Natureza do objeto matemático “tabela”
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Dec 6, 2017
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Soledad Estrella
http://orcid.org/0000-0002-4567-2914
Arturo Mena-Lorca
http://orcid.org/0000-0002-8150-2832
Raimundo Olfos-Ayarza
http://orcid.org/0000-0002-9886-4282
http://orcid.org/0000-0002-4567-2914
Arturo Mena-Lorca
http://orcid.org/0000-0002-8150-2832
Raimundo Olfos-Ayarza
http://orcid.org/0000-0002-9886-4282
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Resumo
Este artigo de reflexão oferece uma visão ampla do processo de evolução das ideias sobre tabelas, sua conotação de ferramentas, surgimento e desenvolvimento em diversas sociedades e culturas em diferentes momentos da história, questões que contribuem ao conhecimento sobre estes objetos e seus alcances didáticos. A reflexão sobre a trajetória da tabela e sua presença como ferramenta de armazenamento e de cálculo em sistemas de numeração e de metrologia, e como ferramenta de análise em âmbitos científicos e matemáticos, ajuda a precisar sua origem e natureza como objeto matemático.
Keywords
References
Aaboe, Asger (1964). Episodes from the Early History of Mathematics. Washington, DC: The Mathematical Association of America.
Anellis, Irving H. (1995). Peirce Rustled, Russell Pierced: How Charles Peirce and Bertrand Russell Viewed Each Other's Work in Logic, and an Assessment of Russell's Accuracy and Role in the Historiography of Logic. Modern Logic, 5 (3), 270-328. Disponible en: http://www.iupui.edu/~arisbe/menu/library/aboutcsp/ANELLIS/csp&br.htm
Anellis, Irving H. (2012). Peirce's Truth-functional Analysis and the Origin of the Truth Table. History and Philosophy of Logic, 33 (1), 87-97.
Arad, Zvi; Bangteng, Xu; Chen, Guiyun; Cohen, Effi; Hussam, Arisha HajIhia & Muzychuk, Mikhail (2011). On Normalized Integral Table Algebras (Fusion Rings): Generated by a Faithful Non-real Element of Degree 3. London: Springer.
Arad, Zvi & Blau, Harvey I. (1991). On Table Algebras and Applications to Finite Group Theory. Journal of Algebra, 138 (1), 137-185.
Arad, Zvi; Fisman, Elsa & Muzychuk, Misha (1999). Generalized Table Algebras. Israel Journal Mathematics, 114 (1), 29-60.
Bertoloni-Meli, Domenico (2004). The Role of Numerical Tables in Galileo and Mersenne. Perspectives on Science, 12 (2), 164-190. Disponible en: https://pdfs.semanticscholar.org/7b83/70eb76988606f2b0307799a1a5f56caf8927.pdf
Blau, Harvey I. & Zieschang, Paul-Hermann (2004). Sylow Theory for Table Algebras, Fusion Rule Algebras, and Hypergroups. Journal of Algebra, 273 (2), 551-570. Disponible en: http://www.sciencedirect.com/science/article/pii/S0021869303007087
Bocheński, Innocentius M. (1961). A History of Formal Logic. South Bend, Indiana: University of Notre Dame Press.
Campbell-Kelly, Martin; Croarken, Mary; Flood, Raymond & Robson, Eleanor (eds.) (2003). The History of Mathematical Tables. From Sumer to Spreadsheets. Oxford: Oxford University Press.
Chevallard, Yves (1991). La transposición didáctica. Del saber sabio al saber enseñado. Buenos Aires: Aique Grupo Editor S. A.
Estrella, Soledad (2014). El formato tabular: una revisión de literatura. Revista Actualidades Investigativas en Educación, 14 (2), 1-23. Disponible en: http://www.redalyc.org/pdf/447/44731371016.pdf
Estrella, Soledad; Mena-Lorca, Arturo & Olfos, Raimundo (2014). Desarrollo de una taxonomía de comprensión tabular. En Patricia Lestón (ed.). ALME, Acta Latinoamericana de Matemática Educativa, 27, 1041-1048. México: Colegio Mexicano
de Matemática Educativa A. C., Comité Latinoamericano de Matemática Educativa A. C. Disponible en: http://www.clame.org.mx/documentos/alme27.pdf
Euler, Leonhard (1748/1988). Introduction to Analysis of the Infinite. Book I. Berlin: Birkhäuser.
