Asymptote It is a term that originates in a Greek word that refers to something that doesn't match . The concept is used in the field of geometry to name a straight which, as it continues indefinitely, tends to approach a certain curve or function , although without finding it.
This means that, while the line and the curve are extending, the distance between the two will tend towards the zero . According to their characteristics, asymptotes can be classified as horizontal (when the line is perpendicular to the axis which corresponds to the ordinates), vertical (the line, in this case, is perpendicular to the axis corresponding to the abscissa) or oblique (they are not perpendicular or parallel to any axis).
It is possible to determine which is the relative position that the function occupies with respect to the asymptote line if the cut points Of the two. These points will indicate the changes 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 former is not an integral part of the analytical expression of the latter; 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, 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 of Canton , about six hundred meters high), the asymptotic lines give stability as 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 doesn't fall together Or simply, that 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 and analgesic. When combined with the root ne-, of Indo-European origin, which in turn is 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 both, together or with. We see it, for example, in the words labor union, synecdoche, syntagma and syncretism;
* the root of the Greek verb piptein whose translation is fall. This one is tied to the root pet- (of Indo-European origin and with the meanings fly or fall), which we find in terms with Latin roots pain, panaché, ask for, competition, corduroy, banner, repetition and centripetal, among others;
* the verbal suffix -cough , which refers to a thing that was done or that can be done. Some of the terms in which it is found are asbestos, asphalt and antidote.
The famous geometer Apollonius of Perge, born approximately in the year 262 B.C. in the city that gave him the last name, he was the first to take advantage of the asymptote term to refer to the mathematical concept of a line that fails to touch a hyperbola , in his treatise "About conic sections"It should be mentioned that the names of the parable and the ellipse as well as the epicycles theory (which seeks to explain the apparent variation in the speed of the Moon and the supposed movement of the planets).
