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The notion of diagonal , with etymological origin in the Latin word diagonālis, is used to refer to the straight line that allows joining two vertices what they are not contiguous of a polyhedron or a polygon.

The diagonals appear as segments or lines that have a certain inclination . Suppose, in a square the vertices TO and B they are located at the ends of the upper side (TO on the left and B to the right) while the vertices C and D they are at the ends of the lower side (C under TO and D under B ). Inside this square, we will find two diagonals: AD (that goes from TO until D ) and CB (which extends from C until B ). These diagonals are perpendicular to each other.

In the urban framework, the diagonal is called avenue wave Street which cuts obliquely to other arteries that are parallel to each other. The Spanish city of Barcelona , for example, has the Diagonal Avenue , which divides the district from Expansion diagonally in two parts. Lime , in Peru , also has a Diagonal Avenue . In the Buenos aires city , on the other hand, to the avenue President Roque Sáenz Peña It is recognized as North Diagonal while the President Julio Argentino Roca Avenue receives the denomination of South Diagonal .

"Diagonal" Finally, it is the name of a Newspaper Spanish founded in 2005 . It is a publication of progressive ideology that usually includes criticism of the capitalist system.

When studying the etymology of the term diagonal, we discover that its origin is in the Greek language, precisely in the word heck, which can be translated as "sack". The geographer Strabo and the mathematician Euclid , two essential characters of the evolution of science in general, talked about heck to refer to segment that joins two vertices of a cuboid or rhombus.

At first glance, we notice that the components of this Greek word are the following: the prefix day-, which indicates "through", and the term gonia, which can be translated as "angle "and relates to gony, defined as "knee"; the idea, therefore, was "(a line that) passes through the angles." Latin came as diagonus and then arose diagonalis.

The Greek word gonia He has also given us the element -gono, which in our language is used for the description of various flat figures in the field of geometry , what we call polygons, among those found Decagon, Dodecagon, Decagon, Entagon, Heptagon, Hexagon, Octagon, Pentagon, Pentadecagon, Tetragon, Trine and undecagon.

Given a polygon Anyone, to find out the number of diagonals that can be drawn inside, that is, between their vertices, we must solve the following equation: Nd = n (n - 3) / 2 , where Nd is "number of diagonals" and n , "number of sides". In the case of a tetragon (which is also called quadrilateral, since it has four sides, in addition to four angles), the result would be 2 , as 4(4 - 3) / 2 = 2 .

Taking into account the same criterion expressed so far, it is possible to distinguish between upper secondary diagonal and lower , as we are talking about the elements that are directly above or below the main diagonal, respectively.

According to the work of Pythagoras , we can say that the diagonal of a rectangle , taking into account two of its adjacent sides allows us to find an equality that in one term has the diagonal squared and in the other, the sum of the squares of both sides. If the diagonal belongs to a rectangular orthohedron, the sum of the squares of three concurrent edges at a vertex is equal to the square of the diagonal.

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