Of the Nature of Math and Math in Nature – a Sequel About Symmetry for Children and Adults

2021 ◽  
Vol LXIV (4) ◽  
pp. 425-437
Author(s):  
Cvetelin Andreev
Keyword(s):  
Main Thesis ◽  
Informal Environment ◽  
Nature Of Mathematics ◽  
Music And Mathematics ◽  
And Mathematics

The paper describes activities for developing the notion of symmetries. The activities were performed by a group of children between the ages of 5 and 9 and a parent of two of them. Through play and active work the group explores symmetries in sports, architecture, biology, language, music and mathematics. The activities were carried out outdoors in nature. Ideas for complementary activities with computers are presented. As a result the children demonstrate the ability to recognize symmetries in areas and situations different from the ones set in the activities they performed. This proves the main thesis of the paper: the nature of mathematics can be captured successfully in an informal environment at any age.

Music and mathematics: Theophrastus against the number-theorists

1977 ◽  
Vol 23 ◽  
pp. 1-15
Author(s):  
Andrew Barker
Keyword(s):  
Good Deal ◽  
Subsequent Publication ◽  
Music And Mathematics ◽  
And Mathematics ◽  
Partial Translation

A long and important fragment of the Περὶ μοψσικῆς of Theophrastus is preserved in Porphyry's commentary on Ptolemy's Harmonics. Both Porphyry and Ptolemy were reedited earlier in this century by Düring, in works which have rightly been taken to supersede the texts of Wallis: and so far as the Theophrastus passage is concerned, we should expect to be able to abandon in Düring's favour the text published by Wimmer, who in effect reprints Wallis, though adopting a few variant readings and emendations from Schneider. But it seems to me that Düring's text is not in all respects an improvement, and that the comments made on it in a subsequent publication by Alexanderson have muddied the waters still further. It is not only a matter of the text: Alexanderson prints also a (partial) translation and an interpretative commentary, and both are open to serious objections. I intend in this paper to deal only with a portion of the fragment, but it is that portion whose argument is the most intricate, and one which ought to shed a good deal of light on central controversies among the musical theoreticians who follow Aristotle. I am not in a position to dispute any of Düring's findings in the manuscripts, but where emendation has in any event proved necessary or where the manuscripts differ among themselves, I hope to show through a study of the content of the argument that the case in favour of Düring is not always closed.

scholarly journals Le Corbusier: architecture, music, mathematics: longing for classicism?

2015 ◽  
Author(s):  
Clara Germana Gonçalves ◽  
Maria João Dos Reis Moreira Soares
Keyword(s):  
Seventeenth Century ◽  
Le Corbusier ◽  
Palabras Clave ◽  
The Will ◽  
Music And Mathematics ◽  
And Mathematics ◽  
Universal Order ◽  
Siglo Xx ◽  
The Universe

Abstract: This paper aims to study the role of the relationships between architecture, music and mathematics in Le Corbusier's thought and work and their relevance in his reinterpretation of classical thinking. It seeks to understand to what extent working with this triad – a foundational and, up until the seventeenth century, dogmatic aspect of architecture in general and of its aesthetics in particular – expresses a will not to break with the fundamental and defining aspects of what could be considered as architectural thought rooted in classical tradition: that which is governed by the will to follow the universal order in the work of art; building a microcosmos according to the macrocosmos; linking, in proportion to one another, the universe, man and architecture. The Modulor presents itself as a manifestation of that will, synthesizing these aspects while proposing itself as an instrument for interdisciplinary thought and practice in which the aforementioned aspects of classical thought are present, clearly and pronouncedly. Le Corbusier’s thought and work presents itself as a twentieth century memory of an ancient and ever present tradition conscious of its struggle for “humanity”. Resumen: Este artículo pretende estudiar el papel de la relación entre arquitectura, música y matemática en el pensamiento y la obra de Le Cobusier y su significado en su reinterpretación del pensamiento clásico. Intenta entender en qué medida con esta triada – aspecto fundacional y hasta el siglo XVII dogmático de la arquitectura, en general, y de su estética, en particular – Le Corbusier expresa su recusa por cortar el vínculo con los aspectos fundamentales y definidores de lo que puede considerarse un pensamiento de tradición clásica en arquitectura: aquel tutelado por la voluntad de seguir el orden universal en la obra de arte – construyendo un microcosmos según un macrocosmos – para así vincular, a través de la proporción, universo, Hombre y arquitectura. El Modulor se presenta como manifestación de esa voluntad, sintetizando estos aspectos y presentándose como un instrumento para un pensamiento y una práctica interdisciplinares en los cuales el pensamiento clásico se encuentra clara y marcadamente presente. El pensamiento de Le Corbusier, través su mirada hacia la relación arquitectura-música-matemática, se presenta, en el siglo XX, como una memoria de una antigua y siempre presente tradición, consciente de su busca por “humanidad”.  Keywords: Le Corbusier; Architecture, music and mathematics; classical thought; Modulor. Palabras clave: Le Corbusier; Arquitectura, música y mathematica; pensamiento clásico; Modulor. DOI: http://dx.doi.org/10.4995/LC2015.2015.791

