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From: msissom@dna.metronet.com (Marc Sissom)
Subject: Re: Stapp, PK & Physics Today
Message-ID: <DDs0F3.1Dw@dna.metronet.com>
Organization: DNA Enterprises, Inc.
References: <3vv3q6$2h4@ixnews7.ix.netcom.com> <NEWTNews.808521836.13767.richard.caldwell@oufan.oklaosf.state.ok.us> <41571s$12mi@columba.udac.uu.se> <NEWTNews.809021971.17834.richard.caldwell@oufan.oklaosf.state.ok.us>
Date: Wed, 23 Aug 1995 18:23:26 GMT
Lines: 40
Xref: glinda.oz.cs.cmu.edu sci.skeptic:122262 sci.physics:136346 sci.math:115337 comp.ai:32765

In article <NEWTNews.809021971.17834.richard.caldwell@oufan.oklaosf.state.ok.us>,
Richard Caldwell  <richard.caldwell@mhs.oklaosf.state.ok.us> wrote:
>
>In article <41571s$12mi@columba.udac.uu.se>, <m94jbr@sirius.tdb.uu.se> writes:
>
>> Richard Caldwell (richard.caldwell@mhs.oklaosf.state.ok.us) wrote:
>> : phenomenon, but on the simple geometric equation for the surface area of a 
>
>> : sphere.  Geometry, being abstract and not hobbled by the messiness of
>> : reality,  has simple equations with exact values like 2, and totally
>> : inexact values like pi.
>> 
>> What do you mean? pi is just as exact as the number 2, or any other number.
>> Last time I checked, it began something like 3.141592653589793... Of course,
>> if you try to physically measure pi, you won't get an exact result, but
>> that's something different. 
>
>The 2 is an integer and, therefore, a rational number whose value is know 
>exactly.  Pi is an irrational number.  Therefore, although we can calculate it 
>to any desired precision, it is not an exact value like a rational number is.
>
I think that you are having difficulty in separating some concepts. Exact
does not directly relate to precision or accuracy. Pi is exact. Its value
does not vary. The fact that you cannot produce an exact representation
of it(other than Pi or some formula) does not matter. It is just as
exact as "e" or 2. All of the numbers mentioned can be calculated and
displayed(represented) to any desired precision. The "rationalness" or
"irrationalness" has nothing to do with it. The repetitive or nonrepetitive
sequences that occur when a number is represented in base 10 have nothing
to do with it. Try to display one-third in base ten. It is a rational number
yet you cannot display its exact value except as 1/3. If on the other hand,
you choose base 3, then it is easy.

   1/3(in base 10) = 1/10(in base 3) = 0.1(in base 3)

Pi has an exact value. Those that understand what the symbol "Pi"
represents, also comprehend its meaning. The fact that it is not
possible to represent it using a sequence of numerals does not affect
the actual, exact value of the number that is commonly known as "Pi".

