We can make a square into four equal squares. Fine, if we want to make into five.. Then there is a problem. Please discuss, How to make five squares from a single square by using a Pythagorean theorem. Is there any other way to make five squares from one square without using Pythagorean theorem? Please discuss. Thanking you, KKRG
Pythagorean theorem
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$\begingroup$
geometry
euclidean-geometry
triangles
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0What have *you* tried so far? Please post. – 2012-06-26
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2What operations are allowed? Are you cutting the large square into pieces that need to be rearranged to form five smaller squares? Do all the smaller squares need to be the same size? What do you mean without using the Pythagorean theorem? I can know 9+16=25 even without Pythagoras. – 2012-06-26
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0*We can make a square into four equal squares.*, but $9=4\cdot 1.25$, so what do you mean? – 2012-06-26
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0You can cut a big square into 5 equal squares in size and area by using Pythagorean theorem. You are allowed for any operations. the 5 pieces when you add, we should get a big square. – 2012-06-26
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0Do you mean by square a rectangle where all lengths are the same? Then the answer i believe is no – 2012-06-26
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0Yes! I want five equal squares in size and area is same, from one square. This is not rectangle. I want only squares. You can cut, paste etc. Use Pythagorean theorem or without using also allowed. – 2012-06-26
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2@KRRG: We're allowed **any** operations? Then I choose the operation of creating 4 identical duplicates of the original square. – 2012-06-26
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0Assume the original square has side length 1. Using a compass and straightedge, construct the length $1/\sqrt{5}$; now build five squares using that side length. – 2012-06-26
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0Ohhh, so the squares don't have to fit inside the original square like a puzzle? – 2012-06-26
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0See http://math.stackexchange.com/questions/96776/dissection-of-a-1-times-5-rectangle-to-a-square – 2012-06-28