Thirds without a ruler (Haga’s theorem)

One corner fold finds an exact third. Use it to fold the paper into three equal parts.

Why this level: The folds are easy; the trick is marking exactly where the folded edge crosses.

You need: 1 sheet of origami paper

Preview Preview: checked on screen; real-paper verification is in progress.

Steps at a glance

1. Find the middle
White side up. Fold the left edge to the right edge and unfold to mark the middle of the top edge.
2. Corner to the middle of the top edge
Fold the bottom-right corner up to the mark in the middle of the top edge. Look where the folded bottom edge crosses the left edge.
3. Mark and unfold
Pinch a small mark at that point on the left edge, then unfold.
4. Fold the bottom third up
Fold the bottom part up along a horizontal line through your mark.
5. Fold the top third down
Fold the top edge down to meet the edge you just folded up. The paper is now in three equal layers.
6. Unfold and check
Unfold everything: the two creases divide the square into three equal strips. Use it to fold letters or split paper evenly!