Problem of the Week 1027

Folding Shapes

Let P be any point on a square piece of paper. One at a time, take the corners of the square and fold the paper with one fold so that the corner lies atop P. This will crease the paper along four lines and when you lay it flat, the point P will lie inside some polygon determined by the creases and the edges of the square.

Describe the subset S of the square so that if (and only if) P is in S, the polygon described above is a hexagon. In particular, give the area of S.

© Copyright 2005 Stan Wagon. Reproduced with permission.