Sticky Spheres
Two unit spheres are trapped inside a rectangular box with a square bottom, which is 4 by 4 units in size. They move around, but each remains in contact with the bottom of the box and at least one of the walls. They are also continuously in contact with each other. When they make their way all the way around the box, the point of contact between them describes a closed curve. Find the length of this curve to three decimal places.
The answer is 6.283.
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1 solution
The curve is made of four quarter circles radius 1, so its length is 2 π ≈ 6 . 2 8 3 .