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Post date: Jan 28, 2011 9:02:09 PM
Circle Chords & Cutting Planes
January 27, 2011
NOA 1.102
presented by
Jason Ermer
When we put n points on the boundary of a circle and connect all pairs of points, we divide the circle into regions. If no more than two line segments meet at any one point, how many regions will there be?
Trying this for n = 1, 2, 3, 4, and 5, we see a nice pattern emerging. However there is an unpleasant surprise in store when we test our conjecture for n = 6. This problem is a nice example of why we must be careful when generalizing from special cases to the general case. It is also a challenge to find and justify the real pattern at work here!
2 hours CPE credit through UT
2 hours GT credit through TAGT
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