 |
|
| A B C D E F G H I J K L M N O P Q R S T U V W X Y Z |
|
|
asymptote
 |
Imagine facing along the direction of a great wall that is just a meter to your left. Every second, you walk forward a meter and at the same time move sideways slightly so that you halve the distance between you and the wall. The path you follow is an asymptote.
The word comes from the Greek roots a (not), sum (together), and piptein (to fall), so that it literally means "not falling together" and was originally used in a wider sense to describe any two curves that don't intersect. Proclus wrote about both asymptotic lines and symptotic lines (those that do cross). Nowadays, "symptotic" is almost never heard, and "asymptote" is used mainly to denote lines that serve as a limiting barrier for some curve as one of its parameters approaches plus or minus infinity.
The "~" symbol is often used to show that one function is asymptotic to another. For example, f(x)~ g(x) indicates that the ratio of the functions f(x) to g(x) approaches 1 as x tends to infinity. Asymptotes are not always parallel to the x- and y-axes, as shown by the graph of x + 1/x (illustrated here), which is asymptotic to both the y-axis and the diagonal line y = x.
Related categories
• PLANE CURVES
• GEOMETRY
Also on this site:
Encyclopedia of Alternative Energy & Sustainable Living
Encyclopedia of History
Transport Concepts & Designs (partner site)