File:ComplexPolynomiaMapping1.svg
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Captions
Captions
Mapping of small circles by a complex polynomium
Summary[edit]
| Description |
Dansk: Til venstre: Tre cirkler med radier 0.75, 1 og 1.25 og centrum i 0 samt 18 punkter fordelt jævnt på periferien af den midterste cirkel og startende med det komplekse tal z = i (markeret med grøn farve). Til højre: Billederne ved polynomiet P(z) = z³ – 15·z² + (57 + 48·i)·z + (33 – 56·i) af cirkler og punkter. Billedkurven for cirklen med radius 1 går gennem origo, fordi P(i) = 0. Billedkurverne er tæt på at være cirkler med centrum i polynomiets konstantled, 33 – 56·i.
English: Left: Three circles with radii 0.75, 1 and 1.25 and center 0 as well as 18 points distributed equally on the circumference of the middle circle and beginning with the complex number z = i (marked with green color). Right: Images by the polynomium P(z) = z³ – 15·z² + (57 + 48·i)·z + (33 – 56·i) of circles and points. The image of the circle with radius 1 passes through the origin, because P(i) = 0. The image curves are close to be circles with their center at the constant term of the polynomium, 33 – 56·i.
Deutsch: Links: Drei Kreise mit den Radien 0.75, 1 und 1.25 und Mittelpunkt 0 sowie 18 Punkte gleichmäßig auf dem mittleren Kreis verteilt beginnend mit der komplexen Zahl z = i (grün markiert). Rechts: Die Bildmengen des Polynoms P(z) = z³ – 15·z² + (57 + 48·i)·z + (33 – 56·i) von Kreis und Punkte. Das Bild des Kreises mit radius 1 verläuft durch das Origo, weil P(i) = 0. Die Bildkurven sind nahezu Kreise mit Mittelpunkt im Konstantglieds des Polynoms, 33 – 56·i. |
| Date | |
| Source | Own work |
| Author | AstroOgier |
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 14:05, 18 December 2019 | | 638 × 306 (30 KB) | AstroOgier (talk | contribs) | User created page with UploadWizard |
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