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'[OT] measurement accuracy and such'
2005\12\02@113822 by William Chops Westfield

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On Dec 2, 2005, at 7:55 AM, Olin Lathrop wrote:

> There's enough public misundertanding about this concept that it's
> important
> (in fact irresponsible not to) for us engineers and scientists to
> state it
> correctly.  This sort of erroneous statement and imprecise use of terms
> needs to be squashed whenever possible to avoid even more confusion and
> misunderstanding by non-technical people.

Yeah, I found the whole discussion back in Jr High about precision and
significant digits very enlightening, and try to keep it in mind.  The
public misunderstanding shows up pretty clearly when you get something
like conversion from english fractional units to metric decimal units.
1.5875  mm indeed.  Hah!

BillW

2005\12\02@140512 by Gerhard Fiedler

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William ChopsWestfield wrote:

> 1.5875  mm indeed.  Hah!

Yes! I needed to read that... and then they say that 1.5875 mm is not as
"round" as 62.5 mil :)

Gerhard

2005\12\02@141444 by Mike Hord

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> > There's enough public misundertanding about this concept that it's
> > important
> > (in fact irresponsible not to) for us engineers and scientists to
> > state it
> > correctly.  This sort of erroneous statement and imprecise use of terms
> > needs to be squashed whenever possible to avoid even more confusion and
> > misunderstanding by non-technical people.
>
> Yeah, I found the whole discussion back in Jr High about precision and
> significant digits very enlightening, and try to keep it in mind.  The
> public misunderstanding shows up pretty clearly when you get something
> like conversion from english fractional units to metric decimal units.
> 1.5875  mm indeed.  Hah!

Yep.  Ask a smart-alec high school student what the value of pi is,
he'll say "3.1415926535897932384626433832795" and be pround of
how many decimal places he knows.

Six years later, after engineering school, he'll say "3.14".  Twenty
years later, he'll say "about 3".

The art in engineering lies in knowing when to use each one of those
answers.

Mike H.

2005\12\02@143934 by David Minkler

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Mike Hord wrote:

>Yep.  Ask a smart-alec high school student what the value of pi is,
>he'll say "3.1415926535897932384626433832795" and be pround of
>how many decimal places he knows.
>
My little sister could do better than that in Junior High School.

3.14159265358979323846264338327950288419716939937510

Dave


2005\12\02@150510 by Spehro Pefhany

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At 11:42 AM 12/2/2005 -0800, you wrote:


>Mike Hord wrote:
>
>>Yep.  Ask a smart-alec high school student what the value of pi is,
>>he'll say "3.1415926535897932384626433832795" and be pround of
>>how many decimal places he knows.
>My little sister could do better than that in Junior High School.
>
>3.14159265358979323846264338327950288419716939937510
>
>Dave


Not that I memorized this, but..

3.141592653589793238462643383279502884197169399375105820974944592
30781640628620899862803482534211706798214808651328230664709384460
95505822317253594081284811174502841027019385211055596446229489549
30381964428810975665933446128475648233786783165271201909145648566
92346034861045432664821339360726024914127372458700660631558817488
15209209628292540917153643678925903600113305305488204665213841469
51941511609433057270365759591953092186117381932611793105118548074
46237996274956735188575272489122793818301194912983367336244065664
30860213949463952247371907021798609437027705392171762931767523846
74818467669405132000568127145263560827785771342757789609173637178
72146844090122495343014654958537105079227968925892354201995611212
90219608640344181598136297747713099605187072113499999983729780499
51059731732816096318595024459455346908302642522308253344685035261
93118817101000313783875288658753320838142061717766914730359825349
04287554687311595628638823537875937519577818577805321712268066130
01927876611195909216420199

Maple (developed at University of Waterloo) and the symbolic
engine in Matlab can do a lot of things. We use things like
matrix condition numbers to bound errors in critical
calculations-- it's not so easy to estimate errors in complex
calculations even with linear systems.

http://www.cse.uiuc.edu/eot/modules/linear_equations/condition_number/

Note the effect of changing the matrix A to represent two almost
linearly dependent equations. I imagine every engineer spends at least
one undergraduate semester mostly on this subject.

>Best regards,

Spehro Pefhany --"it's the network..."            "The Journey is the reward"
spam_OUTspeffTakeThisOuTspaminterlog.com             Info for manufacturers: http://www.trexon.com
Embedded software/hardware/analog  Info for designers:  http://www.speff.com
->> Inexpensive test equipment & parts http://search.ebay.com/_W0QQsassZspeff


2005\12\02@163739 by Russell McMahon

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>>>Yep.  Ask a smart-alec high school student what the value of pi is,
>>>he'll say "3.1415926535897932384626433832795" and be pround of
>>>how many decimal places he knows.
>>My little sister could do better than that in Junior High School.

