A square table (a meter a side) has two spheres on its surface. The spheres have two special properties:

1. The larger is twice the diameter of the smaller, and
2. They are the largest size that will fit on the table without falling off. (They may extend over the edge of the table.)

I. What are the dimensions of the spheres?

II. A third sphere is added next to the other two. What is its largest possible size?

Not terribly difficult, but very interesting results.

I liked it enough to make a picture.

http://www.mohawk.mtrsd.k12.ma.us/site/dept/math/jgalvagni/perplexpedestal.bmp

The central image is the top view showing the pedestal as a square, the 3 spheres and the points of tangency.

Each of the others is a projection perpendicular to the base of the pedestal and one of the lines connecting the centers of two spheres.
(The upper center is the solution for part I, the upper left and bottom together show part II, the upper right is just another projection)

Posted by Jer on 2005-06-20 17:09:20