Paradox with a rectangle and a Fibonacci series. Effective trick and its solution

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Paradox with a rectangle and a Fibonacci series. Focus Secret

Spectacular tricks and their clues

Directory / Spectacular tricks and their clues

Focus Description:

There are many ways in which a rectangle can be cut into a small number of pieces and then folded into another rectangle of larger or smaller area. On fig. 1 shows a paradox, also based on the Fibonacci series. Like the square case just discussed, choosing some Fibonacci number From the "second" subsequence as the width of the first rectangle (13 in this case) results in an increase in the area of the second rectangle by one square unit.

Focus Paradox with Rectangle and Fibonacci Series
Ris.1

If we take some Fibonacci number from the "additional" subsequence as the width of the first rectangle, then the area in the second rectangle will decrease by one unit. Losses and gains in area are explained by small overlaps or gaps along the diagonal section of the second rectangle. Another version of such a rectangle, shown in Fig. 2. when constructing the second rectangle, it leads to an increase in the area by two square units.

Focus Paradox with Rectangle and Fibonacci Series
Ris.2

If the shaded part of the area of the second rectangle is placed over the unshaded part, the two diagonal cuts will merge into one large diagonal. Now rearranging parts A and B (as in Fig. 61), we get a second rectangle of a larger area.

Author: M.Gardner

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