Franco Eugeni remembers Bruno Rizzi: in this brief introduction, I would like to remember an afternoon spent in “ Roma Tre ” with Bruno, since we were both Ordinary Professors at that University. We passed it doing a dense program of work for the next three years. At 6.00 pm, I left for “Roseto degli Abruzzi”. At six o'clock a.m. of the next morning, I still have the voice in my ears. A phone call from the Headmaster Ciro d'Aniello, who (...) told me " The Professor is dead" In that afternoon, Emilio Ambrisi and I went to Rome; we were stunned and desperate. Not many days later, a conference was held at the University of Teramo; it was the conference that we had prepared for Bruno, to celebrate his 60th birthday, but it was his memory. In the opening conference, Prof. Antonino Giambo, also fraternal friend of Bruno, burst into a tearful cry, which expressed in a moment, the senses of friendship and love that we all had for the missing friend! Starting from this work with Fabrizio Maturo, the study of some problems left open by the works of Eugeni and Rizzi will be investigated. Sunto Ricordo di Franco Eugeni su Bruno Rizzi: in questa brevissima introduzione vorrei ricordare un pomeriggio passato a Roma Tre con Bruno, visto che allora eravamo entrambi Professori Ordinari in quella Università. Lo passammo a fare un denso programma di lavoro per i successivi tre anni. Alle 18.00 ripartii per Roseto degli Abruzzi. Alle sei del mattino successivo, ho ancora la voce nelle orecchie, una telefonata del Preside Ciro d’Aniello, che mi diceva “ Il Professore è morto” Nel pomeriggio Emilio Ambrisi ed io ci recammo a Roma, eravamo attoniti e disperati. Non molti giorni dopo si tenne presso l’Università di Teramo un Convegno, era il Convegno che avevamo preparato per Bruno, per festeggiare i suoi 60 anni, fu invece il ricordo. Nella conferenza di apertura il prof. Antonino Giambò, anche lui, come noi, fraterno amico di Bruno, scoppiò in un pianto dirotto, che espresse in un attimo, i sensi dell’amicizia e dell’amore, che tutti noi avevamo per l’amico scomparso! A partire da questo lavoro con Fabrizio Maturo verrà approfondito lo studio di alcune problematiche rimaste aperte dai lavori di Eugeni e Rizzi. (shrink)

Our goal is to prove that the golden section, however important, is not the only key to understand a mathematical-formalizing approach to the idea of beauty. Having developed, from this point of view, reading keys linked to the post-modern, it is necessary to link together the multiple rivulets of knowledge that gather in this direction. Moreover the canons of the approaches presented up to now are very indicative for the understanding of many aspects of beauty, which however depends on the (...) historical moment and the cultures created in the various civilizations. Therefore we can affirm that there is no effective definition of "beauty" that can be codified through fixed canons, but that the concept is expressed by a series of stratifications and interpretations that tend to link several major variations, expressing the various answers given by man to the question: what is the beauty? (shrink)

All logic instruments and tools in possession of, and used by researchers are generally considered as the results of bivalent logic. A common error to people interested in science is that, usually, they don’t known with certainty which things are true and which are false. But they are sure that things are true or false. No ways in the middle. The fuzzy principle asserts that this is completely a question of measure. Fuzziness is the opposite concept to bivalency, while fuzzy (...) quality means polyvalency. Fuzzy logic is able to manage uncertain knowledge and, more precisely, to manage those rules difficult to formalize. In many cases, such rules haven’t got, or cannot have, the necessary precision, required for a whole formalization. (shrink)

Our goal is to prove that the golden section, however important, is not the only key to understand a mathematical-formalizing approach to the idea of beauty. Having developed, from this point of view, reading keys linked to the post-modern, it is necessary to link together the multiple rivulets of knowledge that gather in this direction. Moreover the canons of the approaches presented up to now are very indicative for the understanding of many aspects of beauty, which however depends on the (...) historical moment and the cultures created in the various civilizations. Therefore we can affirm that there is no effective definition of "beauty" that can be codified through fixed canons, but that the concept is expressed by a series of stratifications and interpretations that tend to link several major variations, expressing the various answers given by man to the question: what is the beauty? (shrink)

Our goal is to prove that the golden section, however important, is not the only key to understand a mathematical-formalizing approach to the idea of beauty. Having developed, from this point of view, reading keys linked to the post-modern, it is necessary to link together the multiple rivulets of knowledge that gather in this direction. Moreover the canons of the approaches presented up to now are very indicative for the understanding of many aspects of beauty, which however depends on the (...) historical moment and the cultures created in the various civilizations. Therefore we can affirm that there is no effective definition of "beauty" that can be codified through fixed canons, but that the concept is expressed by a series of stratifications and interpretations that tend to link several major variations, expressing the various answers given by man to the question: what is the beauty? (shrink)