Rafed English

Nine Squares in One

By : Ali R. Amir-Moez

Have you ever wanted a perfect tic-tac-toe grid? Here's a clever way to divide a square into nine smaller squares of equal size.

Start by cutting out a square from a rectangular sheet of paper. Use a pencil to mark the corners of the paper P, Q, R, and S.

Pull the corner P down to the side SR. Carefully fold the paper so that the side SP is even with SR and a crease goes through corner S.

Then cut off and discard the extra piece of paper, which is to the right of the folded part. (This area is shaded in the diagram.) What is left is a square.

I believe you can think of a way to divide this square into four equal squares. Can you see any way to divide it into nine equal squares? You may want to try to figure out this problem for yourself. If you can't, try my way.

Here's how to do it. Erase the labels P and S, then mark the corners of the square A, B, C, and D.

In the process of making the square, you have already made a crease along a diagonal. In the diagram this diagonal is the line BD.

By folding the side AB carefully, you can get its midpoint. Label this midpoint L. In the same way, find the midpoint of the side DC and call it M. Use a ruler or straight edge to draw the lines LC and AM. These lines cut the diagonal BD at two points. Label them E and F.

Now fold the paper to create two creases through E. Make one crease parallel to side AD and the other crease parallel to side DC.

Fold the paper again to create two creases through F—one parallel to side AB and the other parallel to side BC.

These four creases outline nine small squares all the same size. Of course, to play a lot of tic-tac-toe, it's more fun just to draw the grids. They're not perfect, but they work fine.

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