Asymptotic geometry of algebraic curves (Q1969338)
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scientific article; zbMATH DE number 1416125
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Asymptotic geometry of algebraic curves |
scientific article; zbMATH DE number 1416125 |
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Asymptotic geometry of algebraic curves (English)
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18 July 2000
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The purpose of this paper is to apply nonstandard analysis to the study of infinite branches of algebraic curves. If an unlimited point \(M\) of an algebraic curve \(C\) is \(\omega\vec V_1+\omega\vec V_2\), then \(C\) has an asymptotic of direction \(\vec V_1\Leftrightarrow\omega e\) is limited. We can learn the intention from the author's analysis of the example \(x^3-x^2y+ y^2=0\) by some intuitive properties of infinitesimals.
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halo
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nonstandard analysis
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infinite branches of algebraic curves
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unlimited point
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