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A triangle is it a polygon or figure which has three sides . These sides are composed of segments of different straight found in the points known as vertices . Triangles meet several conditions: the sum of what two of its sides measure, for example, always exceeds the length of the remaining side.

A equilateral It is a figure that presents all sides equal to each other . The term usually applies to triangles of this type. A equilateral triangle therefore it is a identical three-sided polygon , which has three acute angles equal to 60º.

These characteristics (equal sides length and congruent angles) make the creation of an equilateral triangle simple. One way to build an equilateral is by drawing a circle with a compass , then open the measure in a measure of 60º and mark three equidistant points. By joining the three points, the equilateral triangle is formed.

Another option is to link a point X and a point AND through a straight line You have to draw a circle that has its center in X , whose radius is identical to the distance between X and AND , and a circle with its center in AND and radius identical to the distance between X and AND . By joining the point where both circumferences are cut with X and AND , a new equilateral triangle is created.

But triangles are not the only polygons whose sides can measure the same. A known case is the rhombus, an equilateral quadrilateral, which includes the figure of the square. Among the properties that this type of polygons presents, it is said that:

* in the case of an equilateral polygon whose angles are all of it measure, we talk about a regular polygon;

* if an equilateral polygon is also cyclic, that is to say that its vertices are perched on a circle, it will also be a regular polygon;

* any equilateral quadrilateral is convex, although this is no longer true in the case of polygons that exceed four sides.

The mathematician and physical Italian Vincenzo Viviani developed a theorem that bears his name and proposes that if the distances from each side of an equilateral triangle are added to a point, the result will be equal to the height of that figure. Viviani's theorem can also be proven with equilateral and equiangular polygons. One of its applications in the real world is its use for plot coordinates in ternary diagrams (representing systems composed of three variables), such as flammability, and in simplex, which is the equivalent of a triangle in dimensions greater than 2.

Other theorem known in the field of geometry is that of Napoleon, whose authorship can't make sure it belongs to Bonaparte. In its statement, it is explained that by constructing three equilateral triangles based on the sides of a triangle of any type, provided that all three are inside or all three outside the first, the central points of each of the new ones will form an equilateral triangle .

Humans have learned to build equilateral triangles in remote times , as can be seen in several deposits of archeology presenting figures made thousands of years ago.

For the theology, the equilateral triangle is of great importance. In principle, the number three symbolizes the spiritual order, the balance. According to some religious representations, the Catholic god is plotted as an inverted triangle with an eye inside him, alluding to his omnipresence and omniscience. Plato, on the other hand, explained that this geometric figure could be understood as harmony, proportion and divinity.

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