... and Learning About The World ... and Learning About The World There are many mathematical ideas joined to special symbols used to
concisely portray them (once they've been understood). One is the ratio
of the length of the boundary or circumference of a circle to its diameter,
the line through the circle center which defines its widest crossing.
That quantity is called and
pronounced by the sound pi.
Finding to greater accuracy
was a significant task in mathematics up to a few hundred years ago.
Adding or multiplying numbers when there is no last item ...
a situation usually summarized in a shorthand way by the word infinite,
leads to two special symbols. The first represents addition; it is:
. The second uses a
special symbol to represent multiplication: 
Adding or multiplying numbers when there is no last item is a little
like the idea of the rabbit trying to catch a snail who has a one mile
head start. The puzzle goes that while the rabbit runs to the half-mile point
the snail moves forward. That means that when the rabbit makes it to the
three-quarter mile point, the seven-eighths marker, etc., there always
will be distance remaining to catch the snail. The same kind of
reasoning led to the view that the continually-smaller circles inside
the increasing-number-of-side polygons in the following figure get to a
smallest circle ... if we go far enough in the process. This idea is
called limit in mathematics.
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