Definition of Thales' Theorem

In the Vl century a. C there was a movement intellectual in the territory of Greece that can be considered as the beginning of the thought rational and scientifically minded. One of the thinkers who led the new intellectual course was Thales of Miletus, who is considered the first pre-Socratic, the current of thought that broke with mythical thought and took the first steps in philosophical activity and scientific.

The original works of Thales are not conserved, but through other thinkers and historians the main contributions of him are known: he predicted the solar eclipse of the year 585 a. C, defended the idea that water is the original element of nature and also stood out as a mathematician, his most recognized contribution being the theorem that bears his name. According to legend, the inspiration for the theorem comes from Thales' visit to Egypt and the image of the pyramids.

Thales theorem

The fundamental idea of ​​the theorem is simple: two parallel lines crossed by a line that creates two angles. It is about two angles that are congruent, that is, one and the other angle have the same measure (they are also known as corresponding angles, one is on the outside of the parallels and the other on the inside).

It should be borne in mind that sometimes there are two Thales theorems (one refers to the triangles similar and the other refers to the corresponding angles but both theorems are based on the same principle mathematical).

Specific applications

The geometric approach to Thales' theorem has obvious practical implications. Let's look at it with a concrete example: a 15 m high building casts a 32 meter shadow and, at the same instant, an individual casts a 2.10 meter shadow. With these data it is possible to know the height of said individual, since it must be taken into account that the angles that cast the shadows of him are congruent. Thus, with the data of the problem and the principle of Thales' theorem on the angles corresponding, it is possible to know the height of the individual with a simple rule of three (the result would be 0.98 m).

The above example clearly illustrates that Thales' theorem has very diverse applications: in the study of geometric scales and metric relations of the geometric figures. These two questions of pure mathematics are projected onto other theoretical and practical spheres: in the elaboration of plans and maps, in the architecture, the farming or engineering.

By way of conclusion We could remember a curious paradox: that although Thales of Miletus lived 2,600 years ago, his theorem continues to be studied because it is a basic principle of the geometry.

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