Objetos geométricos y figuras en la geometría práctica, pura, y aplicada
Palabras clave:
Concepto Sortal, Diagramas, Elementos, Óptica, Mesopotamia
Resumen
El propósito de este trabajo es abordar qué noción de objeto geométrico y figura geométrica tenemos en diferentes tipos de geometría: práctica, pura y aplicada. Además, abordamos la relación entre objetos geométricos y figuras cuando esto es posible, como es el caso de la geometría pura y aplicada. En la geometría práctica resulta que no existe una concepción del objeto geométrico.
Referencias
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Burton, H. E. (1945). “The optics of Euclid”. Journal of the Optical Society of America 35: pp. 357-372.
Cooper, M. A. R. (2013). “Land surveying in ancient Mesopotamia: ethical ‘algebraic geometry’”. Survey Review 45, pp. 399-409.
Damerow, P. (2016) “The impact of notation systems: from the practical knowledge of surveyors to babylonian geometry”. In Spatial thinking and external representation: towards a historical epistemology of space, edited by M. Schemmel. Berlin: Edition Open Access, pp. 93-119.
Darrigol, O. (2012). A history of optics: from Greek antiquity to the nineteenth century. Oxford: Oxford University Press.
Euclid (1956). The thirteen Books of the Elements Vols. I-III. Translated with introduction and commentary by Sir Thomas L. Heath, from the critical edition of Heiberg. New York: Dover Publications.
Ferreirós, J. (2016). Mathematical knowledge and the interplay of practices. Princeton: Princeton University Press.
Frankfort, H. (1970). The art and architecture of the ancient orient. Harmondsworth: Penguin Books.
Friberg, J. (2007). A remarkable collection of Babylonian mathematical texts: manuscripts in the Schøyen collection cuneiform texts I. New York: Springer.
Gonçalves, C. (2015). Mathematical tablets from Tell Harmal. Heidelberg: Springer.
Giardino, V. (2017). “Diagrammatic reasoning in mathematics”. In Springer handbook of model-based science, edited by L. Magnani and T. Bertolotti. Dordrecht: Springer, pp. 499-522.
Hale, B. (2013). Necessary beings. An essay on ontology, modality, and the relations between them. Oxford: Oxford University Press.
Harari, O. (2003). “The concept of Existence and the role of constructions in Euclid’s Elements”. Archive for History of Exact Sciences 57: pp. 1-23, 2003.
Høyrup, J. (2002). Lengths, widths, surfaces: a portrait of Old Babylonian algebra and its kin. New York: Springer.
Hughes, I., and Hase, T. (2010). Measurements and their uncertainties: a practical guide to modern error analysis. Oxford: Oxford University Press.
Imhausen, A. (2016). Mathematics in ancient Egypt: a contextual history. Princeton: Princeton University Press.
Mackie, P. (2006). How things might have been: individuals, kinds, and essential properties. Oxford: Clarendon Press.
Mueller, I. (1981). Philosophy of mathematics and deductive structure in Euclid’s Elements. Cambridge: MIT Press.
Netz, R. (1999). The shaping of deduction in Greek mathematics: a study in cognitive history. Cambridge: Cambridge University Press.
Panza, M. (2011). “Rethinking geometrical exactness”. Historia Mathematica 38: pp. 42-95.
Panza, M. (2012). “The twofold role of diagrams in Euclid’s plane geometry”. Synthese 186: pp. 55-102.
Panza, M., and Sereni, A. (2013). Plato’s problem. An introduction to mathematical platonism. Houndmills: Palgrave Macmillan.
Robson, E. (2004). “Words and pictures: new light on Plimpton 322”. In Sherlock Holmes in Babylon and other tales of mathematical history, edited by M. Anderson, V. Katz, and R. Wilson. Washington: Mathematical Association of America, pp. 14-26.
Robson, E. (2008). Mathematics in ancient Iraq. Princeton: Princeton University Press.
Shin, S.J., Lemon, O., and Mumma, J. (2008). “Diagrams”. In The Stanford Encyclopedia of Philosophy, edited by E. N. Zalta. Stanford CA: Stanford University. Accessed on 14 March 2020. Available at: https://plato.stanford.edu/entries/diagrams/.