Friberg, Jöran (2007). A Remarkable Collection of Babylonian Mathematical Texts. Manuscripts in the Schøyen Collection: Sources and Studies in the History of Mathematics and Physical Sciences. New York: Springer.
Friendly, Michael & Denis, Daniel J. (2009). Milestones in the History of Thematic Cartography, Statistical Graphics, and Data Visualization. Natural Sciences and Engineering Research Council. Canada: Grant OGP0138748. Disponible en http://www.math.yorku.ca/SCS/Gallery/milestone/milestone.pdf, http://www.datavis.ca/milestones/
Friendly, Michael & Kwan, Ernest (2003). Effect Ordering for Data Displays. Computational Statistics & Data Analysis, 43 (4), 509-539. Disponible en: http://citeseerx.ist.psu.edu/viewdoc/download? doi=10.1.1.445.2938&rep=rep1&type=pdf
Garrow, John S. & Webster, Joan (1984). Quetelet's Index (W/H2) as a Measure of Fatness. International Journal of Obesity, 9 (2), 147-153.
Goody, Jack (1976). Civilisation de l'écriture et classification ou l'art de jouer sur les tableaux. Actes de la Recherche en Sciences Sociales, 2 (1), 87-101. Disponible en: http://www.persee.fr/doc/arss_0335-5322_1976_num_2_1_3384
Goody, Jack (1977). La domesticación del pensamiento salvaje. Madrid: Ediciones Akal.
Hallo, William W. (1964). The Road to Emar. Journal of Cuneiform Studies, 18 (3), 57-88.
Hitotsumatsu, Shin; Okada, Yoshio & Machida, Shouichiro (eds.). (2008). Study with Your Friends Mathematics for Elementary School, 3rd grade, vol. 1, 65-66. Tokyo: Gakko Tosho Co.
Lardner, Dionysius (1834). Babbage's Calculating Engine. Edinburgh Review, 120, 263-327.
Merzbach, Uta C. (1977). Georg Scheutz and the First Printing Calculator. Smithsonian Studies in History and Technology, 36, 1-74. Disponible en http://hdl.handle.net/10088/2435
Neugebauer, Otto & Hoesen, Henry B. van (1959). Greek Horoscopes. En Memoirs of the American Philosophical Society. Baltimore, Maryland: J. H. Furst Company.
Parnas, David Lorge; Asmis, G. J. Kurt & Madey, Jan (1991). Assessment of Safety-Critical Software in Nuclear Power Plants. Nuclear Safety, 32 (2), 189-198. Disponible en: https://www.researchgate.net/publication/242413466_Assessment_of_safety-critical_software_in_nuclear_power_plants
Pearson, Karl (1904). On the Theory of Contingency and its Relation to Association and Normal Correlation; on the General Theory of Skew Correlation and Non-linear Regression. Cambridge: Cambridge University Press.
Pecharromán-Gómez, Cristina (2013). Naturaleza de los objetos matemáticos: representación y significado. Enseñanza de las Ciencias, Revista de Investigación y Experiencias Didácticas, 31 (3), 121-134. Disponible en: http://www.raco.cat/index.php/Ensenanza/article/view/285795/373798
Pedersen, Olaf (1974). Logistics and Theory of Function: An Essay in the History of Greek Mathematics. Archives Internationales d'Histoire des Sciences, ARIHS, 24 (94), 29-50.
Peirce, Charles Sanders (1931). Division of Signs. En Charles Hartshorne & Paul Weiss (eds.). Collected Papers of Charles Sanders Peirce, Volume II, Chapter 2. Cambridge, Massachusetts: Harvard University Press.
Peirce, Charles Sanders (1931-1958). Collected Papers of Charles Sanders Peirce. Cambridge, Massachusetts: Harvard University Press.
