The concept of an asymptotic curve is a fundamental concept in mathematics, and it is used in various fields such as physics, engineering, and computer science. An asymptotic curve is a curve that approaches a line or another curve, but it never intersects it. In this article, we will explore the definition and meaning of asymptotic curve, its origin, associations, synonyms, antonyms, and example sentences.
Definitions
An asymptotic curve is a curve that approaches a line or another curve, but it never intersects it. In other words, the distance between the curve and the line or another curve becomes smaller and smaller as the curve extends to infinity. An asymptotic curve may have a horizontal, vertical, or oblique asymptote.
Origin
The term “asymptotic” comes from the Greek words “a-” (not) and “symptotos” (converging). The concept of an asymptotic curve was first introduced by the French mathematician Pierre de Fermat in the 17th century.
Meaning in different dictionaries
According to the Oxford English Dictionary, an asymptotic curve is “a curve that approaches a given line or curve arbitrarily closely as a variable parameter tends to infinity.” Merriam-Webster defines it as “a curve that approaches a straight line or another curve but does not meet it at any finite distance.” The Cambridge Dictionary defines it as “a curve that gets closer and closer to another curve or line but does not meet it.”
Associations
Asymptotic curves are associated with various mathematical concepts such as limits, derivatives, integrals, and differential equations. They are also used in physics to describe the behavior of physical systems as they approach infinity.
Synonyms
Some synonyms of asymptotic curve include approaching curve, limiting curve, and tangent curve.
Antonyms
There are no direct antonyms for asymptotic curve, but a curve that intersects a line or another curve is not asymptotic.
The same root words
The root word of asymptotic curve is “asymptote,” which refers to a straight line that a curve approaches but never intersects.
Example Sentences
- The graph of the function y = 1/x has a horizontal asymptotic curve at y = 0.
- The curve of the parabola approaches the x-axis as x tends to infinity, but it never intersects it, making it an asymptotic curve.
- The exponential function has an asymptotic curve at the x-axis as x tends to negative infinity.