Recentemente diversi studi hanno mostrato come la distanza tra i Grundlagen e le precedenti pubblicazioni di Hilbert non sia tanto abissale come ritenuto in passato, ma vi sia una significativa consequenzialità con la teoria dei campi numerici. Nel ribadire questa visione, si intende mostrare come i risultati ottenuti da Hilbert, in particolare sui teoremi di Pappo e di Desargues, siano conseguenza di una ricerca più ampia sulla possibilità di introdurre all’interno della geometria dei sistemi numerici atti a coordinatizzare il piano (...) o lo spazio. Nello sviluppo della ricerca hanno avuto un ruolo determinante la scoperta di Hurwitz delle uniche quattro algebre di divisione normate e le idee maturate, già agli inizi della sua carriera, sulla finitezza degli strumenti da utilizzare in geometria, in particolare la rinuncia al concetto di continuità e la limitazione a sistemi numerici ordinati e numerabili. Nelle conclusioni dei Grundlagen, Hilbert rimarca l’importanza di dimostrare l’impossibilità delle assunzioni, tra cui l’impossibilità di determinare, attraverso solo relazioni geometriche di incidenza, dei sistemi numerici ordinati che abbiano le stesse proprietà dei quaternioni e degli ottonioni rispetto alle operazioni dell’aritmetica. (shrink)

The "clinical" method is one of the possible methodological choices for Pedagogy as a profession and as a research, for Social Sciences and for other sciences, as well as for the professions that refer to these sciences. It can also be called "casuistic and situational method", and it is an exclusive alternative to the statistical operational method, with a full community of scientific rigor and technical applicativeness. It consists in the consideration of the individual case and of the single person (...) with all its specific symptomatic and phenomenal characteristics, through the mediation of the professional to a general case within the limited number of general cases whose corpus makes science, profession and scientific and professional community, and in obtaining the indications for the help and the service to whom the professional has addressed. A particular reflection is dedicated to the specific technique for the transition from the particular to the general through the mediation provided by the professional, that is through human mediation, according to a non-tautological technique known from ancient Greece with the name of "abduction" or "retroduction" "Ἐπιχείρημα” or “Reductio ad absurdum” by Zeno from Elea, or 'απαγωγή known to Aristoteles. The theme offers a precious opportunity for various reflections on the profession of pedagogist and on his practice: a profession that has recently had its legal recognition in Italy too. (shrink)

This work, in continuity with the article published by Ferdinando Casolaro and Giovanna Della Vecchia in Vol 5, 2017 of this series, in which we noted that in the centuries since the eight century B.C. at the 13th century A.D. the evolution of Astronomy and historical events have influenced the development of Mathematics, intends to demonstrate how the Architecture and Literature of the following centuries have further conditioned the development of the sciences in Italy and, in particular, of Mathematics, identifying (...) the affinities and, in some cases, the coincidences between the different forms of thought that invite us to make a serious reflection on the uniqueness of culture. (shrink)

Recent programs aimed at the independent living of persons with disabilities, allow them to be costumers of sectors in which they have never had full access in the past. The Lisbon Treaty has distinctly recognized the existence of a community tourist area within the primary law, and CRPD has defined the principles of accessibility and accessible tourism as tools for the inclusion. In addition, tourism and transportation stakeholders must guarantee non-discriminatory services; they must approach persons with disabilities as every other (...) customer, by taking in consideration their needs and rights, especially when it comes to their accessibility, assistance, and information. Companies of transportation must cooperate with DPOs in order to define disability-related training procedures. (shrink)

The pedagogical research constitutes a critical, dynamic, intentional, active process oriented towards the investigation of the educaional reality under all its aspects. The present paper brings in the forefront the effort of pedagogy to crystalize its own methodology of research in its demarche of affirmation and consolidation of its scientifical status. The complexity and the high number of inter-depedent variables present in the study of the human condition foiled the effort to apply a model of scientific research underlain on the (...) method of natural sciences in the field of social-human sciences. In this context, the pedagogy was bound to shade its methods of research in order to surprise as truthful as possible the complexity and diversity of the educational processes. Thus, besides the empirical-experimental method, the pedagogy was enriched with new methods of research such as the hermeneutic method, the historical method, the rhetorical method, the descriptive method, the problematization method. (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)

The journey of phenomenology apparently is not so extensive, because it was the first half of the twentieth century when Edmund Husserl appeared as the founder of phenomenology. But, it has its very roots in the works of ancient Greek philosophers like Socrates, Plato, and Aristotle. This journey did not stopped here, as various phenomenologists have also been contributing in this field and establishing the linkage between phenomenology and symbolic interactionism as well as its very relation to research. Researchers in (...) the presented work have critically analyzed the contributions of prominent phenomenologists, i.e. from Hegel to Dreyfus and have applied relational analysis. The present study propounds that with the passage of time, the concept of phenomenology has been constructively evolving; in a sense that it has become more calculative. (shrink)

