Übersetzung und Analyse von Wörtern durch künstliche Intelligenz
Auf dieser Seite erhalten Sie eine detaillierte Analyse eines Wortes oder einer Phrase mithilfe der besten heute verfügbaren Technologie der künstlichen Intelligenz:
- wie das Wort verwendet wird
- Häufigkeit der Nutzung
- es wird häufiger in mündlicher oder schriftlicher Rede verwendet
- Wortübersetzungsoptionen
- Anwendungsbeispiele (mehrere Phrasen mit Übersetzung)
- Etymologie
punctured surface - Übersetzung nach russisch
![disk surface]], square surface, and hemisphere surface. The boundaries are shown in red. All three of these are topologically equivalent to each other.](https://commons.wikimedia.org/wiki/Special:FilePath/SurfacesWithAndWithoutBoundary.svg?width=200 "disk surface]], square surface, and hemisphere surface. The boundaries are shown in red. All three of these are topologically equivalent to each other.")
![[[sphere]]](https://commons.wikimedia.org/wiki/Special:FilePath/SphereAsSquare.svg?width=200 "[[sphere]]")
![[[real projective plane]]](https://commons.wikimedia.org/wiki/Special:FilePath/ProjectivePlaneAsSquare.svg?width=200 "[[real projective plane]]")
![[[torus]]](https://commons.wikimedia.org/wiki/Special:FilePath/TorusAsSquare.svg?width=200 "[[torus]]")
![[[Klein bottle]]](https://commons.wikimedia.org/wiki/Special:FilePath/KleinBottleAsSquare.svg?width=200 "[[Klein bottle]]")
математика
поверхность с вынутой точкой
математика
открытая поверхность
математика
топологическая поверхность
Definition
Wikipedia
In the part of mathematics referred to as topology, a surface is a two-dimensional manifold. Some surfaces arise as the boundaries of three-dimensional solids; for example, the sphere is the boundary of the solid ball. Other surfaces arise as graphs of functions of two variables; see the figure at right. However, surfaces can also be defined abstractly, without reference to any ambient space. For example, the Klein bottle is a surface that cannot be embedded in three-dimensional Euclidean space.
Topological surfaces are sometimes equipped with additional information, such as a Riemannian metric or a complex structure, that connects them to other disciplines within mathematics, such as differential geometry and complex analysis. The various mathematical notions of surface can be used to model surfaces in the physical world.
