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Topic: irrationals
Replies: 25   Last Post: Nov 4, 1997 7:57 PM

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Chi-Tien Hsu

Posts: 144
Registered: 12/6/04
RE: irrationals
Posted: Nov 4, 1997 7:57 PM
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The problem is how to define a uniform grid and label the numbers between
0 and pi.

In addition, I hope one realizes that the identity

10-3=.314159....

is neither in base 10 nor in base pi. It is interesting to see what base system
it belongs, if there is any!

If it is possible to establish a base pi number system, then
0.abc = a*pi^(-1) + b*pi^(-2) + c*pi^(-3)

Chi-Tien

----------

----------
From: Charles J. Masenas[SMTP:u6420@btv.ibm.com]
Sent: Friday, October 31, 1997 10:35 AM
To: Ron Ferguson
Cc: math-teach@forum.swarthmore.edu
Subject: Re: irrationals

Message Dated: 30 Oct 1997 14:49:00 EST
>> Here is my problem. If pi is the base, I can imagine integer powers
>> of pi, but for the life of me, I cannot imagine appropriate "digits"
>> to use in such a numeration system. Maybe I missed the point of the
>> original post, or perhaps the idea of unit length was confounded with
>> the idea of a numeration system. The numeration system should only
>> change the representation (appearance?) not the value of a "number."
>> On the other hand how do we select a unit measure for constructions?
>> If we want to begin with a unit of pi, do we have to first select
>> another unit, use it for a diameter to construct a circle from which
>> to peel the unit pi? Then is there a "hidden" unit inside our unit
>> selection? Wow! I wish I could imagine this better? :-)


How about counting 0, 1, 2, 3, 10,... where regrouping is done in units of
powers of pi. The unusual thing is that 10-3 = .14159... This system
requires regrouping very different from what we are used to. But, isn't
it possible?

-------
Regards,
Charles J. Masenas








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