File:01 Rechtwinkliges Dreieck-inverser Satz.gif
Original file (889 × 443 pixels, file size: 2.72 MB, MIME type: image/gif, looped, 202 frames, 40 s)
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Summary
[edit]Description01 Rechtwinkliges Dreieck-inverser Satz.gif |
Deutsch: Rechtwinkliges Dreieck, Inverser Satz des Pythagoras als Animation, 2 Pausen mit 10 sec
English: Rectangular triangle, Inverse Pythagorean theorem, as Animation, 2 pauses with 10 sec |
Date | |
Source | Own work |
Author | Petrus3743 |
Inverser Satz des Pythagoras
[edit]Hauptartikel: Inverser Satz des Pythagoras
Der Inverse Satz des Pythagoras für ebene rechtwinklige Dreiecke ist definiert durch
Die nebenstehende Darstellung sowie die Animation veranschaulichen die Affinität dieses Satzes zum Satz des Pythagoras. Darin ist als Beispiel die Strecke , folglich entspricht der Bezugsgröße .
Nach Umformung der Quadrate und in Rechtecke mit der Grundlinie gleich (siehe Quadratur des Polygons), passen die Rechtecke exakt in das Quadrat
Inverse Pythagorean theorem
[edit]Main article: Inverse Pythagorean theorem
The Inverse Pythagorean theorem for plane right triangles is defined by
The adjoining representation as well as the animation illustrate the affinity of this theorem to the Pythagorean theorem. In it, as an example, the distance , consequently corresponds to the reference quantity .
After reshaping the squares and into rectangles with the baseline equal to (see Quadratur des Polygons), the rectangles fit exactly into the square .
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- ↑ Reimund Albers, Universität Bremen, Eine geometrische Lösung 2. Vorbereitung "Das Baseler Problem", Eine geometrische Lösung 2. Vorbereitung, S. 10 ff., abgerufen am 24. Juni 2022.
- ↑ Reimund Albers, Universität Bremen, Eine geometrische Lösung 2. Vorbereitung "Das Baseler Problem", Eine geometrische Lösung 2. Vorbereitung, S. 10 ff., retrieved on 24. Juni 2022.
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