|nahtmmm||Jul. 24th, 2009 12:15 pm Everybody likes circles. Let's do a circle problem|
In the Cartesian plane, draw a circle of radius r = 0.1 centered at (1, 0). Also draw identical circles centered at each of (0, 1), (-1, 0), and (0, -1).Leave a comment
Define a function P(R) such that, if a circle C of radius R is drawn centered at the origin and a point (x1, y1) on (but not within) circle C is randomly chosen, P(R) equals the probability that (x1, y1) lies on or within any of the smaller circles.
1. Is the shape of P(R) symmetric or asymmetric? (If you plot P as a function of R, will the line you draw have any axes of symmetry?)
2. For what value of R does P(R) reach a maximum value?
3. What is P(R)'s maximum value?
Extra credit: Generalize your solution to apply to all values of r.