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1. A first guess: 1/8
White side up; we will divide the bottom edge into seven. Fold the right edge to the left edge and unfold (1/2). Fold the left edge to that crease and unfold (1/4). Fold the left edge to the newest crease and unfold (1/8).
2. Another round
Fold the right edge to the 1/8 crease and unfold (close to 4/7). Fold the left edge to that new crease and unfold (close to 2/7). Fold the left edge to the newest crease and unfold (close to 1/7).
3. The last round
Repeat the same three folds once more: right edge to the newest crease, left edge to the new one, left edge to the newest again, unfolding each time. Now you have creases at 1/7, 2/7 and 4/7.
4. Make 3/7
Fold the left part over so that the 2/7 crease lies exactly on the 4/7 crease, then unfold. The new crease is 3/7.
5. Make 5/7 and 6/7
Fold the right edge to the 3/7 crease and unfold (5/7). Fold the right edge to the 5/7 crease and unfold (6/7). All six creases that split the edge into sevenths are made.
6. Stand it up like a folding screen
Fold the six creases from 1/7 to 6/7 into valley and mountain folds in turn, and stand the paper up like a folding screen: seven panels of the same width.
1. A first guess: 1/8
White side up; we will divide the bottom edge into seven. Fold the right edge to the left edge and unfold (1/2). Fold the left edge to that crease and unfold (1/4). Fold the left edge to the newest crease and unfold (1/8).
Tip:
Finished!
Well done! Watch it again or try another model.
The maths
- Folding the right edge to a crease at x makes a new crease at (1 + x) ÷ 2; the left edge makes x ÷ 2. One round (right, left, left) turns x into (1 + x) ÷ 8. Only x = 1/7 stays where it is, so the creases gather at 1/7.
- Each round makes the error 8 times smaller. On a 15 cm sheet the first guess, 1/8, is about 2.7 mm off; after one round about 0.3 mm, after two less than 0.05 mm.
- Written in binary, 1/7 is 0.001001001… Read it right to left with 1 = “right edge” and 0 = “left edge”, and you get exactly the folding order.