Hauptartikel: Inverser Satz des Pythagoras

Der Inverse Satz des Pythagoras für ebene rechtwinklige Dreiecke ist definiert durch

${\displaystyle {\mathsf {{\frac {1}{a^{2}}}+{\frac {1}{b^{2}}}={\frac {1}{h^{2}}}}}}$^[1]

Die nebenstehende Darstellung sowie die Animation veranschaulichen die Affinität dieses Satzes zum Satz des Pythagoras. Darin ist als Beispiel die Strecke ${\displaystyle {\overline {AB}}=c=5}$, folglich entspricht ${\displaystyle {\tfrac {1}{5}}c}$ der Bezugsgröße ${\displaystyle 1}$.

Nach Umformung der Quadrate ${\displaystyle {\tfrac {1}{a^{2}}}}$ und ${\displaystyle {\tfrac {1}{b^{2}}}}$ in Rechtecke mit der Grundlinie gleich ${\displaystyle {\tfrac {1}{a}}}$ (siehe Quadratur des Polygons), passen die Rechtecke exakt in das Quadrat ${\displaystyle {\tfrac {1}{h^{2}}}}$

Main article: Inverse Pythagorean theorem

The Inverse Pythagorean theorem for plane right triangles is defined by

${\displaystyle {\mathsf {{\frac {1}{a^{2}}}+{\frac {1}{b^{2}}}={\frac {1}{h^{2}}}}}}$^[2]

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 ${\displaystyle {\overline {AB}}=c=5}$, consequently ${\displaystyle {\tfrac {1}{5}}c}$ corresponds to the reference quantity ${\displaystyle 1}$.

After reshaping the squares ${\displaystyle {\tfrac {1}{a^{2}}}}$ and ${\displaystyle {\tfrac {1}{b^{2}}}}$ into rectangles with the baseline equal to ${\displaystyle {\tfrac {1}{a}}}$ (see Quadratur des Polygons), the rectangles fit exactly into the square ${\displaystyle {\tfrac {1}{h^{2}}}}$.

I, the copyright holder of this work, hereby publish it under the following license:

This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.

You are free:

• to share – to copy, distribute and transmit the work
• to remix – to adapt the work

Under the following conditions:

• attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
• share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

https://creativecommons.org/licenses/by-sa/4.0CC BY-SA 4.0 Creative Commons Attribution-Share Alike 4.0 truetrue

1. ↑ 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.
2. ↑ 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.