Proust, Christine (2005). Le calcul sexagésimal en Mésopotamie. Disponible en http://culturemath.ens.fr/histoire%20des%20maths/pdf/Calcul%20sexa_Proust.pdf
Proust, Christine (2008). Quantifier et calculer: usages des nombres à Nippur. Revue d'Histoire des Mathématiques, 14 (2), 143-209. Disponible en: http://smf4.emath.fr/Publications/RevueHistoireMath/14/pdf/smf_rhm_14_143-209.pdf
Proust, Christine (2009). Numerical and Metrological Graphemes: From Cuneiform to Transliteration. Cuneiform Digital Library Journal, 1, 1-27. Disponible en: http://cdli.ucla.edu/files/publications/cdlj2009_001.pdf, http://www.cdli.ucla.edu/pubs/cdlj/2009/cdlj2009_001.html
Proust, Christine (2010). Mesopotamian Metrological Lists and Tables: Forgotten Sources. En Florence Bretelle-Establet (ed.). Looking at it from Asia: The Processes that Shaped the Sources of History of Science, 245-276. New York: Springer.
Quetelet, Lambert Adolphe Jacques (1835). Sur l'homme et le développement de ses facultés, ou Essai de physique sociale. Paris: Bachelier. Disponible en https://archive.org/stream/surlhommeetled00quet#page/n5/mode/2up
Rashed, Roshdi (2003). History of Science and Diversity at the Beginning of the 21st Century. En Proceedings of the XXI International Congress of History of Science, vol. I, 15-29. Ciudad de México: Universidad Nacional Autónoma de México, UNAM, Sociedad Mexicana de Historia de la Ciencia y la Tecnología.
Robson, Eleanor (2001). The Tablet House: A Scribal School in Old Babylonian Nippur. Revue d'assyriologie et d'archéologie orientale, 93 (1), 39-66.
Robson, Eleanor (2003). Tables and Tabular Formatting in Sumer, Babylonia, and Assyria, 2500 BCE-50 CE. En Martin Campbell-Kelly, Mary Croarken, Raymond Flood & Eleanor Robson (eds.). The History of Mathematical Tables. From Sumer to Spreadsheets, 19-48. Oxford: Oxford University Press.
Roegel, Denis (2010). A Reconstruction of the Tables of Briggs and Gellibrand's. Trigonometria Britannica (1633). En The LOCOMAT Project: Recomputing Mathematical and Astronomical Tables. Technical Report. Nancy, France: LOCOMAT, The LOria COllection of MAthematical Tables. Disponible en: http://locomat.loria.fr/briggs1633/briggs1633doc.pdf
Ross, Micah T. (2011). Survey of Graphical and Numerical Tables in Egypt. Oberwolfach Reports, 12, 650-652. Disponible en: http://www.academia.edu/7451497/Survey_of_Graphical_and_Numerical_Tables_in_Egypt
Schubring, Gert (2005). Conflicts between Generalization, Rigor and Intuition. Number Concepts Underlying the Development of Analysis in 17th19th Century France and Germany. New York: Springer. Sources and Studies in the History of Mathematics and Physical Sciences, SHMP.
Schubring, Gert (2011). Conceptions for Relating the Evolution of Mathematical Concepts to Mathematics Learning - Epistemology, History, and Semiotics Interacting. Educational Studies in Mathematics, 77 (1), 79-104.
Sidoli, Nathan (2014). Mathematical Tables in Ptolemy's Almagest. Historia Mathematica, 41 (1), 13-37. Disponible en: http://individual.utoronto.ca/acephalous/Sidoli_2014b.pdf
Tournès, Dominique (2000). Pour une histoire du calculgraphique. Revue d'Histoire des Mathématiques, 6, 127-161. Disponible en: http://www.numdam.org/article/RHM_2000__6_1_127_0.pdf
Tournès, Dominique (2011). What is a Numerical Table? Milestones for a Historical Research Project. Oberwolfach Reports, European Mathematical Society, 8 (1), Mini-Workshop: History of Numerical and Graphical Tables, 643-645. Disponible en: https://www.academia.edu/30940430/What_is_a_numerical_table_Milestones_for_a_historical_research_project
Tournès, Dominique (2014). Mathematics of Engineers: Elements for a New History of Numerical Analysis. En Proceedings of the International Congress of Mathematicians, Vol. 4, 1255-1273. Disponible en: https://hal.archives-ouvertes.fr/hal-01479456/document
Vergnaud, Gérard (1990). La théorie des champs conceptuels. Recherches en Didactique des Mathématiques, RDM, 10 (23), 133-170.
Vergnaud, Gérard (2013). Pourquoi la theorie des champs conceptuels? Infancia y Aprendizaje, 36 (2), 131-161. Disponible en: http://www.tandfonline.com/doi/pdf/10.1174/021037013806196283
Wiese, Heike (2003). Iconic and Non-iconic Stages in Number Development: the Role of Language. Trends in Cognitive Sciences, 7 (9), 385-390.
