Open AccessAsymptotes of Plane Curves - Revisited
Author(s) -
Ana Katalenić,
Aleksandra Čižmešija,
Željka Milin Šipuš
Publication year - 2021
Publication title -
kog/kog
Language(s) - English
Resource type - Journals
eISSN - 1846-4068
pISSN - 1331-1611
DOI - 10.31896/k.25.9
Subject(s) - asymptote , tangent , plane curve , infinity , mathematics , plane (geometry) , mathematical analysis , line (geometry) , limiting , tangent vector , position (finance) , point (geometry) , geometry , algebraic curve , pure mathematics , mechanical engineering , finance , engineering , economics
In this paper we present a review of the basic ideas and results concerning asymptotic lines of plane curves. We discuss their different definitions, namely that of a limiting position of tangent lines, of the tangent line at infinity, and finally the one that requires that the distance between points of a curve and asymptotic line tends to 0 as the point moves along an infinite branch of the curve. We also recall the method of determining asymptotes of algebraic curves from theleading coefficients in their equation and provide examples.