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Items from 1 to 20 out of 119 results

article

On the Resolution of Third and Fourth Degree Equations

Alessandra Cauli

International Journal of Applied and Computational Mathematics > 2019 > 5 > 4 > 1-12

In this paper we deal with the resolution of third and fourth degree equations by means of radicals. We present some historical details about this fundamental problem. We also discuss practical methods for the resolution of third and fourth degree equations from the algebraic point of view. Finally, we introduce some results about the equations of greater degree.

article

Why to publish on mathematics education so as to be useful? Educational Studies in Mathematics and its founder Hans Freudenthal

Danny Beckers

Educational Studies in Mathematics > 2019 > 101 > 1 > 7-17

In 1968, Hans Freudenthal launched the journal Educational Studies in Mathematics. This paper describes the events leading to the foundation of this journal. It turns out that his wife, Suus Freudenthal, deserves more credit for her husband’s interest and achievements in mathematics education. The couple was interested in education from a social democratic perspective. The events leading to the foundation...

article

Book review of Didattica della matematica by A. Baccaglini Frank, P. Di Martino, R. Natalini and G. Rosolini

Paolo Freguglia, Enrico Rogora

Lettera Matematica > 2018 > 6 > 3 > 193-197

In recent years, the Italian school system has undergone a radical process of evolution that is transforming it, necessitating urgent reflection on the training of mathematics teachers. The book under review aims at offering some basic tools for pedagogical research, which in our opinion is necessary but not sufficient. We believe that the scheme: “teacher training = mathematical contents equal to...

article

Analyzing the use of history in mathematics education: issues and challenges around Balacheff’s cKȼ model

Thomas Vittori

Educational Studies in Mathematics > 2018 > 99 > 2 > 125-136

Part of the international reflection on the use of history in mathematics teaching consists in a quest of frameworks and models suitable for empirical studies. Following this demand, this paper explores the way Balacheff’s cKȼ model, a model taken from the didactics of mathematics, can be used in the analysis of learning at student level. In the first part of this paper, Balacheff’s cKȼ model (conceptions,...

article

Textbooks revealing the development of a concept—the case of the number line in the analytic geometry (1708–1829)

Marcello Amadeo

ZDM > 2018 > 50 > 5 > 907-920

The purpose of this paper is to use historical textbooks to explore the number line, a mathematical object common to our time, contextualizing its use during its initial development period in the seventeenth century until its current use as in the nineteenth century. Relevant analytic geometry textbooks are explored, mainly from France and from Germany of that time, to understand when and how this...

article

Bernard Bolzano: pierwsze (historycznie) matematyczne ujęcie pojęcia kontinuum

Jerzy Dadaczyński

Zagadnienia Filozoficzne w Nauce > 2018 > 64 > 195-199

Recenzja książki: Lukas Benedikt Kraus, Der Begriff des Kontinuums bei Bernard Bolzano, Beiträge zur Bolzano-Forschung, vol. 25, Academia Verlag, Sankt Augustin 2014, ss. 112.

article

O liczbach ujemnych z perspektywy historycznej i dydaktycznej

Piotr Błaszczyk, Mirosława Sajka

Annales Universitatis Paedagogicae Cracoviensis | Studia ad Didacticam... > 2017 > 9 > 5-36

We identify two ways of introducing negative numbers. In the first one, a totally ordered set (L, $\prec $) is presupposed, an element 0 in L is arbitrarily taken, and a number a is negative when a 0. In the second one, a negative number is defined by the formula a + (−a) = 0. From a mathematical perspective, the first method involves the idea of a totally ordered group (G,+, 0,<), while the second...

article

A protagonist of the 18th-century mathematics: Maria Gaetana Agnesi

Renato Betti, Jacopo Tullio

Lettera Matematica > 2018 > 6 > 2 > 93-102

We revisit the life and work of Maria Gaetana Agnesi, Milanese mathematician, whose 300th birthday is being celebrated this year. In particular, we describe the main features of her books Propositiones philosophicae and Instituzioni analitiche ad uso della gioventù italiana. A third appendix is devoted to an algebraic curve that has taken its name from Agnesi: the versiera, or witch of Agnesi.

article

Mysticism in the history of mathematics

Ralph H. Abraham

Progress in Biophysics and Molecular Biology > 2017 > 131 > C > 261-272

We examine the relationship between mysticism and mathematical creativity through case studies from the history of mathematics.

article

A Categorization Model for Educational Values of the History of Mathematics

Xiao-qin Wang, Chun-yan Qi, Ke Wang

Science & Education > 2017 > 26 > 7-9 > 1029-1052

There is not a clear consensus on the categorization framework of the educational values of the history of mathematics. By analyzing 20 Chinese teaching cases on integrating the history of mathematics into mathematics teaching based on the relevant literature, this study examined a new categorization framework of the educational values of the history of mathematics by combining the objectives of high...

article

Comments on Indivisibles and Infinitesimals: A Response to David Sherry, by Amir Alexander: In View of the Original Book

Patricia Radelet-de Grave

Foundations of Science > 2018 > 23 > 4 > 597-602

A set of six publications have introduced, commented, criticized and defended Amir Alexander’s book on infinitesimals published in 2014. The aim of the following article is to bring the various arguments together.

