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What is Parabola | Meaning and Concept

In the area of ​​mathematics, the word parabola comes from the Greek παραβολή and refers to a geometric area where the points located in a plane are equidistant from a fixed point and a straight line . Its concept is based on the conical section of eccentricity equal to 1, resulting from dividing a straight cone with a surface whose tip of deviation with respect to the base of alteration of the cone is equal to that shown by its generator. Therefore, the plane will be parallel to this line.


Parable



On the other hand, it is understood that in the area of ​​projective geometry, the parabola details how the surrounding curve of the straight lines couples matching pairs of points in a similar projectivity . It is important to mention that the parabola arises in many branches of the applied sciences because its shape belongs with the graphs of the quadratic equations . For example, parables are the ideal paths of bodies that move under the exclusive authority of gravity.


According to the story, tradition shows that the conic units were discovered by Menecmo in his study of the problem of cube reproduction, where he manifests the presence of a solution through the cutting of a parabola with a hyperbola, which is valid later on Proclus and Eratosthenes. However, the first to use the term parabola was Apollonius of Perge in his treatise Conics, cherished as a masterpiece on the subject of Greek mathematics and where the study and analysis of tangents to conic sections is deployed. 


Therefore, if a cone is cut by a plane by means of its axis and is also cut by another plane that cuts the cone platform in a straight line perpendicular to the base of the axial triangle, and if additionally the diameter of the section is similar to one side of the axial triangle, then any straight line that is drawn from the unit of a cone to its line parallel to the frequent section of the cutting plane and one of the cone platforms, will be equal in square to the rectangle contained by the straight line sectioned by it in the diameter that starts from the vertex of the section and by another straight line that is in reason to the straight line between the angle of the cone and the vertex of the section that the square at the base of the axial triangle has the rectangle contained by the two remaining sides of the triangle. And such a session will be named a parable.

 

An important fact in this subject all the parables are similar, that is, only the scale that creates the appearance of having unequal shapes. Since the parabola is a conical section, it can also be detailed as the only conic section that has an eccentricity. Uniqueness refers to the fact that all parables are similar, that is, they have the same form, except for their scale.
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Jack Evans

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