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Topic: MYSTERIOUS TRIANGLE AREA (Read 5189 times) |
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troll314
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MYSTERIOUS TRIANGLE AREA
« on: Aug 24th, 2002, 7:21am » |
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William I suggest you remove this problem, since its really stupid and in fact "faked" and bends the truth. Those are the not same triangles. This problem would never work on paper.
Solution
The second picture has a modifidied gradient of the two top triangles, the extra area fills the space created. I checked in Photoshop.
Pretty lame hey?
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william wu
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Re: MYSTERIOUS TRIANGLE AREA
« Reply #1 on: Aug 24th, 2002, 8:25am » |
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I was first presented with the problem in high school, when they gave us the problem printed on paper -- is that what you mean by on "paper"? If you mean the math doesn't work out for the fake triangle, that's true. It bends the truth, but the challenge is to figure out what's wrong (hypotenuse in top triangle is not a true hypotenuse.) I don't think it's that bad. If I ever database the site though, I'll put it in the easy section.
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troll314
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Re: MYSTERIOUS TRIANGLE AREA
« Reply #2 on: Aug 24th, 2002, 2:22pm » |
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Well actually by paper I meant u only had one set of shapes that had been cut out and you could arranged them. That would never work.
If you look at the top triangle you can see the bend. Yeah so in actual fact the top shape is a Quad and the bottom is a Triangle (if u include the missing area).
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Chronos
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Re: MYSTERIOUS TRIANGLE AREA
« Reply #3 on: Aug 27th, 2002, 4:24pm » |
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The first time I ever saw this problem, it was using little cut-out pieces of paper that you could re-arrange. In fact, it makes the problem work even better, because the bends aren't as obvious. If a person sees that the "hypoteneuse" isn't quite straight, then he'll assume that it's because he didn't quite line up the pieces perfectly.
Incidentally, neither "triangle" is a true triangle. The one with the "missing piece" bends upwards, and the "complete" one bends downwards.
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Eric Yeh
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Re: MYSTERIOUS TRIANGLE AREA
« Reply #4 on: Aug 28th, 2002, 5:47am » |
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I agree that this is a one minute problem, but I wouldn't call it "really stupid" and certainly wouldn't think it should be removed.
The best part is verifying that the difference quadrilateral has area 1 by Pick's Theorem.
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| « Last Edit: Aug 28th, 2002, 5:47am by Eric Yeh » |
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NickH
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Re: MYSTERIOUS TRIANGLE AREA
« Reply #5 on: Aug 28th, 2002, 1:09pm » |
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"The best part is verifying that the difference quadrilateral has area 1 by Pick's Theorem."
That's hardly necessary, but thanks for the pointer to this beautiful theorem.
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wmenezes
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Re: MYSTERIOUS TRIANGLE AREA
« Reply #6 on: Jan 1st, 2010, 5:46pm » |
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I was wondering how you determine if the hypotenuse is false.
I tried it by determining the angles of the two triangles the blue and the larger triangle that encompasses it
the blue triangle has a tan(theta) of 8/3
and the red triangle has 5/2
As these angles are different the hypotenuse of the larger encompassing triangle is false.
Is there another solution other than visual.
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ThudnBlunder
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Re: MYSTERIOUS TRIANGLE AREA
« Reply #7 on: Jan 2nd, 2010, 6:16am » |
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on Jan 1st, 2010, 5:46pm, wmenezes wrote:.
Is there another solution other than visual. |
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As it is an optical illusion, a 'visual' solution ought to be sufficient.
There is a thread here.
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