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Third Squared (Posted on 2004-09-15) Difficulty: 2 of 5
Given a square piece of paper, show how by creasing and folding only, a square of one third the area of the original can be obtained.

  Submitted by Jer    
Rating: 4.2500 (4 votes)
Solution: (Hide)
This will require the square root of one-third = tan(30). 30 degree angles aren't too difficult with origami. Call the original square ABCD. 1. Fold A and D onto B and C. Unfold. Call this crease 'v'. 2. Fold A and B onto D and C. Unfold. Call this crease 'h'. 3. Fold D onto v in such a way as to form a crease through C. Unfold. Call the point where this crease intersects AD 'X'. Angle DCX is 30 degrees. DC/XD is in the required ratio. Similar folds will give this ratio on side AB -Jer

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re: partial explanationJer2004-10-12 16:15:01
partial explanationrixar2004-09-22 21:25:15
re: MAYBE?Steve2004-09-21 20:35:51
re: SolutionRichard2004-09-15 19:29:42
re: MAYBE?David Shin2004-09-15 16:33:10
MAYBE?Ira Jewell2004-09-15 16:21:59
SolutionSolutionDavid Shin2004-09-15 16:05:26
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