Search results for "Mathematics - History and Overview"
showing 10 items of 10 documents
Robert de Montessus de Ballore's 1902 theorem on algebraic continued fractions : genesis and circulation
2013
Robert de Montessus de Ballore proved in 1902 his famous theorem on the convergence of Pad\'e approximants of meromorphic functions. In this paper, we will first describe the genesis of the theorem, then investigate its circulation. A number of letters addressed to Robert de Montessus by different mathematicians will be quoted to help determining the scientific context and the steps that led to the result. In particular, excerpts of the correspondence with Henri Pad\'e in the years 1901-1902 played a leading role. The large number of authors who mentioned the theorem soon after its derivation, for instance N\"orlund and Perron among others, indicates a fast circulation due to factors that w…
Introduction to Gestural Similarity in Music. An Application of Category Theory to the Orchestra
2019
Mathematics, and more generally computational sciences, intervene in several aspects of music. Mathematics describes the acoustics of the sounds giving formal tools to physics, and the matter of music itself in terms of compositional structures and strategies. Mathematics can also be applied to the entire making of music, from the score to the performance, connecting compositional structures to acoustical reality of sounds. Moreover, the precise concept of gesture has a decisive role in understanding musical performance. In this paper, we apply some concepts of category theory to compare gestures of orchestral musicians, and to investigate the relationship between orchestra and conductor, a…
Quantum GestART: Identifying and Applying Correlations between Mathematics, Art, and Perceptual Organization
2020
Mathematics can help analyze the arts and inspire new artwork. Mathematics can also help make transformations from one artistic medium to another, considering exceptions and choices, as well as artists' individual and unique contributions. We propose a method based on diagrammatic thinking and quantum formalism. We exploit decompositions of complex forms into a set of simple shapes, discretization of complex images, and Dirac notation, imagining a world of "prototypes" that can be connected to obtain a fine or coarse-graining approximation of a given visual image. Visual prototypes are exchanged with auditory ones, and the information (position, size) characterizing visual prototypes is con…
The dawning of the theory of equilibrium figures: a brief historical account from the 17th through the 20th century
2014
A brief but complete historical survey of the theory of equilibrium figures from its early origins, dating back to 17th-century, until the latest 20th-century developments, with a view towards its applications, is carried out.
Historical Origins of the nine-point conic -- The Contribution of Eugenio Beltrami
2020
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 quadrat…
From the theory of “congeneric surd equations” to “Segre's bicomplex numbers”
2015
We will study the historical pathway of the emergence of Tessarines or Bicomplex numbers, from their origin as "imaginary" solutions of irrational equations, to their insertion in the context of study of the algebras of hypercomplex numbers.
The Journal de Math\'ematiques Pures et Appliqu\'ees(1917-1937) : correspondence between Henri Villat and Robert de Montessus de Ballore
2014
We are interested in the "Journal de Math\'ematiques Pures et Appliqu\'ees" (JMPA) over the period 1917-1937. From the end of 1921, two mathematicians worked to its publication, Henri Villat as editor in chief and Robert Montessus Ballore as associate editor. Through unpublished letters, we descrive the operation of the JMPA.
The early historical roots of Lee-Yang theorem
2014
A deep and detailed historiographical analysis of a particular case study concerning the so-called Lee-Yang theorem of theoretical statistical mechanics of phase transitions, has emphasized what real historical roots underlie such a case study. To be precise, it turned out that some well-determined aspects of entire function theory have been at the primeval origins of this important formal result of statistical physics.
Bridging probability and calculus: the case of continuous distributions and integrals at the secondary-tertiary transition
2018
International audience; This paper focuses on two mathematical topics, namely continuous probability distributions (CPD) and integral calculus (IC). These two sectors that are linked by the formula P(a<=X<=b)=int_a^b f(x)dx are quite compartmented in teaching classes in France. The main objective is to study whether French students can mobilize the sector of IC to solve tasks in CPD and vice versa at the transition from high school to higher education. Applying the theoretical framework of the Anthropological Theory of the Didactic (ATD), we describe a reference epistemological model (REM) and use it to elaborate a questionnaire in order to test the capacity of students to bridge CPD and IC…
From art to geometry: Aesthetic and beauty in the learning process
2015
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