Greeks of Pontian ancestry migrated, forcibly, from Pontus to Greece where they founded Pontian Greek communities, mainly in northern Greece. The rapid increase in usage of the Internet during the past years appears to be significantly affecting the activity of cultural associations in general. The Greek Pontian associations of Thrace have begun taking advantage of the Internet and social networks for their diversified activities, a “modernization” which has not been studied extensively thus far. In this paper, a corresponding analysis is (...) performed, concluding that the activity of the associations on the Internet reflects an upward trend, while an increasing number of them seek to maintain an active presence on the Internet through web sites and social networks. This activity includes primarily press conferences and informative announcements. (shrink)

Some important results about art gallery theorems are proposed, starting from Chvátal’s essay, using also polygon triangulations and orthogonal polygons.

Science is a process of inquiry: a process of asking and answering questions. However, a good question is more than an interrogatory, and a good answer is more than information: there are logical constraints that dictate when a question is answerable and what qualifies as an answer. This paper will provide an understanding of when a question is answerable, when a question is not ready to be asked, when a question is trivial, what is required for a response to be (...) an answer, and what sequence of inquiry is required to identify an answer. Equipped with this understanding, a scientist can better determine an appropriate sequence of study for a research program as well as identify the necessary arguments to warrant claims of understanding, funding, and the publication of research findings. (shrink)

This paper is dealing with one of the greatest novels in the British literature, The Golden Notebook by Doris Lessing. The novel and its main character, Anna Wulf can be interpreted in myriad ways, but our analysis is a psychoanalytical one. The introductory part of the paper gives the definitions of the psychoanalytical words that will be later on used in the paper.In The Golden Notebook, the life of Lessing’s main character offers an understanding of issues such as political repression, (...) sexual abuse, single parenthood, writer’s block, and the women’s movement. Anna Wulf’s fragmented personality is caught in the four notebooks that she writes, each one being concerned with one of Anna’s selves. Anna is the most complicated heroine analysed and we will try to discover which of her various selves are confirmed and which are repressed. In Anna’s process of healing, there are two moments of climactic confirmation: the first one when she admits that she is mad and the second one when she admits she has a writer’s block. (shrink)

The ‘continuous’ and the ‘discrete’ in nature and in science live and fight forever. The questionnaires and the Lickert scales are indispensable and widely used tools in social sciences research. Vougiouklis & Vougiouklis bar is a new tool introduced as an alternative to Lickert scales. We believe that such an alternative might offer some solutions to problems that crop up during the fight between continuous and discrete. Nevertheless, the greatest contribution of the V&V bar is that it offers the researchers (...) freedom in all stages of the research procedure using a questionnaire. (shrink)

In this article the authors intend to present a very important topic of the geometry of space: the polyhedra. After having introduced their definition, their presence will be shown in nature, in everyday life and in art, starting from ancient Greece up to the present day. First of all, we will deal with regular polyhedra; subsequently we will introduce the important family, especially in the applications, of the Archimedean polyhedra. Finally, the interesting Goldberg polyhedra will be presented.

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)

This paper argues that: a) the indiscriminate application of the German model to all European countries has fostered economic growth in the EU at different speeds; b) Italy, the cradle of Catholic capitalism, is currently attempting to react against austerity measures - imposed by the economic constrictions of the German model – by focusing on the third sector and non-profit companies.

This paper investigates how Schleiermacher’s universal hermeneutics can be considered as a better alternative to both, German rationalist aesthetics as pioneered by Christian Wolff, and Kant’s transcendental idealism, to the extent of overcoming the problematics of rule-following. A general account of the necessity of a universal hermeneutics and its meaning from historical practices of exegeses is given. This is then followed by the account of rule-following in the tradition of both German rationalist aesthetics and Kant’s transcendental idealism with latter as (...) expounded in Kant’s Critique of Pure Reason. The investigation is comparative and descriptive. The purpose of this study is to discuss the hermeneutic possibilities in research methodologies for human sciences. (shrink)

National, European, and international institutions should implement social policies to help the persons with disabilities. Strategic sectors include education, training, and work, with the equal protection of the laws. In addition, this essay is focused on another crucial “sector" that is part of the primary law, which include tourism along with public transportation and non-discrimination. In conclusion, legislators, and public institutions, as well as transport companies must comply the principles of accessibility, equality, and social justice for the social inclusion of (...) persons with disabilities. (shrink)

We present original remarks on some possible applications of classical results of Calculus. Suggestions to the higher schools teachers are also given.