asymptote

Asymptote is a term originating from a Greek word that refers to something that has no match. The concept is used in the field of geometry to name one straight which, as it continues indefinitely, tends to approach a certain curve or function, although without being able to find it.

This means that, while the line and the curve are extending, the distance between them will tend towards the zero. According to their characteristics, the asymptotes can be classified into horizontal (when the line is perpendicular to the axis which corresponds to the ordinate), vertical (the line, in this case, is perpendicular to the axis corresponding to the abscissa) u oblique (They are not perpendicular or parallel to any axis).

It is possible to determine what is the relative position that the function occupies with respect to the asymptotic line by calculating the cut points Of the two. These points will indicate the modifications in the position of the function against the asymptote. It is worth mentioning that, although the asymptote and the function are usually represented together, the first is not an integral part of the analytical expression of the second; for this reason, it is often indicated by means of a line dotted, or it is excluded from the graph.

The utility of asymptotes is found, for example, when representing a curve graphically. These lines, which indicate future behavior and provide support for the curve, can be expressed analytically according to the reference system in question.

This knowledge is usually put into practice in fields such as engineering wave architecture. In a hyperboloid structure (like the famous television tower in Canton, about six hundred meters high), asymptotic lines confer stability since they function as support.

Etymology of the term asymptote

The Greek word from which we obtained "asymptote" can be written asymptotos and translate as that does not fall together Or simply, that which does not fall. Regarding your structure, the following parts are distinguished:

* the prefix to-, which can also be found in its form an-. It has a proprietary value that is associated with the meaning of the word "no", and is appreciated in terms such as anacoluthon, anarchy, apathetic Y analgesic. When combined with the root ne-, of Indo-European origin, which in turn is found in the prefix in-, which comes from Latin, we get be unable, misfit and unheard, among others;

* the prefix without-, which can be defined as at once, together or with. We see it, for example, in the words labor union, synecdoche, syntagma Y syncretism;

* the root of the Greek verb piptein, whose translation is fall. This is linked to the root pet- (of Indo-European origin and with the meanings fly or fall), which we find in terms with Latin roots pain, panache, ask, competence, corduroy, banner, repetition Y centripetal, among others;

* the verb suffix -cough, which refers to a thing that was done or that can be carried out. Some of the terms in which it is found are asbestos, asphalt Y antidote.

The famous Geometer Apollonius of Perge, born approximately 262 BC in the city that gave him his surname, was the first to take advantage of the term asymptote to refer to the mathematical concept of a line that cannot touch a hyperbola, in his treatise «About conic sections«. It is worth mentioning that the names of the parable and the ellipse, as well as the epicycles theory (which seeks to give an explanation to the apparent variation in the speed of the Moon and the supposed movement of the planets).