On Fri, 05 Sep 2008 23:12:36 -0500, John J wrote:
>Art wrote:
>> On Fri, 05 Sep 2008 07:48:58 -0500, John J wrote:
>>
>>> Art wrote:
>>>
>>>> 22/7 = 3.1428 ...
>>>> pi = 3.1415 ....
>>>>
>>>> As you can see, they fail to be equal at only the third decimal place.
>>> Question: how does the presumed precision of Pi (that is, Pi to 4
>>> decimal places) function in terms of, say, machining some parts that all
>>> use Pi, for example a series of different sized wheels that must
>>> interact to function properly as a machine? That is, if the largest
>>> wheel is, say 100 times larger than the smallest, with n number of
>>> wheels between, does choosing 22/7 over 3.1415 make a significant
>>> difference? And if the wheels interacted as toothed gears, does that
>>> change anything? (The later is clearly fractionalized.)
>>
>> Ok, so some clown comes along and claims that the magic number 3
>> is the secret of the universe since it equals pi. You say that's close
>> enough ... that's wonderful ... you've found the secret of the
>> universe :)
>>
>> The point is that "equals" has mathematical (and logical) meaning,
>> and since 22/7 <> pi the guy made a false statement. He didn't
>> say "approximately equals" since he obviously enjoys deluding himself
>> with a bunch of worthless numerical mumbo jumbo.
>
>You did not address my post. I don't know why you included it.
And I don't know why you asked a question that obviously has as
the only possible answer, "it depends". Whether or not fourth
significant digit precision is important depends on details and
requirements you did not specify. If a engineer is designing
some inexpensive plastic toy having molded gears, great imprecision
is both expected and quite tolerable. If a engineer is designing
a computer, he/she will no doubt have as a goal computation
precision far in excess of a mere four significant decimal digits.
If a engineer is desgining a scientific instrument to be used
for measurement purposes, he/she may require that the
model shop and toolmaker go to extraordinary lengths to
acheive precisions that exceed four decimal digit accuracy
in the circumference of a disc used in the instrument.
Art
http://home.ptd.net/~artnpeg
