Quadruple squares. Effective trick and its solution

EFFECTIVE FOCUSES AND THEIR CLUES
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Quadruple squares. Focus Secret

Spectacular tricks and their clues

Directory / Spectacular tricks and their clues

Focus Description:

There are paradoxes obtained by completely different methods. You can, for example, cut a square into four parts of the same shape and size (Fig. 1), and then compose them in a new way, as shown in Fig. 2. This results in a square, the dimensions of which seem to have not changed and at the same time with a hole in the middle.

Focus Squares of four parts
Ris.1

Focus Squares of four parts
Ris.2

Similarly, you can cut a rectangle with any ratio of side lengths. It is curious that the point A, at which two mutually perpendicular cut lines intersect, can then be located anywhere inside the rectangle. In each case, when the parts are redistributed, a hole appears, and its size depends on the angle formed by the cut lines with the sides of the rectangle.

This paradox is comparatively simple, but it loses a lot because even a superficial study shows that the sides of the second rectangle should be slightly larger than the sides of the first.

A more complicated way of cutting a square into four parts, which results in an inner hole, is shown in Fig. 3. It is based on the chessboard paradox that opens this chapter.

Focus Squares of four parts
Ris.3

Note that when redistributing the parts, two of them must be turned upside down. Note also that when part A is discarded, we get a right-angled triangle made up of three parts, inside which a hole can be formed.

Author: M.Gardner

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