Chord Star 3: Remote Radii

remoteRadiusTeaserSuppose you find some big curved thing out in the world. Some things are curved more tightly than others. But how much more? How can we put a number on how tightly curved something is?

One way is to figure out the radius of curvature. The smaller the radius, the tighter the curve. (Would you tell students this at the beginning? Of course not. But I can’t describe how this can work without giving things away. So consider this a report on my own investigation.)

Let’s apply what we learned two posts ago. To review, we found out that if you pick a point inside a circle, and run a chord through it, the point divides the chord into two segments. The lengths of those segments are inversely proportional, that is, their product is a constant—it’s the same no matter which chord you pick.

Then, last time, we saw how that product varies with the point’s distance from the center.

Let’s see how we can use this to measure radii of curves out in the world. The cool thing is that we can do this remotely. Unlike most radii in school geometry, we can figure out the radius of curvature without ever finding the center of the circle.

The picture above is a hint. If that’s enough for you, don’t read further! Go do it! Continue reading Chord Star 3: Remote Radii

Advertisements