## Tuesday, June 11, 2013

### Links: How to Learn Math, WSJ Mentions Me

Jo Boaler wrote What's Math Got to Do With It, which is an excellent book (with an unhelpful title). This summer she will be conducting a free online course through Stanford Online.

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I wrote a guest post for MathBabe, which is a modified (hopefully improved) version of my post last October on Proving the Pythagorean Theorem. The day after she posted it, the Wall Street Journal made it the headline piece for their Train Reading blog series. (I got almost double my usual traffic yesterday. Nothing like the spike I imagined.) What fun.

1. Wow, congrats on getting in the WSJ!

2. Did you ever get around to figuring out the centroid question? I think you can make a reasonable argument based on angular momentum that the mass needed to balance should be less as you get farther away from the fulcrum/centroid, but not necessarily why it would be linear with distance.

3. I never did.

Your suggestion sounds interesting. I'm slow with physics (or with not enough sleep). Can you help me see why that must be so?

4. If one wants to impose a rotation on an object about some axis, one has to apply torque (rotational force) proportional to the moment of inertia. Depending on how much physical intuition (or Physics) your students have, they might know that if you keep the mass the same, but reduce the radius, a spinning object will speed up to preserve angular momentum. (e.g. when figure skaters do a spin, you can visibly notice this as they pull their appendages closer to the axis, the angular velocity increases)

In the limit, one could imagine that trying to rotate an object that only has mass along the rotational axis should require 0 force, because no mass is actually being pushed around anywhere.

I think it would be reasonable to infer then, that more torque needs to be applied as the mass is moved away from the rotational axis. (Maybe the limit argument is actually sufficient, if one is allowed to assume that torque as a function of distance from the axis is monotonic.)