Mathematics Problem Of the Week

Fall 2005

POW #3

Triangular Circles

Assume that the triangle shown below is equilateral with each side of length 1 and that circles in the pyramid inside the triangle are all the same size and tangent to each other and the triangle.

(a) What is the total area inside the circles when there are four at the base (as shown above)?

(b) Using n circles at the base would mean 1+2+...+n=n(n+1)/2 circles in the pyramid. If we let n go to infinity, will we eventually (in the limit) cover all the area inside the circle?

Due Friday, September 16^th at Noon.

Solutions should be submitted to Dr. R. Lock's mailbox in the Math office or sent via e-mail to rlock@stlawu.edu.