
RE: irrationals
Posted:
Nov 4, 1997 7:57 PM


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
103=.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)
ChiTien

 From: Charles J. Masenas[SMTP:u6420@btv.ibm.com] Sent: Friday, October 31, 1997 10:35 AM To: Ron Ferguson Cc: mathteach@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 103 = .14159... This system requires regrouping very different from what we are used to. But, isn't it possible?
 Regards, Charles J. Masenas

