Given a square piece of paper, show how by creasing and folding only, a square of half the area of the original can be obtained.

(In reply to re: Variation: by Jer)

Jer wrote:

1. Fold and unfold the diagonal AC.
2. Fold AB onto AC (B lies on AC.)
3. Fold AD onto AC (D lies on AC too.)
4. Fold C onto A.
5. Unfold steps 2, 3, and 4.

These 4 folds could be simplified into 3 as follows:

1. Fold B onto D and crease.
2. Fold AB (and AD underneath) onto AC. 
3. Fold A onto C.
4. Unfold steps 1, 2, and 3.

Basically, steps 2 and 3 of Jer's solution are combined by leaving the diagonal AC folded.  Total folds for the variation: 5.

 

Posted by stan on 2004-04-14 15:25:28