File:Riemann zeta function. Riemann Hypothesis and the axis of symmetry.svg
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English: Applying an axis of symmetry to a funicular polygon, produced by the Riemann zeta (s) function, is possible only if the real part of (s) is 1/2.
It is symmetry that allows a funicular polygon, produced by the Riemann zeta (s) function, to converge on the origin of the complex plane; a funicular polygon can however be symmetrical even if it converges in a point that is not the origin. To be able to apply the axis of symmetry in a simple and precise way, it is necessary to know the point of covergence, which must be different from the origin of the complex plane. In the case depicted in the image, the value s=1/2+20,000,000,000i did not allow me to calculate the convergence point. Despite this I managed to position the axis of symmetry; thanks to the symmetry I also found the point of convergence. Further information can be found at the following link http://doi.org/10.5281/zenodo.7117684 The most updated article can be found at the following link http://doi.org/10.5281/zenodo.8026759Italiano: Applicare un asse di simmetria ad un poligono funicolare, prodotto dalla funzione zeta(s) di Riemann, è possibile solo se la parte reale di (s) è 1/2.
È la simmetria a consentire che un poligono funicolare, prodotto dalla funzione zeta(s) di Riemann, possa convergere sull'origine del piano complesso; un poligono funicolare può però essere simmetrico anche se converge in un punto che non è l'origine. Per riuscire ad applicare in modo semplice e preciso l'asse di simmetria, occorre conoscere il punto di covergenza, che deve essere diverso dall'origine del piano complesso. Nel caso raffigurato nell'immagine, il valore s=1/2+20.000.000.000i non mi ha permesso di calcolare il punto di convergenza. Nonostante questo sono riuscito a posizionare l'asse di simmetria; grazie alla simmetria ho anche trovato il punto di convergenza. Ulteriori informazioni si trovano al seguente link http://doi.org/10.5281/zenodo.7117684 L'articolo più aggiornato si trova al seguente link http://doi.org/10.5281/zenodo.8026728 |
| Date | |
| Source | Own work |
| Author | 52Dante21 |
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| current | 18:49, 11 October 2022 | | 1,726 × 1,214 (23 KB) | 52Dante21 (talk | contribs) | Uploaded own work with UploadWizard |
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