Search results for "history of mathematics"
showing 10 items of 28 documents
Algebra Without Context Is Empty, Visualizations Without Concepts Are Blind
2018
In the acquisition and formalization of mathematical concepts, the transition between algebraic and geometric representations and the use of different modes of representation contextualizes abstract algebra. Regrettably, the role of geometry is often limited to the visualization of algebraic facts and figurative memory aids. Such visualizations are blind for the underlying concepts, since transitions between concepts in different representations assume the existence of symbols, language, rules and operations in both systems. The history of mathematics offers contexts to develop geometrical language and intuition in areas currently being taught in school in a purely algebraic fashion. The ex…
Il fondo Maria Del Re e l’insegnamento della Geometria nell’Universita’ di Napoli negli anni Venti e Trenta del Novecento
2014
On the myriad mathematical traditions of ancient greece
2002
To exert one’s historical imagination is to plunge into delicate deliberations that involve personal judgments and tastes. Historians can and do argue like lawyers, but their arguments are often made on behalf of a picture of the past, and these historical images obviously change over time. Why should the history of mathematics be any different? When we imagine the world of ancient Greek mathematics, the works of Euclid (Heath 1926), Archimedes (Heath 1897b), and Apollonius (Heath 1897a) easily spring to mind. Throughout most of the twentieth century, our dominant image of Greek mathematical traditions has been shaped by the high standards of rigor and creative achievement that are purporte…
European and Chinese Cognitive Styles and Their Impact on Teaching Mathematics
2010
A General Framework and Theoretical References.- The Chinese Written Language as Tool for a Possible Historical and Epistemological Reflections on the Mathematics and the Impact of Teaching/Learning of Mathematics.- The Meta-rules between Natural Language and History of Mathematics.- Common Sense and Fuzzy Logic.- The Experimental Epistemology as a Tool to Observe and Preview Teaching/Learning Phenomena.- Strategy and Tactics in the Chinese and European Culture: Chess and Weich'i.- Rhythm and Natural Language in the Chinese and European Culture.- Conclusions.
Historical Notes on Star Geometry in Mathematics, Art and Nature
2018
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!”
Bayesian classification for dating archaeological sites via projectile points
2021
Dating is a key element for archaeologists. We propose a Bayesian approach to provide chronology to sites that have neither radiocarbon dating nor clear stratigraphy and whose only information comes from lithic arrowheads. This classifier is based on the Dirichlet-multinomial inferential process and posterior predictive distributions. The procedure is applied to predict the period of a set of undated sites located in the east of the Iberian Peninsula during the IVth and IIIrd millennium cal. BC.
Who Linked Hegel’s Philosophy with the History of Mathematics?
2018
Standard histories of mathematics are filled with names, dates, and results, but seldom do we find much attention paid to the contexts in which mathematics was made or past achievements recorded. Yet by widening the net, one can easily retrieve many interesting examples that reveal how mathematicians thought about these matters and much else besides. This column deals with one such person – whose identity readers are hereby challenged to uncover – in order to illustrate in a particularly striking way the potential confluence of mathematical and philosophical ideas. The sources to which I allude below are all in print and readily accessible, so I have reason to hope that these hints will lea…
L'epistolario ritrovato. Le lettere “napoletane” di Baldassarre Boncompagni a Gilberto Govi.
2016
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
Modelos de enseñanza de los algoritmos de la división de fracciones
2016
La identificación de aspectos específicos considerados parte de los elementos constitutivos de los modelos de enseñanza de los algoritmos para la división de fracciones es uno de los objetivos principales del estudio cuyos resultados se exponen en este artículo. Con la intención de rastrear esos elementos a lo largo del tiempo se han analizado textos escritos para la enseñanza de las matemáticas de los siglos XIII a XXI. El escrutinio de estos documentos se sustenta en análisis histórico- epistemológico y de contenido. La información obtenida de este tipo de indagaciones, además de contribuir a la historia de la educación matemática conforma un corpus valioso para la formación de profesores…
Aportaciones al cálculo de la latitud en la náutica española de principios del siglo XVII contenidas en el manuscrito de Diego Ramírez de Arellano &l…
2013
In 1620, was named chief pilot of the Casa de Contratación de Sevilla Diego Ramírez de Arellano, author of a manuscript entitled Reconocimiento de los estrechos de Magallanes y San Vicente, con algunas cosas curiosas de navegación. He had participated in the reconnaissance mission referred by the title of the manuscript, and in that book developed same methods and tools for a nautical understood scientifically, and even used a methodology close to modern science, as in refuting the theory about Figueiredo of the linear relationship between longitude and magnetic variation of the needle navigation. This article is based on some conclusions that can get an analysis of the manuscript. It focus…