f(t): Help Me With Some Algebra

f(t): Help Me With Some Algebra

Given a chord AB and the intercepted arc S, is it possible to find radius r algebraically? (problem stated at f(t)) The consensus there seems to be no, due to the transcendental nature of sin(x).

But I find it interesting that r could be constructed with a compass and straightedge. However, I feel like I'm cheating with Geogebra since I had to place C in order to draw arc S. So I really wasn't given S; I picked one based on C. Circular logic! (that's a little math joke ... ha ha ha.)

Update: http://www.mathforum.com/dr.math/faq/faq.circle.segment.html#1 Dr. Math has a nice page about solving circles given arbitrary parts. They reinforce the idea that this is a problem with numerical-only solution. Their solution involves Newton's Method, something I myself am not very well versed in these days!


Kate said...

well...yeah...you already knew where the center was, right, to construct your arc? so the radius is given, in your sketch. (unless I'm missing something, I don't know Geogebra, but I'm familiar with Sketchpad.)

In my problem, I would like to be able to say: the arc is 12 inches long, the chord is 36/pi inches long, what is the radius and angle?

Scott said...

Geogebra is nice because it is free, web-based, and open source. Your students can access it from any computer that can run Java applets on webpages.

I have small compilation of applets I've created here: http://scottfarrar.googlepages.com/

So, yes I had to specify the radius in order to draw the arc. So it is cheating... (otherwise how would Geogebra know the curvature?) Its rather a strange thing to know the arclength and chord length but not the angle or radius. Could such a predicament exist without being esoteric? I wonder...