On Euclidean diagrams and geometrical knowledge

Magro, Tamires Dal; García-Pérez, Manuel J.

doi:10.1387/theoria.20026

Cited by 7 publications

(3 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Another motivation is that having models of the neural representation of geometric concepts gives us a new venue to address the issue of the relationship between geometric figures and geometric objects. That has already been addressed from a historical perspective (see, e.g., Valente, 2020), and also cognitive considerations have been taken into account in somewhat related issues (see, e.g., Giaquinto, 2007;Dal Magro & García-Pérez, 2019;and Ferreirós & García-Pérez, 2020). But here, we present specific models developed in the context of a theoretical framework (the hub-and-spoke theory), which provides a more 'tangible' way to address this issue (since we have models of the neural representation of geometric figures and objects).…”

Section: Introductionmentioning

confidence: 99%

A hub-and-spoke model of geometric concepts

Valente¹

2023

THEORIA

View full text Add to dashboard Cite

The cognitive basis of geometry is still poorly understood, even the ‘simpler’ issue of what kind of representation of geometric objects we have. In this work, we set forward a tentative model of the neural representation of geometric objects for the case of the pure geometry of Euclid. To arrive at a coherent model, we found it necessary to consider earlier forms of geometry. We start by developing models of the neural representation of the geometric figures of ancient Greek practical geometry. Then, we propose a related model for the earliest form of pure geometry – that of Hippocrates of Chios. Finally, we develop the model of the neural representation of the geometric objects of Euclidean geometry. The models are based on the hub-and-spoke theory. In our view, the existence of specific models opens the possibility of addressing the relationship between geometric figures and geometric objects, in a novel way, in terms of their neural representation.

show abstract

Section: Introductionmentioning

confidence: 99%

A hub-and-spoke model of geometric concepts

Valente¹

2023

THEORIA

View full text Add to dashboard Cite

show abstract

“…Cf., e.g.,(Tarski, 1959);(Beeson, 2019, pp. 35-36); and http://geocoq.github.io/GeoCoq/ (Dal Magro et al, 2019),. referring to forthcoming work by Lassalle Casanave, also note differences between Euclidean proofs by diagrams and Hilbert's axiomatic proof conception.…”

mentioning

confidence: 99%

Newton's experimental proofs

Lampert¹

2021

THEORIA

View full text Add to dashboard Cite

Newton's claim to provide experimental proofs is often criticized. It is argued that his proofs are based on hypotheses and not inferred from the experiments alone. This criticism, however, applies a hypothetico-deductive analysis to Newton's experimental reasoning. Such an analysis is not consistent with Newton's own understanding of his proof method. The following reconstruction of Newton's proof method is intended to do justice to his understanding by applying the conception of iconic proofs to Newton's proofs by experiment. The main purpose of this analysis is to explain Newton's dictum that the experiment alone serves as the source of evidence from which his theorems are derived. After drawing a general distinction between symbolic and iconic proofs and illustrating this distinction by means of Euclidean proofs and Aristotelian syllogisms, I will apply this distinction to Newton's experimental proofs and analyze Newton's proof of the heterogeneity of sunlight by his experimentum crucis as an iconic proof. Finally, I will show that this experiment and its underlying method remain prominent in Newton's Opticks.

show abstract

“…Bukti geometri dalam pengertian post-Hilbert modern adalah urutan pernyataan yang didefinisikan secara tepat dalam bahasa formal dengan menggunakan postulat, teorema atau lemma yang telah terbukti sebelumnya (Lindsay, 1998). Pemilihan terhadap postulat dan teorema yang akan digunakan dalam menyusun bukti akan menentukan kebenaran bukti yang diajukan (Magro, 2019). Pemahaman terhadap postulat, teorema dan prinsip-prinsip geometri sangat dibutuhkan dalam kegiatan mengkonstruksi bukti geometri (Maarif, Perbowo, Noto & Harisman, 2019).…”

unclassified

Kemampuan Mengkonstruksi Bukti Geometri Mahasiswa Calon Guru Matematika Pada Perkuliahan Geometri

Maarif

Wahyudin

Alyani

et al. 2020

jel

View full text Add to dashboard Cite

This study aims to analyze and describe the ability to construct proofs of perspective teacher mathematics students in basic geometrical lectures on the concepts of alignment, triangles, and concordance of two triangles. This research uses a descriptive qualitative method involving 35 prospective mathematics students at the Universitas PGRI Semarang. This study uses a qualitative descriptive method involving 35 students. The results of this study show that: (1) 28% of students sketched diagrams and used geometric labels appropriately on the constructed evidence; (2) 28.57% of students have the correct initial step of proof; (3) 28.57% of students can determine the exact conjecture that leads to the correct proof; (4) 25.71% of students are correct in compiling proof arguments by the correct postulate and theorem; (5) 25.71% of the thought flow process used by coherent students leads to valid evidence; and (6) 22.86% of students mastered theorems and concepts used in compiling constructing proof.

show abstract

On Euclidean diagrams and geometrical knowledge

Cited by 7 publications

References 20 publications

A hub-and-spoke model of geometric concepts

A hub-and-spoke model of geometric concepts

Newton's experimental proofs

Kemampuan Mengkonstruksi Bukti Geometri Mahasiswa Calon Guru Matematika Pada Perkuliahan Geometri

Contact Info

Product

Resources

About