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) | Gäbe es das Werkzeug "Spiegelung an einer Kugel", so gäbe es viele
interessante geometrische Objekte zu entdecken:
Die Kugel-Inversion ist
- punkttreu, wenn man den einen Punkt mit hinzunimmt
- kreistreu, wenn man Geraden als Kreise durch betrachtet
- kugeltreu, wenn man Ebenen als Kugeln durch erkennt
- winkeltreu, allerdings orientierungsumkehrend.
Wie sehen die Bilder unter einer Kugel-Spiegelung aus von:
- Zylindern
- Kegeln
- einem Torus
- einem Hyperboloid oder anderen Quadriken
- Kurven, Spiralen
- platonischen Körpern und anderen Polytopen ???
|