Do Futility Closet: William Hooper publicou esta bizarrice em 1774. O retângulo no topo mede 10 unidades por 3, dando uma área de 30. Mas suas peças dissecadas parecem produzir dois outros retângulos, com áreas 12 e 20. De onde vieram as duas unidades extras?
(From the Futility Closet: William Hooper published this oddity in 1774. The rectangle at the top measures 10 units by 3, giving an area of 30. But its dissected pieces seem to produce two other rectangles, with areas 12 and 20. Where did the two extra units come from?)
PCFilho
The slanting "line" in the second figure isn't straight; it bends a little at the boundary between the two rectangles. Moreover, if the second diagram were truly a rearrangement of the four regions in the first, the first rectangle's height would actually be 1.8 units instead of 2 units, and the second rectangle's height would be 4.8 (= 3 + 1.8) units instead of 5 units, and we'd get a total area of (1.8)(6) + (4.8)(4) = 10.8 + 19.2 = 30 square units, which is exactly what we would expect.
ResponderExcluirPerfect, Jake. :)
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