The first six books of the elements of Euclid, in which coloured diagrams and symbols are used instead of letters for the greater ease of learners

Euclid,; Byrne, Oliver; Oechslin, Werner; Lamers-Schütze, Petra

doi:10.5479/sil.317414.39088000863027

Cited by 12 publications

(9 citation statements)

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“…Este estudo baseia-se em uma abordagem qualitativa com pesquisa bibliográfica, desenvolvida com base em material já elaborado, principalmente livros e artigos científicos, conforme preconizado por Gil (2010). A pesquisa teve como ponto de partida a investigação da edição do século XIX dos "Elementos", intitulada "The first six books of the Elements of Euclid, in which coloured diagrams and symbols are used instead of letters for the greater ease of learners" (Byrne, 1847). O objetivo principal é compreender a constituição do sistema desenvolvido por Byrne e sua abordagem semiótica para essa versão dos "Elementos" de Euclides.…”

Section: Procedimentos Metodológicosunclassified

“…Neste trabalho, buscamos não apenas descrever, mas também explorar de forma dinâmica a demonstração da Proposição XXXIV, com o intuito de utilizá-la no ensino de conteúdos da geometria euclidiana plana. Essa exploração foi conduzida por meio de um objeto de aprendizagem que foi desenvolvido no GeoGebra, utilizando como base a obra Elementos, de Byrne (1847). Além de abordar a demonstração em si, diversas considerações foram destacadas para enriquecer a proposta.…”

Section: Considerações Finaisunclassified

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Explorando a proposição XXXIV do livro I dos elementos de Oliver Byrne no GeoGebra

Castillo,

Sánchez

2024

BOCEHM

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Neste trabalho descreve-se o andamento de uma proposta baseada na edição de Oliver Byrne dos Elementos de Euclides, que usa diagramas coloridos. A ideia de Byrne era apresentar as afirmações, as construções e até as provas dos Elementos de Euclides com um uso simples e rigoroso de cores, como forma de sintetizar descrições e argumentações verbais mais explícitas. Na proposta deste estudo o sistema semiótico e a abordagem de Byrne são materializados digitalmente com a utilização de um ambiente de geometria dinâmica, o GeoGebra, e o uso do caso da Proposição XXXIV do Livro I, de Byrne. O recurso interativo no GeoGebra no estilo de Byrne foi criado como um objeto de aprendizagem para a exploração de propriedades e discussões matemáticas e como uma ferramenta para tornar explícita a compreensão e aprendizagem da geometria euclidiana pelos estudantes.

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Section: Procedimentos Metodológicosunclassified

Section: Considerações Finaisunclassified

Explorando a proposição XXXIV do livro I dos elementos de Oliver Byrne no GeoGebra

Castillo,

Sánchez

2024

BOCEHM

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“…Plato (3) and Kant (4) claimed that all humans are equipped with a cognitive faculty-often called geometric intuition-allowing them to reach general geometric truths through a pure exercise of the deductive mind. Euclid himself relied on his geometric intuition to make numerous deductions essential to the geometric proofs of his foundational treatise (5,6). The most famous example occurs in the very first proposition of the Elements where Euclid drew the following inference (I1): 1 We can all see that if each point is inside one of the circles and lies on the other one, then the two circles must intersect, and this conclusion is as certain for us as it was for the ancient Greeks.…”

Section: Significance Statementmentioning

confidence: 99%

Going round in circles: A cognitive bias in geometric reasoning

Hamami¹,

Amalric²

2023

Preprint

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Deductive reasoning is essential to most of our scientific and technological achievements and is a crucial component to scientific education. In Western culture, deductive reasoning first emerged as a dedicated mode of thinking in the field of geometry, but the cognitive mechanisms behind this major intellectual achievement remain largely understudied. Here, we report an unexpected cognitive bias in geometric reasoning that challenges existing theories of human deductive reasoning. Over two experiments involving almost 250 participants, we show that educated adults systematically mistook as valid a set of elementary invalid inferences with points and circles in the Euclidean plane. Our results suggest that people got “locked” on unwarranted conclusions because they tended to represent geometric premisses in specific ways and they mainly relied on translating, but not scaling, the circles when searching for possible conclusions. We conducted two further experiments to test these hypotheses and found confirmation for them. Although mathematical reasoning is considered as the hallmark of rational thinking, our findings indicate that it is not exempt from cognitive biases and is subject to fundamental counter-intuitions. Our empirical investigations of the source of this bias provide some insights into the cognitive mechanisms underlying geometric deduction, and thus shed light on the cognitive roots of intuitive mathematical reasoning.

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“…Keywords: Dynamic geometry Á Oliver Byrne Á Theory of semiotic mediation Argumentation Á Euclidean geometry 1 Oliver Byrne's Euclid [3] and recently reprinted [4], is a quite original educational material developed in the XIX century. Byrne's idea was to present Euclid's statements, constructions and even proofs with a simple and (in a certain sense) rigorous use of colors-which in many situations synthesizes more explicit verbal descriptions and argumentations.…”

Section: Byrne's Euclidean Geometrymentioning

confidence: 99%

“…Byrne itself underlines the features of his system of representation that may affect understanding and learning (these are all quotations from [3]):…”

Section: Byrne's Euclidean Geometrymentioning

confidence: 99%