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How can this be true?
Posted by zack on Sat, 2007-09-29 21:12.
logic | puzzle | strange
Fascinating!
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full explanation
Posted by Anonymous on Sat, 2008-02-23 07:44.
lets say each box is 1in x 1in
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Green Triangle - 5in squared
Red Triangle - 12in squared
Orange Block - 7in squared
Light Green Block - 8in squared
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In both figures the same amount of area is taken. Each piece is the same size.
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The slope of the two triangles are different, but because they are so slight your mind sees them as the same angle. However slight this angle is, it is large enough to give the optical illusion that 1sq.in. has magically disappeared.
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If you can not grasp this. Take a straight edge and put it along the top corner and left corner and you can see that the slopes of the two triangles are not the same. You can also copy/paste this image in Paint then use the line tool to do the same thing.
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Hopefully this clears everything up!
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If you look closely at the
Posted by Anonymous on Tue, 2007-10-02 11:23.
If you look closely at the bottom image, the visible white grid 'fragments' backing the sloping angle are smaller. Add these increments together and you get enough for a full square.
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Concave -> Convex Hypotenuse
Posted by Anonymous on Thu, 2007-10-11 03:11.
The longest side (hypotenuse) goes from concave to convex. It "points in" on top and "points out" on the bottom. The difference in the area at that "point" is 1 unit.
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confusing as hell
Posted by Anonymous on Fri, 2008-02-22 00:33.
I've read the above posts over and over but I just can't understand this shit...
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similar triangles
Posted by Anonymous on Fri, 2008-02-22 17:12.
the top triangle is slightly inflated; the bottom triangle had a little air let out. the difference is not obvious, but its enough to explain the "empty" box.
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The whole figure is not a triangle
Posted by Anonymous on Fri, 2008-02-22 17:08.
In fact, both figures have 4 sides, not three. The "slope" is in fact two different lines. It is concave in the first one, and convex in the second one. Unfortunately, I can't say I figured it out, because someone explained it to me to allow me to finally go to sleep!
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Or...you've been had?
Posted by Anonymous on Fri, 2008-02-22 23:57.
It has to do with the length of the boxes, not the supposed curve of the slope.
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Don't be technical!
Posted by Anonymous on Fri, 2008-02-22 21:12.
I don't understand where you are coming up with the triangle part! It's the boxes, one is shorter than the other. When you move them to fit one is longer than the other. Don't be over technical on it.
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too much analysis!
Posted by Anonymous on Fri, 2008-02-22 21:55.
the red triangle is simply larger than the blue triangle. :P
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you are correct.
Posted by Anonymous on Fri, 2008-02-22 22:44.
the red triangle is larger, but the red and blue triangles are like triangles. having all of the same angles just different length sides. :P
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Or not
Posted by Anonymous on Sat, 2008-02-23 02:27.
Take some time to figure the areas of each of the colored areas in each figure. The same shapes have the same area in both figures. Now, look at the slope of the longest side of each triangle. You will find that the triangles are in fact not similar. They are close to being similar, but there is a small difference between the angles of the two. This difference in the slope is what actually accounts for the "missing" piece.
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Simple Solution
Posted by Anonymous on Sat, 2008-02-23 03:52.
The slope of the red triangle is 3/8, while the slope of the green triangle is 2/5. This means that it _ISN'T_ a triangle.
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I made the 2nd Fig. in Ms.
Posted by Anonymous on Sat, 2008-11-01 06:43.
I made the 2nd Fig. in Ms. Paint by using the first fig. The area is exactly same but I dont understand any thing about th white space#########@2222222222CONfuSinG
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haha... yes, it is
Posted by Anonymous on Sun, 2008-11-09 23:13.
haha... yes, it is frustrating. Okay, the small triangle is 2 high, by 5 long; so the diagonal has a slope of "2/5": I.e. the bottom is 2.5 units long for each unit of height. Now, the big triangle is 3 high, so for the diagonal to be the same slope as the small triangle it should have a bottom length of 2.5 x 3 = 7.5. However, it is actually 8 units long. Thugs the small and large triangles do not have the same slope. In other words, if you connect the small and large triangles together, their diagonals do not form a perfect line... in fact they make a slight angle as pointed out before.
In the top image, this angle is pointed inward, and in the bottom image the angle is pointed outward (to offset the missing block on the base). Hold a piece of paper up to your computer screen to see that the "diagonal" of the overall picture is in fact not a straight line but has a slight bend in the middle.
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How it doesn't work
The trick is the size of the triangles. The red triangle height/base is 3/8 the green triangle is 2/5. There is slight angle between the hypotenuses of the two triangles. This is where the trick comes from.