In the 5th century BC there was an intellectual movement in the territory of Greece that can be considered as the beginning of rational thought and scientific mentality. 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 thinking and took the first steps in philosophical and scientific activity.
The original works of Thales are not preserved, but through other thinkers and historians his main contributions are known: he predicted the solar eclipse of 585 BC. 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. These are two angles that are congruent, that is, both angles have the same measure (they are also known as corresponding angles, one is on the outside of the parallels and the other is on the inside).
It must be borne in mind that there are sometimes two theorems of Thales (one refers to similar triangles and the other refers to the corresponding angles, but both theorems are based on the same mathematical principle).
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 their shadows are congruent. Thus, with the data in the problem and the principle of Thales' theorem on the corresponding angles, 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 the metric relationships of geometric figures. These two questions of pure mathematics are projected onto other theoretical and practical spheres: in the elaboration of plans and maps, in architecture, agriculture or engineering.
By way of conclusion we could recall 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 geometry.
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