What is equilateral?
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What Does equilateral Mean
A triangle is a polygon or figure that has three sides . These sides are made up of segments of different lines that meet at points known as vertices . Triangles meet several conditions: the sum of what two of their sides measure, for example, always exceeds the length of the remaining side.
An equilateral is a figure that has all sides equal to each other . The term is often applied to triangles of this type. An equilateral triangle , therefore, is a polygon with three identical sides , presenting three acute angles equal to 60º.
These characteristics (sides of equal length and congruent angles) make creating an equilateral triangle simple. One way to construct an equilateral is to draw a circle with a compass , then open the compass by 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 Y through a line. You have to draw a circle which has its center in X , whose radius is equal to the distance between X and Y , and a circle with its center in Y and radius equal to the distance between X and Y . By joining the point where both circles intersect with X and Y , 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, where the figure of the square is included. Among the properties that this type of polygons present, it is said that:
* in the case of an equilateral polygon whose angles are all of the same measure , we are talking about a regular polygon;
* If an equilateral polygon is also cyclic, that is, 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 for polygons that exceed four sides.
The Italian mathematician and physicist Vincenzo Viviani developed a theorem that bears his name and that 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 to draw 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.
Another well-known theorem in the field of geometry is that of Napoleon, whose authorship cannot be assured that it belongs to Bonaparte . In its statement, it is explained that when 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 ancient times , as can be seen in various archaeological sites that present figures made thousands of years ago.
For theology , the equilateral triangle is of great importance. In principle, the number three symbolizes spiritual order, balance. According to some religious representations, the Catholic god is depicted as an inverted triangle with an eye inside it, alluding to his omnipresence and omniscience. Plato, on the other hand, stated that this geometric figure could be understood as harmony, proportion and divinity.