I first saw this video over at MathFail. It’s cute, and I have to admit, kind of cool.
But anything this simplistic always sends me into skeptical mode.
Before we go any further, check it out:
Do you believe it?
This might be the question to start a discussion with a student. It’s certainly the first question that comes to my mind.
If it were really this simple, wouldn’t we have used it to “prove” the formula for the area of a circle much earlier?
What’s wrong with it?
For the “proof” in the video to work, you have to assume (or believe) that the circumference is 2πr. This seems a bit cheesy to me, since that formula is as complex as the one we’re trying to prove. Not to mention quite closely related. But I’ll let this one go.
The thing that really bothers me is that they use only a few chains – each of which has thickness.
If you filled the inside of a circle (a disk) with concentric circles, none of those circles would have a thickness. In fact there’s an infinite number of those circles.
Is it realistic to take each of those circles and fold them out and get a triangle?