Actually I like the circle one. I find it interesting that a program which
mentions only sqrt(x^2 + y^2) produces rational numbers that converge (in a
non-deterministic sense) to pi.
But to give the problem the spice of calculus it could be phrased as the
area under the curve sqrt(1 - x^2) on [0,1].
Perhaps better yet (relative to my own taste, of course) might be the area
under exp((-x^2)/2) (the normal curve if memory serves) from 0 to, say, 100.
Better from the point of view of an open-ended question, with no
algebraically determined answer.
As an afterthought, although I am an expert programmer I don't spend a lot
of time programming calculators. They are too slow, and their programming
"language" is archaic. Better to learn FORTRAN, Pascal, C, or some high
level language, or perhaps Mathematica.
However, to the extent that they have introduced programming to a wider
community, I'm glad these calculators are programmable. And I have had fun
with them - my favorite is a program to simulate the quincunx (if I spelled
it correctly) the thing in which you drop balls through a forest of pegs
and the balls line up at the bottom in a binomial distribution - science
museums have them.
Phil Mahler
Middlesex CC
Bedford, MA
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