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
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)
---------- From: Charles J. Masenas[SMTP:firstname.lastname@example.org] Sent: Friday, October 31, 1997 10:35 AM To: Ron Ferguson Cc: email@example.com 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?