Hilbert Problem 15 and Ritt-Wu Method (II)
| Autor: | Dingkang Wang, Banghe Li |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Cusp (singularity)
0209 industrial biotechnology Mathematical analysis Tangent 02 engineering and technology Intersection (Euclidean geometry) Generic point 020901 industrial engineering & automation Inflection point Tangent lines to circles Line (geometry) 0202 electrical engineering electronic engineering information engineering Computer Science (miscellaneous) 020201 artificial intelligence & image processing Point (geometry) Information Systems Mathematics |
| Zdroj: | Journal of Systems Science and Complexity. 33:2124-2138 |
| ISSN: | 1559-7067 1009-6124 |
| Popis: | This paper proves three statements of Schubert about cuspal cubic curves in a plane by using the concept of generic point of Van der Waerden and Weil and Ritt-Wu methods. They are relations of some special lines: 1) For a given point, all the curves containing this point are considered. For any such curve, there are five lines. Two of them are the tangent lines of the curve passing through the given point. The other three are the lines connecting the given point with the cusp, the inflexion point and the intersection point of the tangent line at the cusp and the inflexion line. 2) For a given point, the curves whose tangent line at the cusp passes through this point are considered. For any such curve, there are four lines. Three of them are the tangent lines passing through this point and the other is the line connect the given point and the inflexion point. 3) For a given point, the curves whose cusp, inflexion point and the given point are collinear are considered. For any such curve, there are five lines. Three of them are tangent lines passing through the given point. The other two are the lines connecting the given point with the cusp and the intersection point of the tangent line at the cusp and the inflexion line. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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