Suppose I have a disc and am able to measure it's diameter and its
circumference with complete accuracy using a unit of measurement as small
as I like. If I choose a small enough unit of measurement I will get a
whole numbers for both the diameter and circumference.
The moment I choose ANY radius to draw a circle, its diameter, as also its
circumference, are fixed. This ambiguity shall continue, so lonag as *a line
is NOT defined, which is made from infinite points*.
I had given THIS poser, during a heated discussion on Pi at INSA, New Delhi
- some time in mid-70's.
I recall DR BK Nayyar/BV Subrayyappa was then Secretary, at National Science
Academy, Delhi.
Brij Bhushan Vij
(Thursday, Kali 5106-W41-04)/D-028 (Saturday, 2006 January 28H11:21(decimal)
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Telephone: +001(201)684-0191
From: Pat Naughtin <[EMAIL PROTECTED]>
Reply-To: [EMAIL PROTECTED]
To: "U.S. Metric Association" <[email protected]>
Subject: [USMA:35897] Diameter and distance
Date: Sat, 28 Jan 2006 18:19:44 +1100
Dear Phil and All,
Recently, I visited a Sunday Market where, amongst a lot of junk, I found a
measuring instrument that I think is called a trundle wheel. It has a small
wheel that is geared to turn a four digit indicator and it measures in
metres.
Four digits means that it can be used to measure up to 999.9 metres. I
tested it over a measured (with a tape) twenty metre path and it seems to
be
accurate enough for approximations.
However, I have a problem. The little wheel that drives this device is
exactly 142 millimetres in diameter and I can't figure out out why this
value might have been chosen because the 142 millimetre wheel has a
circumference of 446.1 millimetres and this seems to me rather an odd
value.
Cab anyone help?
Cheers,
Pat Naughtin LCAMS (USMA), Member NSAA*
PO Box 305, Belmont, 3216
Geelong, Australia
Phone 61 3 5241 2008
Pat Naughtin is the editor of the free online monthly newsletter,
'Metrication matters'.
You can subscribe by going to http://www.metricationmatters.com/newsletter
* Pat is the editor of the 'Numbers and measurement' chapter of the
Australian Government Publishing Service 'Style manual for writers,
editors and printers', he is a Lifetime Certified Advanced Metrication
Specialist (LCAMS) with the United States Metric Association, a member of
the National Speakers Association of Australia and the International
Federation for Professional Speakers. For more information go to:
http://metricationmatters.com
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On 28/01/06 7:53 AM, "Philip S Hall" <[EMAIL PROTECTED]> wrote:
> Jon
>> In one of your documents you say: "Since by definition the value for
Pi
>> is the ratio between the circumference of the circle to its diameter,
it
>> must be representable in the form a/b ..."*
>> *
>> This is your fundamental mistake. The *vast* majority of numbers are
>> simply not expressible as integer ratios. Pi is just one of those.
>>
>> There is no pair of integers (p, q) such that p/q = pi. None.
>
> As a matter of interest Jon, how would you answer this challenge if
someone
> put it to you:
>
> Suppose I have a disc and am able to measure it's diameter and its
> circumference with complete accuracy using a unit of measurement as
small as
> I like. If I choose a small enough unit of measurement I will get a
whole
> numbers for both the diameter and circumference.
>
> If I divide the measured circumference by the diameter I will get a
rational
> number. So how come pi is irrational?
>
> Phil Hall
>
