[HM] Roman Numerals
Ralph A. Raimi (rarm@math.rochester.edu)
Tue, 11 May 1999 15:15:16 -0400
Around 1960 I was asked to address a group of high school math
teachers who were attending an NSF-sponsored Summer Institute here. I was
a "Visiting Speaker", one of a series, for all that I lived here too.
The NSF would pay for anything in those days, if it was called "new math".
I asked Jerrold Zacharias, a well-known physicist I happened to
know, and who himself was in charge of an important curriculum project in
physics called PSSC, what I ought to tell the teachers about. He said,
"Give them something they can use," by which he meant use *in their
teaching*, and not just as an addition to their "higher" mathematical
culture.
So I junked my speech about the isomorphism of vectors in the
plane and the solutions of x"+x=0, and the polar and rectangular form of
solutions of the latter, and decided to tell them how to multiply in Roman
numerals. I had never heard of a paper on the subject, and I certainly
didn't try to write one of my own. I just invented what I thought would
be convenient, to show how knowing the products from I*I to IX * IX, and
some simple additions, could be strung together via the distributive law
to obtain all products whatever.
What was cute was that since X already meant ten, I decided it
would be nice to write all numbers as polynomials in X, with coefficients
I through IX, and use what was familiar as polynomial multiplication to
get ordinary products, later replacing X^2 by C, etc. "Long division,"
too, though I didn't burden them with details about division, which as I
recall takes a lot more bookkeeping. The lecture went over very well, with
many students coming up afterwards with questions, especially about
pedagogy. They really intended to "use" it. They also wanted to know how
I found out the Roman method. I should have said I did it the way any
historian does, by guessing.
I doubt that the Romans used polynomial *notation*, but surely the
abacus models polynomials in that particular X.
Ralph A. Raimi Tel. 716 275 4429 or (home) 716 244 9368
Dept. of Mathematics FAX 716 244 6631
University of Rochester Webpage http://www.math.rochester.edu/u/rarm
Rochester, NY 14627 (Webpage contains links to papers)