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 says:

    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 says:

    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…