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Optical illusion, basically. Using Pythagorean, find the hypotenuse of the triangles of which are added together to create the bisecting line of the rectangle. (One of the triangles is actually a portion of the larger trapezoid). You will find that the hypotenuse of the triangle created by the bisecting, diagonal line does not equal the original lengths of the lines that make up the shape itself. In effect, it's just trickery based on the fact that the values are close, but no cigar. Another way to look at it is this: With both final shapes next to each other, treat both as a basic graph. The intersection of the green, orange, and blue shapes is at point (3,5). Picture it as the only point where you could stand on 3 colors at once if you were a magic, little man. Now, in the second shape, the implication is that the shapes are the same size as the first square, but it is mathematically impossible. The intersecting point at (8,3) on the rectangle is implied, but is not actually where that bisecting line would be. I believe the top of the green triangle near the implied intersecting point is actually at (8,3.10112882673), and not at the implied (8,3) - BG |
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64 Quoted: Optical illusion, basically. Using Pythagorean, find the hypotenuse of the triangles of which are added together to create the bisecting line of the rectangle. (One of the triangles is actually a portion of the larger trapezoid). You will find that the hypotenuse of the triangle created by the bisecting, diagonal line does not equal the original lengths of the lines that make up the shape itself. In effect, it's just trickery based on the fact that the values are close, but no cigar. - BG ^ This |
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Quoted: Optical illusion in the alignment. The unit squares don't match up. the top cut is 3 in 8, so the angle is arctan (3/8) = 20.56 The bottom cut is 2 in 5, so the angle is 21.8. Hence, some overlap that can lose a single unit square. Is my guess. Doesn't that only work if the triangles are similar? - BG |
