0000000001180301
AUTHOR
Nicla Palladino
Vuibert’s geometric anaglyphs: their historical origins and present applications
Giovanni Novi (1826-1866). La corrispondenza con Enrico Betti ed il suo contributo matematico
La corrispondenza epistolare Niccolò De Martino - Girolamo Settimo. Con un saggio sull’inedito Trattato delle Unghiette Cilindriche di Settimo
Il fondo Maria Del Re e l’insegnamento della Geometria nell’Universita’ di Napoli negli anni Venti e Trenta del Novecento
Algoritmi elementari del calcolo aritmetico e algebrico. Tradizione e modernità
Thought and Body. An activity of Logic in primary school
Abstract In the recent decades, the pedagogical debate has been formerly traversed by the emergence an then by the assertion of a matured awareness on the importance of the psychomotor skills in the educational-didactic path. The interpretive bio-psycho-social matrix has today become one of the pivotal points on which the educational-didactic activity rests and develops for the training of child's personality in its full motor, mental, perceptual, emotional, sensory development. Pedagogues, educators, and training professionals are increasingly confident that, since the birth, children are sensitive to the stimuli and to the environmental intervention, therefore it's essential to know their…
L'epistolario ritrovato. Le lettere “napoletane” di Baldassarre Boncompagni a Gilberto Govi.
In questa nota forniamo il testo di numerose lettere inviate dallo storico della matematica Baldassarre Boncompagni al fisico e storico della fisica Gilberto Govi. Queste lettere erano conservate presso il Dipartimento di Matematica ed Applicazioni “Renato Caccioppoli” dell’Università di Napoli Federico II. Esse attualmente devono essere considerate disperse. Il testo allora è tratto da alcune fotografie ritrovate tra le carte dello storico della matematica Franco Palladino recentemente scomparso
La storia della Matematica come chiave per l’inclusione interculturale nella pratica d’aula attuale
The research on the intercultural phenomenon in Italy increased with the growing phenomenon of migration, highlighting the problem of cultural diversity and social policies. The school has, in this process, a key role. The goal of a good educational project is to understand that the intercultural requires continual reference to the concrete experiences of the people. Theoretical assumptions of our project are the concepts of “interaction”, “empathy”, “decentralization” and “cognitive transitivity" (Nanni 1998). In this theoretical direction, we present an experimental multidisciplinary mathematical laboratory where students and teachers can understand that a discipline that seems static and…
From the fourteenth century to Cabrì: convuleted constructions of star polygons
The Genesis of the Italian School of Algebraic Geometry Through the Correspondence Between Luigi Cremona and Some of His Students
Luigi Cremona is considered the founder of the Italian school of algebraic geometry. He formed a group of students of great value, very active in scientific research. Examining the letters from Eugenio Bertini, Ettore Caporali, and Riccardo De Paolis to Cremona preserved in the archive of the Istituto Mazziniano in Genoa, we have reconstructed their biographies, careers, studies, and relationships with their teacher. They had the merit of cultivating the scientific innovations of the period and passing them on to the subsequent generations.
La corrispondenza epistolare Brioschi-Genocchi.
Presso il Dipartimento di Matematica e Applicazioni dell'Università di Napoli Federico II si è conservato un importante fondo ottocentesco di lettere inviate ad Angelo Genocchi dai più significatrivi matematici italiani dell'epoca. Il complesso di lettere era stato rimesso a Siacci, allora a Napoli, sul quale era caduto il compito di comporre un ampia biografia di Genocchi in occasione della sua morte. In questa nota vengono presentate e ampiamente commentate le lettere di Francesco Brioschi, il celebre fondatore del Politecnico di Milano. La corispondenza, abbastanza vasta ( si tratta di circa settanta lettere di Brioschi a Genocchi e di quattro di Genocchi a Brioschi, ritrovate negli arch…
Sieve of Eratosthenes to find new numbers
Why is Math so hard for some children? We want to start from the vision and the teorethical dissertation, supported by educational and philosophical theories that here are presented, to use the concept of reification. A new element in contemporary reason is therefore the re-emergence of the subject, the reconsideration of the distinction between objective and subjective, between that which belongs to the subject and that which belongs to the object. We want to submit an experience of study with 10-year old children, at primary school. The aim is to help children in forming the abstract concept of prime numbers and to use this concept for build other concepts.
