 SIN 0005 × 0006 RTN

This is the result that the HP-35s produces (using ALL mode):

0: 1.74524064373E-2
1: 1.7453283659E-2
2: 1.74532924306E-2
3: 1.74532925091E-2
4: 0.0174532925
5: 0.017453292
6: 0.01745329
7: 0.0174532 WOW!
8: 1.74532925199E-2
9: 1.74532925199E-2

For comparison here are the correct values:

0: 0.0174524064373
1: 0.0174532836590
2: 0.0174532924313
3: 0.0174532925191
4: 0.0174532925199
5: 0.0174532925199
6: 0.0174532925199
7: 0.0174532925199
8: 0.0174532925199
9: 0.0174532925199

Thus it's not that the SIN function of the HP-35s is inaccurate for small numbers.

Cheers
Thomas

Naively I tried to trick the 35s by doing $sin(x) = \frac{e^{ix}-e^{-ix}}{2i}$ to no avail. The results were exactly the same.
06-27-2015, 06:10 AM
Post: #28
 Paul Dale Senior Member Posts: 1,475 Joined: Dec 2013
RE: HP35s Revisited Trig Quandary Bug # 2
I'm surprised the results weren't quite a bit worse.

Both exponential terms approach 1 as x approaches 0 and I'd expect there to be some cancellation involved in the numerator.

- Pauli
07-05-2015, 02:13 AM (This post was last modified: 07-05-2015 04:58 AM by Marcio.)
Post: #29
 Marcio Senior Member Posts: 438 Joined: Feb 2015
RE: HP35s Revisited Trig Quandary Bug # 2
(06-27-2015 06:10 AM)Paul Dale Wrote:  I'm surprised the results weren't quite a bit worse.

Both exponential terms approach 1 as x approaches 0 and I'd expect there to be some cancellation involved in the numerator.

- Pauli

Nah. I just tested it. The 35s seems capable of evaluating exponentials with full 12-digit precision, which leads me to think the problem was caused by the use of complex numbers instead.

Marcio
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