Problem of the Week 1190

Spin the Cube

Take a cube and attach a piece of string to one vertex. Then hold the other end of the string so that the cube dangles down. Now spin the cube along the vertical axis through the string.

Assuming the cube is spinning fast, and that you are viewing it from a distance, with your eye level with the horizontal plane that bisects the cube, what will you see? I.e., what is the projection of the union of all the rotated cubes onto a vertical plane?

Irrelevant aside: That central plane cuts the cube in a regular hexagon.

© Copyright 2014 Stan Wagon. Reproduced with permission.

[View the solution]

8 September 2014