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Good engineering and science students at good universities
have memorized the formulas C = 2*pi*R and A = pi*R^2 but
often do not know which applies when to what, nor that there
is any connection to things they really do know. It would be
awfully useful somewhere to start with the circumference
being about 4*(2R) = 8R (the circumference of the bounding
square) and then see that this is only a bit bigger than
2*pi*R, and to start with the area being about (2R)^2 = 4R^2
(the area of the bounding square) and then see that this is
only a bit bigger than pi*R^2.
An example of confusion is the frequently seen A = 2pi*R^2.
Bruce
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