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They are not kept the original works of such, but through other thinkers and historians know his main contributions: he predicted the solar eclipse of the year 585 a. C, defended the idea that water is the element of nature and also highlighted as mathematician, being his most recognized contribution the theorem that bears his name. According to the legend, the theorem inspiration comes from the visit that made such to Egypt and the image of the pyramids.

### Such theorem

The fundamental idea of the theorem is simple: two parallel lines intersected by a line which creates two angles. It's two angles that are congruent, i.e., one and another angle are the same measure (also known as corresponding angles, one is on the outside of the parallel and the other on the inside).It must take into account that sometimes refers to two theorems of such (one refers to the similar triangles and the other refers to the corresponding angles but both theorems are based on the same mathematical principle).

### Specific applications

The geometrical theorem of such approach has obvious practical implications. See it with a concrete example: a 15 m high building casts a shadow of 32 meters and, at the same moment, an individual casts a shadow of 2.10 meters. With these data it is possible to know the height of said person, since you must be congruent angles that cast their shadows. Thus, with details of the problem and the principle of such theorem about 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 example shown above illustrates clearly that such theorem has many different applications: in the study of geometric scales and metric relations of geometrical figures. These two issues of pure mathematics are projected onto other areas of theoretical and practical: the elaboration of plans and maps, architecture, agriculture or engineering.

By way of conclusion we might recall a curious paradox: that while such of Mileto lived 2600 years ago, his theorem continues to study it because it is a basic principle of geometry.

**Article contributed by the team of collaborators.**