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Re: [Phys-L] playing for keeps



Even at an introductory level, students should be able to follow an explanation based on "units". (Well, it's dimensional analysis, but I don't tell them that.)

Which (A or C) is 2 pi r, which is pi r^2? Well, which one has units of length , which has units of length squared? Oh, area is the one with r^2, circumference is the one with r. Ok.

Same for the volume and surface of a sphere: 4 pi r^2 and (4/3) pi r^3.

Of course, if the students are in or have taken calculus, we go into _why_ the edge _must_ be the derivative of the interior....

KC

-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of Bruce Sherwood
Sent: Saturday, 29 June 2013 5:18 PM
To: Phys-L@phys-l.org
Subject: Re: [Phys-L] playing for keeps

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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