Bell-curve distribution wanted

For a simulation that I'm doing, I'd like to be able to generate
pseudo-random numbers with a "bell curve" distribution. My only
course in probability and statistics was one semester in high
school, in the late 1960s, and I didn't pay attention.

Given a random number in the interval [0.0,1.0], I can generate a
number in the interval [-1.0,1.0] that's somewhat more likely to
be in the middle than at the ends by simply multiplying it by its
absolute value. Cubing it will, of course, squeeze its distribution
in towards the center even more.

I tried walking up and down through the range, driven by coin flips,
but that gives too narrow a distribution if I use more than a few flips.

It seems to me that there must be a function that takes numbers
uniformly distributed over one range and produces numbers distributed
in a bell curve with a given standard deviation. What would a function
that does this look like? It doesn't even have to be exact, if there's
a choice between a complex function that is exact and a simple one
that's close (FSVO "close").

Any suggestions?
--
Michael F. Stemper
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