Showing posts with label triangular paradox. Show all posts
Sunday, February 22, 2015
Triangular Paradox
Games Reviewer
7:23 AM
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triangular paradox puzzle
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Consider the diagram below. Figure 1 shows four shapes. The same
four shapes have been rearranged in Figure 2. However, there is now a gap, but
none of the shapes have changed.
How can this be?
![Triangle Paradox triangle paradox](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjHdOmPIVIIIxBkrPb6eQTu6PcN3RnuthHXUhyphenhyphenX9voTsgwgL4AhDq5NdsuzaXltCybsT20RrJoMDc0tCgP5bnfsDvmD1VXN3aYXHYbh3weo9XRkMOk_ySL3_5w90bhiG20nm_TN5uWF8aVj/s1600/triangle-paradox.gif)
Triangular Paradox Puzzle Solution
You will have tried to calculate the areas of everything involved. The red triangle has an area of 12 squares, the blue triangle has 5 squares, the orange shape has 7, and the green shape has 8. The sum of all these parts is 12 + 5 + 7 + 8 = 32 squares.You might have thought that the large, enclosing figure was (5 × 13) / 2 = 32.5, and wondered how there is a 0.5 square discrepency.
However, this is not the case. The enclosing figures are not actually a triangles at all: the blue triangle has a gradient of 2 / 5 = 0.4, and the red triangle has a gradient of 3 / 8 = 0.375. The thick black lines aid in deceiving the eye into seeing the 'hypotenuse' as a straight line.
![Triangle Paradox Solution triangle paradox solution](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh_TD2HxzZ2cSE9gfkobTf9V7rdn6y_8Ci2YufUiDwt9Eo7Dy6Dz1DHcVxj8m9A6Rn-7zhbEzvw9rkaWURp23UHDokNgyVZoAJaDWywrdl4VkVdC8OEtCJlXxKy9QMTNVHInjuHSS5WYTNQ/s1600/triangle-paradox-solution.gif)
OK, so it's a bit of a trick. But you may note that I never said those big "triangles" were actually triangles!
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