Geometria elementare: dalla geometria del triangolo alla geometria dinamica
Da una decina di anni si discute sull’importanza di presentare, a fini didattici e anche per la formazione dei docenti, la geometria elementare mediante l’utilizzo di software di geometria dinamica. Ciò naturalmente si inserisce in una visione dell’insegnamento della geometria che valorizzi gli aspetti laboratoriali. Occorre comunque rilevare che il laboratorio non va visto, in questo contesto, come una serie di interventi episodici e slegati, ma come la sede naturale per affrontare aspetti che possano destare l’interesse, affiancando quelli curricolari anche attraverso percorsi storici che tocchino spunti di origini differenti, di tipo trasversale, mediante il quale gli argomenti del passa…
I poligoni stellati da Broscius a Cabrì: spunti didattici e costruzioni geometriche
Historical Notes on Star Geometry in Mathematics, Art and Nature
Gamma: “I can. Look at this Counterexample 3: a star-polyhedron I shall call it urchin. This consists of 12 star-pentagons. It has 12 vertices, 30 edges, and 12 pentagonal faces-you may check it if you like by counting. Thus the Descartes-Euler thesis is not true at all, since for this polyhedron \(V - E + F = - 6\)”. Delta: “Why do you think that your ‘urchin’ is a polyhedron?” Gamma: “Do you not see? This is a polyhedron, whose faces are the twelve star-pentagons”. Delta: “But then you do not even know what a polygon is! A star-pentagon is certainly not a polygon!”
Intorno alla risoluzione delle equazioni algebriche di quinto grado per funzioni ellittiche in Betti e Brioschi. Tra opere a stampa e corrispondenze epistolari (1850-1860)
La conica per nove punti: il contributo di Beltrami. Considerazioni storiche e didattiche
L’avvento dei software di Geometria dinamica ha ridato attualità al valore didattico, ma più in generale formativo, di molti aspetti della Geometria elementare, in voga soprattutto fino ai primi anni dello scorso secolo. Tra i numerosi ed interessanti argomenti di Geometria elementare, intendiamo qui approfondire quello legato alla “conica per nove punti”, soggetto spesso “riscoperto” nel corso del tempo. Lo scopo di questo intervento è duplice: innanzitutto abbiamo provato a ricostruire il reale sviluppo storico dello studio della conica per nove punti, per la sua rilevanza sia sul piano storiografico, sia su quello didattico e divulgativo. In secondo luogo, presentiamo alcune importanti r…
From art to geometry: Aesthetic and beauty in the learning process
Starting from the concept that knowledge comes as element of mediation between the convergent thinking, founded on experience, and the divergent thinking, placed in the perceptive, intuitive, creative dimension, in this paper we want to present an idea for developing an educational path combining the concept of “beauty” and some historical notes. It is possible to use this dissertation as a starting point to conceive a geometric laboratory that drawing inspiration from artistic works, get to create geometric shapes provided with fascinating symmetries
Gli Anaglifi di Vuibert. Origine storica e applicazioni in Didattica basata sui modelli di superfici matematiche.