article

P for π

Pietro Greco

Lettera Matematica > 2017 > 5 > 2 > 163-166

The number π, or pi, has crossed the author’s life. But most of all, it has crossed the entire history of mathematics. It was known in Mesopotamia and in Egypt. It gave Archimedes the opportunity to elaborate the method of exhaustion. It has been studied both in its nature (we now know that it is a transcendental irrational number) and to search for methods to compute its decimal digits. Even today...

article

Y for y = f(x)

Angelo Guerraggio

Lettera Matematica > 2017 > 5 > 2 > 213-216

This paper surveys the history of the notion of function, back to its original identification with curves and (only) elementary functions. Making the definitions of the derivative and of limit rigorous leads to making calculus for functions of one and n variables rigorous as well, and to the subsequent extension to the functional calculus due to Vito Volterra.

article

Z for Zero

Renato Betti

Lettera Matematica > 2017 > 5 > 2 > 217-220

This article traces the rise of zero as both symbol and number in Western culture.

article

History of mathematics in secondary school teachers’ training: towards a nonviolent mathematics education

David Guillemette

Educational Studies in Mathematics > 2017 > 96 > 3 > 349-365

In the context of mathematics teachers’ training, the concept of dépaysement épistémologique (epistemological disorientation) emphasizes that the contact with the history of mathematics, particularly with the use of original sources, pushes aside commonplace students’ perspectives about the discipline and offers them a critical look towards mathematics’s historical, social and cultural aspects. Conceptually...

article

I for Imaginary numbers

Liliana Curcio

Lettera Matematica > 2017 > 5 > 2 > 125-129

This paper surveys the history of complex numbers from their initial discovery to their complete acceptance and their use in contemporary physics and mathematics. The initial rejection of these new numbers by figures as important as Leibniz and Cauchy is what strikes us most and makes us reflect on how distrust, by even competent people, sometimes delays the adoption of important and valuable content.

article

J for Jordan

Frédéric Brechenmacher

Lettera Matematica > 2017 > 5 > 2 > 131-135

A case study on the early publications of Jordan in the 1860s sheds a new light on an important form of circulation of mathematics between France and Italy through a specific connection between newly founded specialized mathematical journals, such as the Annali di Matematica Pura ed Applicata, and much older organisations of mathematics, such as the Académie des sciences de Paris. Academic prizes...

article

Pythagorejská matematika vo svetle karteziánskej fyziky

Ladislav Kvasz

Filosofický časopis (Philosophical Journal) > 2017 > 65 > 4 > 513-541

This paper is the second part in a series of articles aimed at reconstructing the emergence of mathematics as a deductive discipline in ancient Greece in the period between Thales and Euclid. We understand the emergence of mathematics as the birth of a language which enables the undertaking of deductive proofs. While in the preceding part we focused on the beginnings of Greek mathematics in Thales,...

chapter

Guarino Guarini and Universal Mathematics

Clara Silvia Roero

Nexus Network Journal > Nexus Network Journal > Guarino Guarini: Open Questions, Possible Solutions > 415-439

Guarini considered the mathematical studies to be of fundamental importance for all artists and scholars. His own knowledge of mathematics was vast and profound. The aim of this present paper is to show, through an analysis of the most substantial of his mathematical works, Euclides adauctus, along with the Appendix to this printed a few months later, the role that philosophical and mathematical studies...

chapter

Some Origins of TMM Arisen from Pseudo-Aristotle and Hero of Alexandria

Agamenon R.E. Oliveira

International Symposium on History of Machines and Mechanisms > 35-44

This paper is an attempt to investigate the remote origins of the theoriesof machines and mechanisms. The work "Mechanica" (Lindsay, Energy: HistoricalDevelopment of the Concept, 1975; Dugas, A History of Mechanics, 1988),attributed to Aristotelian tradition and considered the first explanation of the behaviorof machines, is studied and discussed. His author is known as "pseudo-Aristotle",...

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On the Resolution of Third and Fourth Degree Equations

Why to publish on mathematics education so as to be useful? Educational Studies in Mathematics and its founder Hans Freudenthal

Book review of Didattica della matematica by A. Baccaglini Frank, P. Di Martino, R. Natalini and G. Rosolini

Analyzing the use of history in mathematics education: issues and challenges around Balacheff’s cKȼ model

Textbooks revealing the development of a concept—the case of the number line in the analytic geometry (1708–1829)

Bernard Bolzano: pierwsze (historycznie) matematyczne ujęcie pojęcia kontinuum

O liczbach ujemnych z perspektywy historycznej i dydaktycznej

A protagonist of the 18th-century mathematics: Maria Gaetana Agnesi

Mysticism in the history of mathematics

A Categorization Model for Educational Values of the History of Mathematics

Comments on Indivisibles and Infinitesimals: A Response to David Sherry, by Amir Alexander: In View of the Original Book

P for π

Y for y = f(x)

Z for Zero

History of mathematics in secondary school teachers’ training: towards a nonviolent mathematics education

I for Imaginary numbers

J for Jordan

Pythagorejská matematika vo svetle karteziánskej fyziky

Guarino Guarini and Universal Mathematics

Some Origins of TMM Arisen from Pseudo-Aristotle and Hero of Alexandria

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