Re: [HM] base 5, base 3
Prof. Lueneburg (luene@mathematik.uni-kl.de)
Tue, 13 Apr 1999 15:49:38 +0200 (MESZ)
Ed Sandiver wrote:
>
> I learned a base 3 arithmetic using the digits +1, 0 and -1, from
> R. W. Hamming at the University of Pennsylvania in the summer of 1967.
> At the time, he thought that perhaps core memory could be designed to
> have either no magnetic field, a clockwise one, or a counterclockwise
> one, and so that perhaps this base 3 arithmetic would become the
> "natural" base for computer applications.
>
> To my knowledge, he was only wrong about a very few things.
>
> Ed Sandif
The possibility of representing numbers using the digits +1, 0, -1 in base 3
is implicit in the solution of the so-called Bachet's weighing problem in so
far, as one can put the weights 1, 3, 9, 27, 81, ... in either pan of the
balance. Actually, this problem was already solved by Fibonacci in his liber
abbaci (p. 297 in the Boncompagni edition). The reference to Bachet is:
Problemes plaisans et delectables qui se font par les nombres. 2nd ed.
Lyon 1624, pp.215-219. (The original title has no accents and plaisans no t.)
I have not seen the first edition. I presume that the weighing problem is
already there.
Heinz Lueneburg