In the second image the red triangle is taller than in the first.
Vlad
11-Dec-2009 8:53 PM
Nope, all the pieces are the same in both images. You can see that by measuring their length and width using the squares. Also, the answer is pretty simple. You can clearly see that the yellow piece has a 3 squares long bar near the yellow square itself and the the green piece has a 2 squares long bar near the rectangle. So, by putting the yellow one over the green one, there is no possible way to remove the ‘hole’ left except for overlapping the pieces. I also think that it might not always result in the same shape only by moving the pieces around, but the total surface of these pieces is the same. For example, if you have two books of the same size, the way you put them around doesn’t matter, it only changes the shape, but not the total surface they have. Still, the situation itself is pretty strange indeed.
The answer is pretty simple, and involves minimum math knowledge. The trick here is that what we see is not an actual triangle. It’s a polygon with four edges. And in the first image, the point of contact between the red triangle and the blue triangle forms an angle oriented down, and in the second, it forms an angle oriented up. So the square that is missing is the actual difference of area between the first polygon (convex) and the second (concave).
You can check to see that the whole figure is not a triangle by a simple rule. Take the red triangle. For 8 block sideways, it has 3 blocks up. Therefore, the blue triangle should have something proportional to this. For five blocks sideways it should have had 3*5/8. That is 15/8=1.875. And in reality, it has two blocks up. Hurray, we found the missing link :P
Lup the Dude
11-Dec-2009 9:16 PM
You guys must be pretty bored if you took the time to explain all that stuff.
Negative0
11-Dec-2009 11:50 PM
alexxadn is right. Geeks.
Check out this and this.
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In the second image the red triangle is taller than in the first.
Nope, all the pieces are the same in both images. You can see that by measuring their length and width using the squares. Also, the answer is pretty simple. You can clearly see that the yellow piece has a 3 squares long bar near the yellow square itself and the the green piece has a 2 squares long bar near the rectangle. So, by putting the yellow one over the green one, there is no possible way to remove the ‘hole’ left except for overlapping the pieces. I also think that it might not always result in the same shape only by moving the pieces around, but the total surface of these pieces is the same. For example, if you have two books of the same size, the way you put them around doesn’t matter, it only changes the shape, but not the total surface they have. Still, the situation itself is pretty strange indeed.
The answer is pretty simple, and involves minimum math knowledge. The trick here is that what we see is not an actual triangle. It’s a polygon with four edges. And in the first image, the point of contact between the red triangle and the blue triangle forms an angle oriented down, and in the second, it forms an angle oriented up. So the square that is missing is the actual difference of area between the first polygon (convex) and the second (concave).
You can check to see that the whole figure is not a triangle by a simple rule. Take the red triangle. For 8 block sideways, it has 3 blocks up. Therefore, the blue triangle should have something proportional to this. For five blocks sideways it should have had 3*5/8. That is 15/8=1.875. And in reality, it has two blocks up. Hurray, we found the missing link :P
You guys must be pretty bored if you took the time to explain all that stuff.
alexxadn is right. Geeks.
Check out this and this.
the second -this- is the best
xD