Math Problem of the Month

PROBLEM OF THE MONTH

November 2004

Is it possible to cover the entire plane by the interiors of a finite number of parabolas? If so, how? If not, why not?

By the "interior of a parabola", we mean a region in the plane similar to the set of points satisying the equation

y &ge x². You are free, however, to rotate, translate, rescale, and overlap the parabolas in any way that you want.

This month's prize will be award to the best explained, correct solution.

Submit your solution to the Mathematics Undergraduate Office (Math P-142) or electronically to Prof. Kudzin at problem@math.sunysb.edu by the due date. Acceptable electronic formats are: PDF, Postscript, DVI, (La)TeX, or just plain text. Please include your name and phone number, or preferably your email address.

Closing date: December 1st at 12 pm.