Some relationships between the calculus of Newton, Bombelli’s Algebra and Leibniz
Meaningful learning and new technologies: e-learning and mathematical surfaces
E-learning is undoubtedly a unique and exciting opportunity for interaction between the traditional teaching-methodological framework and the new technologies. It gives the opportunity for each student to build their own personal path of interpretation and ease the reticulated structure of knowledge. The learning process assumes, in this way, a fundamental creative-ideational dimension. Multimedia and interactivity have, in fact, reason to exist and meaning in the cortical structure and in the reticular human thought. The media ducation (and e-learning in particular) lies then in a scenario in which human relationships and communication at all levels are no arbitrary situations, assigned to…
Dalla retta di Simson-Wallace all’ipocicloide tricuspide. Storia di un soggetto elementare che ha affascinato celebri matematici
L’ipocicloide tricuspide è una ben nota curva del quarto ordine e di terza classe che nel corso di un paio di secoli ha incuriosito numerosi matematici del calibro di Steiner, Cremona, Beltrami, Cesàro, Fréchet, Schröter, Clebsch, Battaglini, Laguerre, Cayley, volendo citare solo i più famosi. Tale interesse si connette con vari aspetti della Matematica: a. la sua generazione come inviluppo della retta di Simson-Wallace, la cui storia è di per sé intrigante; b. il suo legame con il cerchio di Feuerbach, che, a sua volta, ha una storia interessante; c. il fatto che essa si può ottenere come inversione quadrica di un cerchio e quindi la stretta connessione con le origini delle trasformazioni …
THE GEOMETRY THROUGH THE BODY: DOING, ACTING, THINKING
The geometry has been for more than two millennia one of the most important fields of knowledge of mathematics, identifying with it for a long time. In education, the relationship between the geometry and the physical world has always been considered one of the main elements for the acquisition of specific skills and competences. In the teaching-learning processes the thinking and the interconnection between doing, acting, thinking is therefore crucial. Teaching through the body may prove effective for teaching mathematics which, very often, is hard to be learned because of difficulties that the child encounters in assimilating mathematical symbolism and, after, applying it to real life and…
Dalla “moderna geometria” alla “nuova geometria” italiana. Viaggiando per Napoli, Torino e dintorni. Lettere di Sannia, Segre, Peano, Castelnuovo, D’Ovidio, Del Pezzo, Pascal e altri a Federico Amodeo
Per la costruzione dell’Unità d’Italia. Le corrispondenze epistolari Brioschi - Cremona e Betti - Genocchi, Firenze
Un dibattito che continua in geometria elementare: La retta di Simson-Wallace e le sue molteplici generalizzazioni
For some years now the importance has been appraised of demonstrating elementary geometry to pupils and future teachers through interactive geometry software. This fits within a view of the teaching of geometry that stresses a hands-on approach, thanks to which it is possible to teach the subject via historical syllabi, touching on ideas from different origins and of a transversal nature. The debate about the role of elementary geometry in the last 30 years is connected to this, with contributions by scholars such as Yaglom, Scimemi and Betti. In the perspective of following a sequence of elementary geometry constructions historically connected with each other, we suggest a path that analys…
Intercultural education in italy. Cultural identity, educational emergency and teaching strategies: a mathematics laboratory
The research about the intercultural phenomenon in Italy increased with the growing phenomenon of migration, highlighting the problem of cultural diversity and social policies. "The encounter with the diversity should not be suffered, either tolerated, or rejected it should be accepted as survival strategy" (Callari Galli, 2000). This should go beyond the logic of the social emergency and the perception that people have of the problem. The school has, in this process, a key role. The goal of a good educa-tional project is to understand that the intercultural requires continual reference to the concrete experi-ences of the people Theoretical assumptions of the project are the concepts of “in…
La corrispondenza di Giuseppe Battaglini a Luigi Cremona
Dalle Scienze matematiche e fisiche a Scienze dell'informazione. Il caso della Facoltà di Scienze (MM. FF. NN.) dell'Università di Salerno e dei suoi primi computer
An Archimedean research theme: the calculation of the volume of cylindrical groins
Starting from Archimedes’ method for calculating the volume of cylindrical wedges, I want to get to describe a method of 18th century for cilindrical groins thought by Girolamo Settimo and Nicolo di Martino. Several mathematicians studied the measurement of wedges, by applying notions of infinitesimal and integral calculus; in particular I examinated Settimo’s Treatise on cylindrical groins, where the author solved several problems by means of integrals.
