On the relationship between geometric objects and figures in Euclidean geometry

In Diagrammatic Representation and Inference. 12th International Conference, Diagrams 2021. pp. 71-78 (2021)
  Copy   BIBTEX


In this paper, we will make explicit the relationship that exists between geometric objects and geometric figures in planar Euclidean geometry. That will enable us to determine basic features regarding the role of geometric figures and diagrams when used in the context of pure and applied planar Euclidean geometry, arising due to this relationship. By taking into account pure geometry, as developed in Euclid’s Elements, and practical geometry, we will establish a relation between geometric objects and figures. Geometric objects are defined in terms of idealizations of the corresponding figures of practical geometry. We name the relationship between them as a relation of idealization. This relation, existing between objects and figures, is what enables figures to have a role in pure and applied geometry. That is, we can use a figure or diagram as a representation of geometric objects or composite geometric objects because the relation of idealization corresponds to a resemblance-like relationship between objects and figures. Moving beyond pure geometry, we will defend that there are two other ‘layers’ of representation at play in applied geometry. To show that, we will consider Euclid’s Optics.



External links

  • This entry has no external links. Add one.
Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

A hub-and-spoke model of geometric concepts.Mario Bacelar Valente - 2023 - Theoria : An International Journal for Theory, History and Fundations of Science 38 (1):25-44.
Geometrical objects and figures in practical, pure, and applied geometry.Mario Bacelar Valente - 2020 - Disputatio. Philosophical Research Bulletin 9 (15):33-51.
From practical to pure geometry and back.Mario Bacelar Valente - 2020 - Revista Brasileira de História da Matemática 20 (39):13-33.
The Idea of a Diagram.Desmond Fearnley-Sander - 1989 - In Hassan Ait-Kaci & Maurice Nivat (eds.), Resolution of Equations in Algebraic Structures. Academic Press.
Giordano Bruno's Geometry of Language.Arielle Saiber - 1999 - Dissertation, Yale University
Combinatorial analysis of proofs in projective and affine geometry.Jan von Plato - 2010 - Annals of Pure and Applied Logic 162 (2):144-161.


Added to PP

236 (#90,270)

6 months
108 (#51,479)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Mario Bacelar Valente
Pablo de Olavide University

Citations of this work

No citations found.

Add more citations

References found in this work

The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History.Reviel Netz - 1999 - Cambridge and New York: Cambridge University Press.
Images.John V. Kulvicki - 2013 - New York: Routledge.
Canny resemblance.Catharine Abell - 2009 - Philosophical Review 118 (2):183-223.

View all 13 references / Add more references