A good enough answer for every "everyday" situation you will ever meet
is:

- remember the sequence 113355 (shouldn't be hard :-) ).

- Divide 355 by 113

- 355/113 = 3.141592920...

Accurate to better than 1 part in 10^7.


       RM




2005\12\02@175803 by olin piclist

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Russell McMahon wrote:
> A good enough answer for every "everyday" situation you will ever meet
> is:
>
> - remember the sequence 113355 (shouldn't be hard :-) ).
>
> - Divide 355 by 113
>
> - 355/113 = 3.141592920...
>
> Accurate to better than 1 part in 10^7.

Or just punch the PI button on the calculator.  I'm not going to do 355/113
without a calculator, and if I've got one I don't need 355/113.


******************************************************************
Embed Inc, Littleton Massachusetts, (978) 742-9014.  #1 PIC
consultant in 2004 program year.  http://www.embedinc.com/products

2005\12\02@185502 by David Minkler

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Olin Lathrop wrote:

{Quote hidden}

Yes, I always thought it was strange that I should be asked to remember
six digits and perform a division in order to get seven digits of
"accuracy".

Dave


2005\12\03@043426 by Russell McMahon

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flavicon
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> Or just punch the PI button on the calculator.  I'm not going to do
> 355/113
> without a calculator, and if I've got one I don't need 355/113.

For some values of calculator :-).

Often enough the calculators I find in my hand when I want to use Pi
thereon don't have a Pi key. As I have Pi memorised to more places
than that approximation gives it's not an issue for me, but for many
people it's potentially useful.

I always carry a 4 function calculator with square root (which most
calculators have these days) plus a single memory. I carry this one
because it has a hard shell (essential if it is going to survive me
for more than a week), and a large display for it's size and a
reasonably good keyboard.

Occasionally I feel the need to calculate the log of a number -
usually to base 10. Most people find they can overcome such urges but
I sometimes succumb. A usable approximation for log 10 is [where S =
sqrt]

Enter number
SSSSSSSSSSS
-1
=
x 889
=
   Voila / QED.


The first '=' is used to force correct arithmetic precedence as some
calculators trip up on this.

You can take more or less sqrts and adjust the constant.
I have found that 11 x sqrt is a best compromise for accuracy. With
infinite precision the more sqrts the better but due to lsd drop off
11 is usually about right.

About 3 parts in 10,000 inaccuracy.

I leave the reason that this works as an exercise for the student
(except Olin, who doesn't need it :-) ).

FWIW - if you remember a very few logs to about 4 digits you can
derive enough others to do a creditably good job of taking the log of
most numbers - enough so that you can perhaps do it in your head while
clinging to the side of a precipice (oe elsewhere), when using a hand
to access your calculator is liable to be life threatening. Whether
you ever would want to will depend on how deeply engrained
engineeringness is in uour psyche.



       RM




2005\12\03@133958 by Sergey Dryga

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Russell McMahon <apptech <at> paradise.net.nz> writes:
> I always carry a 4 function calculator with square root (which most
> calculators have these days) plus a single memory. I carry this one
> because it has a hard shell (essential if it is going to survive me
> for more than a week), and a large display for it's size and a
> reasonably good keyboard.

I also ***ALWAYS*** have a calculator with me, and it is indestructible.  It
has fairly good speed, although as number of digits goes to 4-6 it calculations
tend to take longer.  But at 3-4 digits, especially for numbers in scientific
notation, my calculator beats most other people's calculators.  
What is my calculator?  My head.

BTW, very often calculations made on-the-fly need only 1-2 significant digits
or even just an approximation.  Which is easy and faster to do in head.

> FWIW - if you remember a very few logs to about 4 digits you can
> derive enough others to do a creditably good job of taking the log of
> most numbers - enough so that you can perhaps do it in your head while
> clinging to the side of a precipice (oe elsewhere), when using a hand
> to access your calculator is liable to be life threatening. Whether
> you ever would want to will depend on how deeply engrained
> engineeringness is in uour psyche.

Couple of square root usefull too, e.g. sqrt(2), (3), (4), (5), (7)
just kidding about sqrt(4)!

Sergey



2005\12\03@164713 by Peter

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On Fri, 2 Dec 2005, Olin Lathrop wrote:

>> Accurate to better than 1 part in 10^7.
>
> Or just punch the PI button on the calculator.  I'm not going to do 355/113
> without a calculator, and if I've got one I don't need 355/113.

Imho 22/7 is easy to remember and can be calculated in the head. The
result is within better than 1/2 thousandth of PI. More accurate than
any lanscaping, carpentry, or metal cutting you are ever likely going to
do without something computer assisted.

Peter

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