TL;DR
This paper explores the moduli space of miraculous pentagrams as a Del Pezzo surface, presents Fibonacci-related examples, and examines connections between Fermat ascent and Poncelet theorem.
Contribution
It provides a detailed analysis of the moduli space of miraculous pentagrams and links it to classical algebraic geometry and number theory concepts.
Findings
The moduli space of miraculous pentagrams is a Del Pezzo surface of degree 5.
Examples related to Fibonacci numbers are constructed.
Relations between Fermat ascent and Poncelet theorem are discussed.
Abstract
This article is a continuation of my previous paper on miraculous pentagrams published in Annales Scientifiques de Facult\'e des Sciences de Toulouse in 2013. We discuss the moduli space of miraculous pentagrams which is the Del Pezzo surface of degree 5, and present some examples related to Fibonacci numbers. We discuss also some relations between Fermat ascent and Poncelet theorem.
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