Geometrical objects and figures in practical, pure, and applied geometry
Keywords:
Sortal Concepts, Diagrams, Elements, Optics, Mesopotamia
Abstract
The purpose of this work is to address what notion of geometrical object and geometrical figure we have in different kinds of geometry: practical, pure, and applied. Also, we address the relation between geometrical objects and figures when this is possible, which is the case of pure and applied geometry. In practical geometry it turns out that there is no conception of geometrical object.
References
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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.
Published
2020-12-31
How to Cite
[1]
Valente, M.B. 2020. Geometrical objects and figures in practical, pure, and applied geometry. Disputatio. 9, 15 (Dec. 2020), 33-51. DOI:https://doi.org/10.5281/zenodo.4625085.
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Section
Articles and Essays
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