Wussing, Hans (1998). Lecciones de historia de las matemáticas. Madrid: Siglo XXI.
Youschkevitch, Adolph-Andrei Pavlovich (1976). The Concept of Function up to the Middle of the 19th Century. Archive for History of Exact Sciences, 16 (1), 37-85.
Anellis, Irving H. (1995). Peirce Rustled, Russell Pierced: How Charles Peirce and Bertrand Russell Viewed Each Other's Work in Logic, and an Assessment of Russell's Accuracy and Role in the Historiography of Logic. Modern Logic, 5 (3), 270-328. Disponible en: http://www.iupui.edu/~arisbe/menu/library/aboutcsp/ANELLIS/csp&br.htm
Anellis, Irving H. (2012). Peirce's Truth-functional Analysis and the Origin of the Truth Table. History and Philosophy of Logic, 33 (1), 87-97.
Arad, Zvi; Bangteng, Xu; Chen, Guiyun; Cohen, Effi; Hussam, Arisha HajIhia & Muzychuk, Mikhail (2011). On Normalized Integral Table Algebras (Fusion Rings): Generated by a Faithful Non-real Element of Degree 3. London: Springer.
Arad, Zvi & Blau, Harvey I. (1991). On Table Algebras and Applications to Finite Group Theory. Journal of Algebra, 138 (1), 137-185.
Arad, Zvi; Fisman, Elsa & Muzychuk, Misha (1999). Generalized Table Algebras. Israel Journal Mathematics, 114 (1), 29-60.
Bertoloni-Meli, Domenico (2004). The Role of Numerical Tables in Galileo and Mersenne. Perspectives on Science, 12 (2), 164-190. Disponible en: https://pdfs.semanticscholar.org/7b83/70eb76988606f2b0307799a1a5f56caf8927.pdf
Blau, Harvey I. & Zieschang, Paul-Hermann (2004). Sylow Theory for Table Algebras, Fusion Rule Algebras, and Hypergroups. Journal of Algebra, 273 (2), 551-570. Disponible en: http://www.sciencedirect.com/science/article/pii/S0021869303007087
Bocheński, Innocentius M. (1961). A History of Formal Logic. South Bend, Indiana: University of Notre Dame Press.
Campbell-Kelly, Martin; Croarken, Mary; Flood, Raymond & Robson, Eleanor (eds.) (2003). The History of Mathematical Tables. From Sumer to Spreadsheets. Oxford: Oxford University Press.
Chevallard, Yves (1991). La transposición didáctica. Del saber sabio al saber enseñado. Buenos Aires: Aique Grupo Editor S. A.
Estrella, Soledad (2014). El formato tabular: una revisión de literatura. Revista Actualidades Investigativas en Educación, 14 (2), 1-23. Disponible en: http://www.redalyc.org/pdf/447/44731371016.pdf
Estrella, Soledad; Mena-Lorca, Arturo & Olfos, Raimundo (2014). Desarrollo de una taxonomía de comprensión tabular. En Patricia Lestón (ed.). ALME, Acta Latinoamericana de Matemática Educativa, 27, 1041-1048. México: Colegio Mexicano
de Matemática Educativa A. C., Comité Latinoamericano de Matemática Educativa A. C. Disponible en: http://www.clame.org.mx/documentos/alme27.pdf
Euler, Leonhard (1748/1988). Introduction to Analysis of the Infinite. Book I. Berlin: Birkhäuser.
Friberg, Jöran (2007). A Remarkable Collection of Babylonian Mathematical Texts. Manuscripts in the Schøyen Collection: Sources and Studies in the History of Mathematics and Physical Sciences. New York: Springer.
Friendly, Michael & Denis, Daniel J. (2009). Milestones in the History of Thematic Cartography, Statistical Graphics, and Data Visualization. Natural Sciences and Engineering Research Council. Canada: Grant OGP0138748. Disponible en http://www.math.yorku.ca/SCS/Gallery/milestone/milestone.pdf, http://www.datavis.ca/milestones/
Friendly, Michael & Kwan, Ernest (2003). Effect Ordering for Data Displays. Computational Statistics & Data Analysis, 43 (4), 509-539. Disponible en: http://citeseerx.ist.psu.edu/viewdoc/download? doi=10.1.1.445.2938&rep=rep1&type=pdf
Garrow, John S. & Webster, Joan (1984). Quetelet's Index (W/H2) as a Measure of Fatness. International Journal of Obesity, 9 (2), 147-153.
