Pythagoras by folding

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1. 

   1. Two centre lines

   White side up. Fold in half side to side and unfold, then bottom to top and unfold, to mark the middle of every edge.

2. 

   2. Find a third (Haga’s fold)

   Fold the bottom-right corner to the middle of the top edge. Pinch where the folded bottom edge crosses the left edge — one third of the way up — and unfold.

3. 

   3. Thirds across

   Fold the bottom part up along a level line through the mark and unfold. Fold the top edge down to that crease and unfold: three equal bands.

4. 

   4. Another third

   Now fold the bottom-left corner to the middle of the right edge. Pinch where the folded left edge crosses the top edge — one third from the left — and unfold.

5. 

   5. Thirds down

   Fold the left part over along an upright line through the mark and unfold. Fold the right edge to that crease and unfold. The paper is now 9 small squares.

6. 

   6. The first right triangle

   Fold the bottom-left corner over along the line joining the upper mark on the left edge (one third down) to the left mark on the bottom edge (one third along).

7. 

   7. The other three corners

   Go round the square the same way and fold the other corners. Each crease runs from the one-third mark on one edge to the one-third mark on the next. The four triangles cover the tilted square without overlapping and leave a small white square window in the middle.