Euclid—The Creation of Mathematics

Artmann, Benno

doi:10.1007/978-1-4612-1412-0

Cited by 61 publications

(14 citation statements)

References 19 publications

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“…Clearly he did not understand symmetry as we do, but when he speaks of the units of his elements as being "most beautiful", it seems very likely that he means at least something like our regularity. Although there is evidence of earlier construction and use of symmetric objects [2,4], it is with Plato, presenting his own ideas, but also relying heavily on Theaetetus, that we can find the first hints, expressed in the language of beauty, of the mathematical ideas which ultimately lead on to our modern symmetry theory.…”

Section: Final Remarksmentioning

confidence: 99%

“…There is of course a grandeur to Euclid's concept of summarising and systematising all known geometry, but there is not much evidence of this being driven by aesthetic considerations. Much of Euclid was derived from earlier work in Plato's Academy [2], particularly that of Theaetetus and of Eudoxus. Indeed it is possible to see much of the structure of the Elements as a slow build-up to the final constructions of Book 13 in which the 'Platonic Solids" are built up in an extraordinary intellectual tour de force.…”

Section: Introductionmentioning

confidence: 99%

“…It is almost certain that it is the work of Theaetetus on the regular solids which forms the base on which Plato builds the second half of his dialogue Timaeus, which is discussed below. There is no surviving written record from Theaetetus, though it is likely that books 10 and 13 of Euclid are largely his work [2]. By default the regular solids have been called Platonic; perhaps Theaetetic would be more accurate, but it does have some pronunciation problems.…”

Section: Introductionmentioning

confidence: 99%

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Symmetry and Beauty in Plato

Lloyd

2010

Symmetry

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Abstract:Plato writes about Beauty in many of his dialogues, particularly in the Symposium, but he has no word equivalent to our "Symmetry", and this concept was not then formalised. Nevertheless, there are indications that some aspects of the concept were understood, if only intuitively. Plato has a very abstract concept of beauty, and when he uses "beauty" to characterise the so-called "Platonic Solids" in the Timaeus, he seems to be emphasising at least their regularity. It can be argued that the way in which he specifies the detailed construction of the solids is remarkably close to a modern description in terms of (point) symmetry. For Plato, something of our symmetry is included in what he means by beauty, and the long mathematical approach to symmetry starts with the Timaeus.

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Section: Final Remarksmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Symmetry and Beauty in Plato

Lloyd

2010

Symmetry

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“…Em um comentário extenso e profundo sobre os Elementos de Euclides (Artmann, 1999) (Artmann, 1999, p. 104).…”

Section: Introductionunclassified

O papel da régua e do compasso nos Elementos de Euclides: uma prática interpretada como regra

Schubring¹,

Roque²

2014

História Unisinos

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Resumo: Neste texto, analisamos as fontes citadas na historiografia tradicional da matemática para afirmar que existiria uma restrição dos instrumentos de construção usados nos Elementos de Euclides, muitas vezes encarada como uma influência platônica. Nosso principal objetivo é investigar se a exclusividade do uso dos métodos de construção por retas e círculos nos Elementos era uma prática ou uma norma no contexto geométrico da época de Euclides. Tomamos como base o estudo de Arthur Donald Steele, publicado em 1936, mas mencionado raramente e de modo alusivo pelos historiadores. A tese principal, que desenvolvemos a partir desse e de outros trabalhos, é a de que as fontes não permitem afirmar que uma tal restrição fosse uma norma. O fato de que as construções nos Elementos de Euclides são feitas, na prática, somente com uso de régua e compasso não permite concluir que essa fosse uma regra, nem que se tratasse de um padrão da época. Mostraremos como uma versão equivocada foi produzida historicamente.Palavras-chave: régua e compasso, geometria euclidiana, história da matemática grega. Abstract:In this text we analyze the sources referred to in traditional historiography of mathematics in order to state that there existed a restriction regarding the instruments used in Euclid's Elements, often emphasized as due to an influence by Platonism. Our principal aim is to analyze whether the exclusivity in the use of ruler and compass as construction methods was a practice or prescribed as a norm in the geometric context of Euclid's epoch. We follow the study published by Arthur Donald Steele in 1936, scarcely cited by historians. Taking also other works as references, we propose the thesis that the sources do not suggest that such a restriction constituted a norm. The fact that constructions in Euclid's Elements are done, in practice, using only the ruler and the compass do not allow us to conclude that this was a rule, or a standard procedure in the time. We also explain how the cited version was historically produced.

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“…(Artmann, 1999) Apesar da importância e influência da obra de Euclides, o que sabemos dele não é muito diferente do que conhecemos de outros matemáticos da Grécia 10 Filósofo da Grécia Antiga, considerado como o primeiro historiador da ciência.…”

Section: Euclidesunclassified

Um Taxi Para Euclides: Uma Geometria Não Euclidiana Na Educação Básica

Loiola¹

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Euclid—The Creation of Mathematics

Cited by 61 publications

References 19 publications

Symmetry and Beauty in Plato

Symmetry and Beauty in Plato

O papel da régua e do compasso nos Elementos de Euclides: uma prática interpretada como regra

Um Taxi Para Euclides: Uma Geometria Não Euclidiana Na Educação Básica

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