The Canterbury Tales and the Arabic Frame Tradition

PMLA ◽  
1983 ◽  
Vol 98 (2) ◽  
pp. 237-251 ◽  
Author(s):  
Katharine Slater Gittes
Keyword(s):  
Random Order ◽  
Canterbury Tales ◽  
Art Music ◽  
Arabic Literature ◽  
Confessio Amantis ◽  
Individual Unit ◽  
Music And Mathematics ◽  
And Mathematics ◽  
The Individual ◽  
The Canterbury Tales

The Canterbury Tales is the culmination of a frame tradition that originated and developed in Arabia, not in the West. The Arabic practice of enclosing tales within a frame may be explained by principles of organization peculiar to medieval Arabic literature, art, music, and mathematics: a preference for concreteness, a stress on autonomous elements, and a reliance on external organizing devices. Most Arabic literature emphasizes the individual unit; frames remain open-ended and inconclusive and rarely determine the subject or form of any included part. Although many Western characteristics are present in medieval European frame narratives like the Disciplina Clericalis, the Decameron, and the Confessio Amantis, those works, nonetheless, reveal themselves as continuations of the Arabic tradition. Even the Canterbury Tales, with all its subtle artistry, retains qualities typical of its Arabic ancestors, notably the controlling travelpilgrimage motif, the pointedly random order of tales, and the prominent authorial personality.

Music and mathematics

1945 ◽  
Vol 26 (1) ◽  
pp. 21-21
Author(s):  
G. Warrack
Keyword(s):  
Music And Mathematics ◽  
And Mathematics

Values and Mathematics: Overt and Covert

2016 ◽  
Vol 4 (1) ◽  
pp. 48-82 ◽  
Author(s):  
Paul Ernest
Keyword(s):  
Ethical Values ◽  
Human Culture ◽  
Nature Of Mathematics ◽  
And Mathematics ◽  
Initial Choice

This paper argues that mathematics is imbued with values reflecting its production from human imagination and dialogue. Epistemological, ontological, aesthetic and ethical values are specified, both overt and covert. Within the culture of mathematics, the overt values of truth, beauty, purity, universalism, objectivism, rationalism and utility are identified. In contrast, hidden within mathematics and its culture are the covert values of objectism and ethics, including the specific ethical values of separatism, openness, fairness and democracy. Some of these values emerge from a dialogical view of the nature of mathematics, and certainly from the dialogical nature of culture. It is acknowledged that the choice of certain perspectives, such as absolutism, lead to the appearance of mathematics as largely value-free through hiding value-assumptions behind the initial choice of philosophy. By uncovering the values of mathematics I show that it more closely resembles other components of human culture than is usually recognised.

Review: Equity and Mathematics: Not a Simple Issue

1996 ◽  
Vol 27 (5) ◽  
pp. 609-615
Author(s):  
Nel Noddings
Keyword(s):  
Mathematics Education ◽  
Mathematics Curriculum ◽  
Cultural Factors ◽  
Curriculum And Pedagogy ◽  
Nature Of Mathematics ◽  
And Mathematics

All four of the books reviewed here are deeply concemed with issues of equiry in mathematics education. I'll say a bit about each book in order to orient readers, and then I'll organize my remarks around the themes that arise again and again: the nature of mathematics. mathematics curriculum and pedagogy, and the philosophical and cultural factors inside and outside classroom that affect our educational efforts.

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