Toulmin, S. (1953). The philosophy of science: an introduction. London: Hutchinson & Co. Publishers.
Burton, H. E. (1945). “The optics of Euclid”. Journal of the Optical Society of America 35: pp. 357-372.
Cooper, M. A. R. (2013). “Land surveying in ancient Mesopotamia: ethical ‘algebraic geometry’”. Survey Review 45, pp. 399-409.
Damerow, P. (2016) “The impact of notation systems: from the practical knowledge of surveyors to babylonian geometry”. In Spatial thinking and external representation: towards a historical epistemology of space, edited by M. Schemmel. Berlin: Edition Open Access, pp. 93-119.
Darrigol, O. (2012). A history of optics: from Greek antiquity to the nineteenth century. Oxford: Oxford University Press.
Euclid (1956). The thirteen Books of the Elements Vols. I-III. Translated with introduction and commentary by Sir Thomas L. Heath, from the critical edition of Heiberg. New York: Dover Publications.
Ferreirós, J. (2016). Mathematical knowledge and the interplay of practices. Princeton: Princeton University Press.
Frankfort, H. (1970). The art and architecture of the ancient orient. Harmondsworth: Penguin Books.
Friberg, J. (2007). A remarkable collection of Babylonian mathematical texts: manuscripts in the Schøyen collection cuneiform texts I. New York: Springer.
Gonçalves, C. (2015). Mathematical tablets from Tell Harmal. Heidelberg: Springer.
Giardino, V. (2017). “Diagrammatic reasoning in mathematics”. In Springer handbook of model-based science, edited by L. Magnani and T. Bertolotti. Dordrecht: Springer, pp. 499-522.
Hale, B. (2013). Necessary beings. An essay on ontology, modality, and the relations between them. Oxford: Oxford University Press.
Harari, O. (2003). “The concept of Existence and the role of constructions in Euclid’s Elements”. Archive for History of Exact Sciences 57: pp. 1-23, 2003.
Høyrup, J. (2002). Lengths, widths, surfaces: a portrait of Old Babylonian algebra and its kin. New York: Springer.
Hughes, I., and Hase, T. (2010). Measurements and their uncertainties: a practical guide to modern error analysis. Oxford: Oxford University Press.
Imhausen, A. (2016). Mathematics in ancient Egypt: a contextual history. Princeton: Princeton University Press.
Mackie, P. (2006). How things might have been: individuals, kinds, and essential properties. Oxford: Clarendon Press.
Mueller, I. (1981). Philosophy of mathematics and deductive structure in Euclid’s Elements. Cambridge: MIT Press.
Netz, R. (1999). The shaping of deduction in Greek mathematics: a study in cognitive history. Cambridge: Cambridge University Press.
Panza, M. (2011). “Rethinking geometrical exactness”. Historia Mathematica 38: pp. 42-95.
Panza, M. (2012). “The twofold role of diagrams in Euclid’s plane geometry”. Synthese 186: pp. 55-102.
Panza, M., and Sereni, A. (2013). Plato’s problem. An introduction to mathematical platonism. Houndmills: Palgrave Macmillan.
Robson, E. (2004). “Words and pictures: new light on Plimpton 322”. In Sherlock Holmes in Babylon and other tales of mathematical history, edited by M. Anderson, V. Katz, and R. Wilson. Washington: Mathematical Association of America, pp. 14-26.
Robson, E. (2008). Mathematics in ancient Iraq. Princeton: Princeton University Press.
Shin, S.J., Lemon, O., and Mumma, J. (2008). “Diagrams”. In The Stanford Encyclopedia of Philosophy, edited by E. N. Zalta. Stanford CA: Stanford University. Accessed on 14 March 2020. Available at: https://plato.stanford.edu/entries/diagrams/.
Toulmin, S. (1953). The philosophy of science: an introduction. London: Hutchinson & Co. Publishers.
Publicado
2020-12-31
Cómo citar
[1]
Valente, M.B. 2020. Objetos geométricos y figuras en la geometría práctica, pura, y aplicada. Disputatio. 9, 15 (dic. 2020), 33-51. DOI:https://doi.org/10.5281/zenodo.4625085.
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Esta obra está bajo licencia internacional Creative Commons Reconocimiento-NoComercial-SinObrasDerivadas 4.0.
