circle – MathFour

Area of a Circle vs. Area of a Triangle

Inspire your kids to think about how circles relate to triangles!

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?

Can you use it to teach?

I believe the makers of the video intended this to be a fun way to remember the area formula of a circle.

But the video would be better used to allow students to ponder the relationship of a circle to an isosceles triangle.

What do you think?

Are you okay with this video? Are you as skeptical as I am, or am I a little too sensitive?

Share your thoughts in the comments or on twitter/x!

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December 31, 2012

GeoGebra – Overcoming the Fear

This is the 5th in the draft purge series where I’m throwing stuff out over a three week period.
One month after starting MathFour.com, I came across an article about GeoGebra. I was quite taken by the software, but a little overwhelmed.

I’m not much into technology — at least when it comes to math. So the power of the tool was much more inhibiting for me than it was empowering.

So the review of it stalled.

Indeed this article was first “drafted” back in March of 2011 — more than a year ago. It only had the link to that article in it. Not much of a draft.

Lucky for us, math is math. It doesn’t change much over a year (or even a few hundred years).

So GeoGebra is pretty much as useful (and as scary) as it was a year ago.

But like all good heros, leaders and people stupid enough to think they might be either, I’m diving in. Regardless of my fear.

First: Get out the users’ manual.

So I found the GeoGebra Quickstart guide and started reading. I downloaded GeoGebra and cranked it up.

The Quickstart has three examples to try. The first one is un-intimidating — merely involving a triangle and a circle.

So I did it.

And I can share it, too!

Turns out you can “share” your work on GeoGebra — those guys are pretty clever, I must say!

Click here to see my first ever attempt at GeoGebra goodies. Notice I named my triangle vertices and the center of the circle with real names — fun!

The Circle Triangle Dance

Following the directions, I learned about the Move Tool. Which means you can move just about anything — the whole triangle, the circle or any of the vertices!

Check out the “dance” I did with my circle and triangle: