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Author

Nicla Palladino

Other affiliations: University of Salerno
Bio: Nicla Palladino is an academic researcher from University of Palermo. The author has contributed to research in topic(s): Beauty & Divergent thinking. The author has an hindex of 3, co-authored 13 publication(s) receiving 21 citation(s). Previous affiliations of Nicla Palladino include University of Salerno.

Papers
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11 Dec 2009
Abstract: In this paper, we want to document the history of the models of mathematical surfaces used for the didactics of pure and applied “High Mathematics”, in Italy and in Europe. These models were built between the second half of nineteenth century and the 1930s. We 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, by using short descriptions and opportune examples.

5 citations

Journal ArticleDOI
Abstract: title SUMMARY /title We present here the general catalogue and the website of the mathematical models found in the Italian universities of Catania, Messina, Bari, Naples, Rome, Florence, Bologna, Modena, Ferrara, Parma, Pavia, Milan, Padua, Turin and Genoa. For the most part they consist of old models published by the firms Ludwig Brill in Darmstadt, Martin Schilling in Halle an der Saale (later Leipzig), by H. Wiener for G. B. Teubner in Leipzig or belonging to the Collections Charles Muret published by Charles Delagrave in Paris. Other models were produced by different firms. A small number were even produced in Italy at the laboratories annexed to universities and, among these we also include the reproduction created in Florence by Luigi Campedelli in the 1950s with the support of the Unione Matematica Italiana. The research on the models (almost all of which are accompanied by the relevant images) can be carried out principally on the basis of the following criteria: Name of model - Catalogue - Material - Year of publication - Designer - Builder - Publisher - Location. The address of the mirrored web sites are: www.dmi.unisa.it/people/palladino/modelli and www.dma.unina. it/~nicla.palladino/catalogo.

3 citations

01 Jan 2010
Abstract: In this paper we develop some relationships between the approximation method Rafael Bombelli used to find the square root of an integer number in his Algebra (1572), Leibniz’s “hidden calculus” in infinitesimal algorithms (Nova Methodus, 1684) and Newton’s procedures of extraction more arithmetico of the root of a binomial: these procedures lead to the series development of a binomial root that Newton used in integral calculus (ca. 1666). Riassunto: Nell’articolo, vengono confrontati alcuni procedimenti di approssimazione, dovuti a Rafael Bombelli per calcolare la radice quadrata di un numero (Algebra, 1572) con il “calcolo nascosto” degli algoritmi infinitesimali di Leibniz (Nova Methodus, 1684) e, ancora, con procedure per l’estrazione della radice di un binomio concepite da Newton: queste ultime conducono agli sviluppi in serie di binomi che Newton adoperò per il calcolo integrale. 1. THE SQUARE ROOT AND METHODS OF APPROXIMATION. It is possible to find direct and recursive methods for calculating square roots of integer numbers since the second century. Bombelli, in his Algebra, and Newton, in Arithmetica Universalis, exposed Claudius Ptolemy’s method that has been used for calculating both exact and nonexact square roots. Newton proposed a graphic scheme (“a danda lunga”, which means all passages included) for calculating the square root following Ptolemy’s method. The extraction of the square root of 22178791 is one of the two examples given by Newton [Newton 1707, pp. 32-33]: I Trav. Ianniello, 7. Frattamaggiore (NA). E-mail: nicla.palladino@unina.it 1 Ptolemy’s method is nearly equal to methods that we can read nowadays in arithmetic manuals for the first level middle school.

1 citations


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Abstract: Up until the French Revolution, European mathematics was an “aristocratic” activity, the intellectual pastime of a small circle of men who were convinced they were collaborating on a universal undertaking free of all space-time constraints, as they believed they were ideally in dialogue with the Greek founders and with mathematicians of all languages and eras. The nineteenth century saw its transformation into a “democratic” but also “patriotic” activity: the dominant tendency, as shown by recent research to analyze this transformation, seems to be the national one, albeit accompanied by numerous analogies from the point of view of the processes of national evolution, possibly staggered in time. Nevertheless, the very homogeneity of the individual national processes leads us to view mathematics in the context of the national-universal tension that the spread of liberal democracy was subjected to over the past two centuries. In order to analyze national-universal tension in mathematics, viewed as an intellectual undertaking and a profession of the new bourgeois society, it is necessary to investigate whether the network of international communication survived the political, social, and cultural upheavals of the French Revolution and the European wars waged in the early nineteenth century, whether national passions have transformed this network, and if so, in what way. Luigi Cremona's international correspondence indicates that relationships among individuals have been restructured by the force of national membership, but that the universal nature of mathematics has actually been boosted by a vision shared by mathematicians from all countries concerning the role of their discipline in democratic and liberal society as the basis of scientific culture and technological innovation, as well as a basic component of public education.

11 citations

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Abstract: This workshop brings together historians of mathematics and science as well as mathematicians to explore important historical developments connected with models and visual elements in the mathematical and physical sciences. It will address the larger question of what mathematicians mean by a model, a term that has been used in a variety of contexts, both within pure mathematics as well as in applications to other fields. Most of the talks will present case studies from the period 1800 to 1950 that deal with the modelling of analytical, geometrical, mechanical, astronomical, and physical phenomena. Some speakers will also show how computergenerated models and animations can be used to enhance visual understanding. This workshop will also consider the role of visual thinking as a component of mathematical creativity and understanding. For the period in view, we hope to form a provisional picture of how models and visual thinking shaped important historical developments.

9 citations

Journal ArticleDOI
Abstract: In this paper, we examine the evolution of a specific mathematical problem, i.e. the nine-point conic, a generalisation of the nine-point circle due to Steiner. We will follow this evolution from Steiner to the Neapolitan school (Trudi and Battaglini) and finally to the contribution of Beltrami that closed this journey, at least from a mathematical point of view (scholars of elementary geometry, in fact, will continue to resume the problem from the second half of the 19th to the beginning of the 20th century). We believe that such evolution may indicate the steady development of the mathematical methods from Euclidean metric to projective, and finally, with Beltrami, with the use of quadratic transformations. In this sense, the work of Beltrami appears similar to the recent (after the anticipations of Magnus and Steiner) results of Schiaparelli and Cremona. Moreover, Beltrami's methods are closely related to the study of birational transformations, which in the same period were becoming one of the main topics of algebraic geometry. Finally, our work emphasises the role played by the nine-point conic problem in the studies of young Beltrami who, under Cremona's guidance, was then developing his mathematical skills. To this end, we make considerable use of the unedited correspondence Beltrami – Cremona, preserved in the Istituto Mazziniano, Genoa.

8 citations