The key to this "Missing Square Puzzle" is that neither of the 13×5 "triangles" is truly a triangle, because what appears to be the hypotenuse is bent.
In other words, the "hypotenuse" does not maintain a consistent slope, even though it may appear that way to the human eye. Overlaying the hypotenuses from both figures results in a very thin parallelogram, which then gets folded up to demonstrate that it has an area of exactly one grid square, which accounts of the "missing" area.
According to Martin Gardner, this particular puzzle was invented by a New York City amateur magician, Paul Curry, in 1953. However, the principle of a dissection paradox has been known since the start of the 16th century. The integer dimensions of the parts of the puzzle (2, 3, 5, 8, 13) are successive Fibonacci numbers, and leads to the exact unit area in the thin parallelogram. Many other geometric dissection puzzles are based on a few simple properties of the Fibonacci sequence.
The missing square puzzle is an optical illusion often used in mathematics classes to help students reason about geometrical figures, or rather to teach them to not reason by making assumptions from using figures, but only using the textual description and math principles to deduce the answer.
#math #geometry #geekhumor
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AT LAST, SIR TERRY, WE MUST WALK TOGETHER.
Terry took Death’s arm and followed him through the doors and on to the black desert under the endless night.
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