Thanks! Vi was fine.

]]>There are those who believe that life would be better if pi had been defined as circumference divided by radius rather than diameter divided by radius. Then there would be pi radians in a circle rather than two pi, which might make this lesson a little more obvious (perhaps too obvious?).

Since pi has already been defined, some people have defined tau as circumference divided by radius, so tau equals two pi. There’s even a website dedicated to it, tauday.com

On it, you can find The Tau Manifesto, which mentions all sorts of science and math things that use two pi.

Tau, of course, changes the nice simple formula for the area of a circle, turning it into one half tau r squared. Though I kind of like the way that points to the commonality of formulas like that. The derivative of kinetic energy (one half m v squared) is momentum (m v). The derivative of distance (one half a t squared) is velocity (a t). The derivative of the area of a circle (one half tau r squared) is its circumference (tau r).

Vi Hart has a nice little video (though she may not be to your taste):

I can imagine.

Sandwich with the crust removed? Peeled orange slice? Egg white versus yolk? Wrapping paper around a present? Dust jacket on a book?

]]>In answer to your first question, I try always to have a good introduction to each new concept. But I still do straight lecture/discussion, too.

Yeah, I wonder if there’s a more intuitive way to do circumference. If you had any idea how often kids get that screwed up with area. It’s amazing.

]]>Sorry, “diameterans”, not “circumferans”.

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