I rather like algorithms especially those that operate in computers and calculators, etc. Very practical, ingenious mathematics which is, for the most part, fairly availiable to a trig student. I even demo Newton's method for square roots in Algebra I for fun. Along that line I just got a great book "Projects in Scientific Computation" by Crandall. Great!!!
But my question. Has anyone ( outside of a programming class) ever presented the algorithms utilized in a calculator ( of course, the precise ones might be difficult to pinpoint) as an example of very practical mathematics? For fun I have given problems that are essentially impossible on a calculator and quite easy with pencil and paper to indicate some of what is going on. And the business with Intel ( I mean how it was determined that there was an error, what it was, and how to 'patch' it) was quite interesting.
I remember when I first realized that numbers in the Handbook of Chemistry and Physics were actually computed by fairly accomplished mathematicans :). Fascinating history!
There is even a history of multiplication and division algorithms which appear and reappear at all levels in mathematics.