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Posted on December 22, 2013

… Think I’ll put together a pdf-with-audio of my Little Explanation of pi r squared.

I’ve seen students absolutely certain that the area of a triangle is length times width, because That Is The Area Formula, Thank YOu.

Sometimes, fortunately, review of what area means and a little visual manipulation to show that all triangles can be expressed as halves of rectangles helps.

It has also helped to go over just what “r” means for the circle (because students think it’s unfair that we have extra terms — diameter and radius)… and how really, “r x r” is doing the same job of saying how far in the x and y dimensions, respectively, our little shape is going.   If we just stopped at “r squared,” though, we’d have the area of a square, not a circle, and… it would only be 1/4 the size of the whole shape we’re looking at.   Fortunately somebody figured out what number that’s a little smaller than four — becaue the curve of the circle slices off parts of that square — we can multiply by to get to as exact a calculation as we’ll need.

(Which reminds me, also, that a *good* visual explanation of those silly problems where you have to “Figure out the shaded area” and subtract a little thing from teh whole area is also in order.)