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Topic: Formation of the bigger square. (Read 642 times) |
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Wonderer
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Formation of the bigger square.
« on: Dec 20th, 2005, 6:43pm » |
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You have 3 identical paper squares, a pencil, a pair of scissors and a ruler (with no markings, so you can only use it to draw straight lines). You must cut these 3 squares into 9 pieces and use them to form a bigger square. How do you do it? (please attach diagrams to illustrate)
Note:
1 the ruler is only used for drawing straight lines
2 you are not allowed to fold the paper
3 since you only have 1 ruler, you can’t draw parallel lines
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Grimbal
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Re: Formation of the bigger square.
« Reply #1 on: Dec 21st, 2005, 2:16am » |
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Technically, a paper square with a ruler could be used to draw parallels. Unless it is very thin paper.
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rmsgrey
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Re: Formation of the bigger square.
« Reply #2 on: Dec 21st, 2005, 11:43am » |
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What about folding?
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SMQ
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Re: Formation of the bigger square.
« Reply #3 on: Dec 21st, 2005, 11:49am » |
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on Dec 21st, 2005, 11:43am, rmsgrey wrote:
Er, I believe that's covered by note 2, unless you want to try to fold the ruler, scissors, or pencil?
--SMQ
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--SMQ
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rmsgrey
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Re: Formation of the bigger square.
« Reply #4 on: Dec 21st, 2005, 11:54am » |
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on Dec 21st, 2005, 11:49am, SMQ wrote:
Er, I believe that's covered by note 2, unless you want to try to fold the ruler, scissors, or pencil?
--SMQ |
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Must learn to read...
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Sjoerd Job Postmus
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Re: Formation of the bigger square.
« Reply #5 on: Dec 21st, 2005, 11:41pm » |
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surface of 3 identical squares = 3 a^2
surface of larger square = b^2
b^2 = 3 a^2
b = a*sqrt(3)
Assuming a = 1, where can we find sqrt(3)? The diagonal would be sqrt(2). But, we know that sqrt(3) is most often found as sqrt(2^2 - 1^2)
Yet, it's difficult to find sqrt(3)... Because the length of a line in the square x can be expressed as: width <= x <= width*sqrt(2)...
So, we must find it in a set of two squares...
I assume I can draw on the ruler... like, make markings at lengts I want to.... The fact that it's unmarked doesn't mean I can't mark it...
Sure, I'm only allowed to draw straight lines with it, according to you, but I'd like to lie the ruler next to two squares, and mark the ruler... (with a straight line  )
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| « Last Edit: Dec 21st, 2005, 11:51pm by Sjoerd Job Postmus » |
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Barukh
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Is the following construction allowed? I guess that's similar to what Sjoerd had in mind. The length of the thick line is [sqrt]3.
If that's allowed, the problem can be solved with just 7 pieces.
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Wonderer
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Re: Formation of the bigger square.
« Reply #7 on: Dec 22nd, 2005, 9:52pm » |
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on Dec 22nd, 2005, 3:57am, Barukh wrote:Is the following construction allowed? I guess that's similar to what Sjoerd had in mind. The length of the thick line is [sqrt]3.
If that's allowed, the problem can be solved with just 7 pieces. |
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Yes, this is allowed! in fact, you can do it with 6 pieces.
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Barukh
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on Dec 22nd, 2005, 9:52pm, Wonderer wrote:| Yes, this is allowed! in fact, you can do it with 6 pieces. |
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Yes, I know.
But I thought the attached 7 pieces dissection is more suited for the tools and restrictions of the problem. The dashed lines indicate the cuts.
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