[USMA:35897] Diameter and distance

[Pat Naughtin]

Title: Diameter and distance

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
>