Triangle paradox. Effective trick and its solution

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EFFECTIVE FOCUSES AND THEIR CLUES
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Triangle paradox. Focus Secret

Spectacular tricks and their clues

Directory / Spectacular tricks and their clues

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Focus Description:

Consider Fig.1. It can be seen that the large triangle A does not change its position, while the other parts move.

Focus Paradox with Triangle
Ris.1

Since this triangle does not play a significant role in the paradox, it can be discarded altogether, leaving only the right triangle cut into four parts. These parts can then be redistributed, thus obtaining a right-angled triangle with a hole (Fig. 2), as if equal to the original one.

Focus Paradox with Triangle
Ris.2

Composing two such right-angled triangles with legs, you can build many variants of isosceles triangles, similar to the one shown in Fig. 3.

Focus Paradox with Triangle
Ris.3

As in the paradoxes discussed earlier, these triangles can be built in two ways: either draw their sides strictly rectilinearly, then the point X will not fall on the intersection of the lines of the square grid, or place the point X exactly at the intersection, then the sides will be slightly convex or concave. The latter method seems to mask inaccuracies in the drawing better. The paradox will seem even more surprising if lines of a square grid are applied to the parts that make up the triangle, thereby emphasizing that the parts were made with the necessary accuracy.

By giving our isosceles triangles different sizes, we can gain or lose any even number of square units. Some typical examples are given in Fig. 4, 5 and 6.

Focus Paradox with Triangle
Ris.4

Focus Paradox with Triangle
Ris.5

Focus Paradox with Triangle
Ris.6

Composing the bases of two isosceles triangles of any of these types, you can build a variety of options for a rhombic view; however, they add nothing essentially new to our paradox.

Author: M.Gardner

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