So a while ago, I mentioned to some of you on twitter that I was getting really frustrated with a particular problem we were presented with. I have a conjecture that I’m almost certain is true, but I can’t prove it.
Consider the unit circle . Plot equally spaced points on the circle starting from . Now draw the chords from to the others. What is the product of the lengths of all of these chords?
(There is an extension problem, which is changing the unit circle to an ellipse , for those who already have seen or find the original problem too easy.)
So feel free to write your own blog post with your solution, or throw your solution in the comments (just write SPOILER at the top so we know…).
What I’m interested in is if we could get a precalculus class to get the solution to this problem. Where they actually understand it. So if you had, say, 15 non-honors precalculus students and one week to work on this problem, how would you design the lesson?
I guess you have to have solved it or have seen a solution to know how to design the lesson. But even if you didn’t solve it (a la me!)… if there’s a solution you’ve read that someone posted in the comments… what would you do?
UPDATE: Mr. Ho has a great GeoGebra applet at his site; Mimi has some nice colorful diagrams and some explanation up at her site. Also, for those who want to wording for the ellipse problem… This extension I haven’t seen before, so I am citing Bowen Kerins (see comments below!) or Darryl Yong: “Take the diagram you drew in [the unit circle problem] and stretch it vertically so that the circle becomes the ellipse . All the points for the chords scale too. What is the product of the lengths of all of these chords?”