Creating “mathematically” sustainable world: from the spirograph, a reverse path
The approach to the subject of mathematic learning, represents, in the pedagogical-educational field, a problematic situation. Nowadays we attend to an heated discussion on the character of the basic mathematical concepts, on the analytical-critical succession between processes and objects. The purpose of these notes is to recover and to value the contribution of the autopoiesis theory in the characterization of the mathematical domain going beyond the mere reiteration, inspecting and testing new and generative paths of ideas. In this mechanism we would insert the use of the spirograph as a disturbing, uncertain element able to nourish the “mind-system”.
The issue of mathematics textbooks in the correspondence of Giovanni Novi to Enrico Betti during the Unification of Italy
The Unification of Italy represented a political, educational and mathematical turning point; leading researchers worked to raise both the mathematical and political standard in Italy through their active role in the reform of the Italian educational system at the secondary as well as at the university levels. One of the aims was to adapt the elementary books of mathematics to the progress of mathematics, through the translation of new works too. In the Archivio Betti, at the Scuola Normale Superiore in Pisa, there are 48 letters that the mathematician Giovanni Novi (1826-1866) sent his friend Enrico Betti (1823-1892) from December of 1850 to October of 1864. Novi translated important treat…
MANIPULATION OF OBJECTS AS INTEGRATION ACTIVITY
The visual disability assumes, in the processes of teaching and learning, a particular connotation for the specificity that over the years the vision in the overall structure of knowledge has had. The whole western tradition on the knowledge stood on a "oculocentric" vision of knowledge. The view has always been considered the “sense for excellence". An educational activity, therefore, that emphasizes and promotes strategies of inclusion / integration of students with visual impairment is significant and essential to the whole class group. We present here an experimentation with primary school children: in a closed bag, there are objects of everyday life: every time a child extracts an obje…
The corrispondences between the mathematicians Brioschi and Cremona and Betti and Genocchi, during Italian Unification
Mathematical surfaces models between art and reality
In this paper, I want to document the history of the mathematical surfaces models used for the didactics of pure and applied “High Mathematics” and as art pieces. These models were built between the second half of nineteenth century and the 1930s. I want here also to underline several important links that put in correspondence conception and construction of models with scholars, cultural institutes, specific views of research and didactical studies in mathematical sciences and with the world of the figurative arts furthermore. At the same time the singular beauty of form and colour which the models possessed, aroused the admiration of those entirely ignorant of their mathematical attractions
A continuing debate in elementary geometry: the Simson–Wallace line and its many generalisations
For some years now the importance has been appraised of demonstrating elementary geometry to pupils and future teachers through interactive geometry software. This fits within a view of the teaching of geometry that stresses a hands-on approach, thanks to which it is possible to teach the subject via historical syllabi, touching on ideas from different origins and of a transversal nature. The debate about the role of elementary geometry in the last 30 years is connected to this, with contributions by scholars such as Yaglom, Scimemi and Betti. In the perspective of following a sequence of elementary geometry constructions historically connected with each other, we suggest a path that analys…
La corrispondenza Giovanni Novi - Enrico Betti
Giovanni Novi
I modelli matematici costruiti per l'insegnamento delle matematiche superiori. Pure e applicate.
Il metodo di eliminazione per la risoluzione di un sistema di equazioni proposto da Nicolò De Martino alla metà del XVIII secolo
L’articolo illustra un metodo per la risoluzione di un sistema di due equazioni in due incognite, contenuto nel poscritto di una lettera del matematico napoletano De Martino inviata dl palermitano Settimo. Il metodo, semplice e interessante, fornisce un esempio significativo della ricerca di automatismo nella risoluzione di problemi e nell’esecuzione di calcoli