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Two squares (Posted on 2006-01-05) Difficulty: 3 of 5
Construct a large square ABCD with AB at the top.

Next construct a smaller square (A'B'C'D') inside ABCD, with any orientation and centre and join the corresponding corners.

This divides the region between the squares into four.

We will name these divisions (and their areas):

(N)orth = ABB'A'
(E)ast = BCC'B'
(S)outh = CDD'C'
(W)est = DAA'D'.

Show that the areas of these regions satisfy the equality
N+S = E+W.

See The Solution Submitted by goFish    
Rating: 4.3333 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): Solution | Comment 3 of 7 |
(In reply to re: Solution by Jer)

Yes, the graphical solution is nice. But, the "complex" solution works for any square A'B'C'D' (inside or outside of square ABCD with any orientation).
  Posted by Bractals on 2006-01-05 18:19:46

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