perplexus.info :: Shapes : Third Squared

Third Squared (Posted on 2004-09-15)

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 explanation	Jer	2004-10-12 16:15:01
partial explanation	rixar	2004-09-22 21:25:15
re: MAYBE?	Steve	2004-09-21 20:35:51
re: Solution	Richard	2004-09-15 19:29:42
re: MAYBE?	David Shin	2004-09-15 16:33:10
MAYBE?	Ira Jewell	2004-09-15 16:21:59
Solution	David Shin	2004-09-15 16:05:26

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