Goody, Jack (1976). Civilisation de l'écriture et classification ou l'art de jouer sur les tableaux. Actes de la Recherche en Sciences Sociales, 2 (1), 87-101. Disponible en: http://www.persee.fr/doc/arss_0335-5322_1976_num_2_1_3384
Goody, Jack (1977). La domesticación del pensamiento salvaje. Madrid: Ediciones Akal.
Hallo, William W. (1964). The Road to Emar. Journal of Cuneiform Studies, 18 (3), 57-88.
Hitotsumatsu, Shin; Okada, Yoshio & Machida, Shouichiro (eds.). (2008). Study with Your Friends Mathematics for Elementary School, 3rd grade, vol. 1, 65-66. Tokyo: Gakko Tosho Co.
Lardner, Dionysius (1834). Babbage's Calculating Engine. Edinburgh Review, 120, 263-327.
Merzbach, Uta C. (1977). Georg Scheutz and the First Printing Calculator. Smithsonian Studies in History and Technology, 36, 1-74. Disponible en http://hdl.handle.net/10088/2435
Neugebauer, Otto & Hoesen, Henry B. van (1959). Greek Horoscopes. En Memoirs of the American Philosophical Society. Baltimore, Maryland: J. H. Furst Company.
Parnas, David Lorge; Asmis, G. J. Kurt & Madey, Jan (1991). Assessment of Safety-Critical Software in Nuclear Power Plants. Nuclear Safety, 32 (2), 189-198. Disponible en: https://www.researchgate.net/publication/242413466_Assessment_of_safety-critical_software_in_nuclear_power_plants
Pearson, Karl (1904). On the Theory of Contingency and its Relation to Association and Normal Correlation; on the General Theory of Skew Correlation and Non-linear Regression. Cambridge: Cambridge University Press.
Pecharromán-Gómez, Cristina (2013). Naturaleza de los objetos matemáticos: representación y significado. Enseñanza de las Ciencias, Revista de Investigación y Experiencias Didácticas, 31 (3), 121-134. Disponible en: http://www.raco.cat/index.php/Ensenanza/article/view/285795/373798
Pedersen, Olaf (1974). Logistics and Theory of Function: An Essay in the History of Greek Mathematics. Archives Internationales d'Histoire des Sciences, ARIHS, 24 (94), 29-50.
Peirce, Charles Sanders (1931). Division of Signs. En Charles Hartshorne & Paul Weiss (eds.). Collected Papers of Charles Sanders Peirce, Volume II, Chapter 2. Cambridge, Massachusetts: Harvard University Press.
Peirce, Charles Sanders (1931-1958). Collected Papers of Charles Sanders Peirce. Cambridge, Massachusetts: Harvard University Press.
Proust, Christine (2005). Le calcul sexagésimal en Mésopotamie. Disponible en http://culturemath.ens.fr/histoire%20des%20maths/pdf/Calcul%20sexa_Proust.pdf
Proust, Christine (2008). Quantifier et calculer: usages des nombres à Nippur. Revue d'Histoire des Mathématiques, 14 (2), 143-209. Disponible en: http://smf4.emath.fr/Publications/RevueHistoireMath/14/pdf/smf_rhm_14_143-209.pdf
Proust, Christine (2009). Numerical and Metrological Graphemes: From Cuneiform to Transliteration. Cuneiform Digital Library Journal, 1, 1-27. Disponible en: http://cdli.ucla.edu/files/publications/cdlj2009_001.pdf, http://www.cdli.ucla.edu/pubs/cdlj/2009/cdlj2009_001.html
Proust, Christine (2010). Mesopotamian Metrological Lists and Tables: Forgotten Sources. En Florence Bretelle-Establet (ed.). Looking at it from Asia: The Processes that Shaped the Sources of History of Science, 245-276. New York: Springer.
Quetelet, Lambert Adolphe Jacques (1835). Sur l'homme et le développement de ses facultés, ou Essai de physique sociale. Paris: Bachelier. Disponible en https://archive.org/stream/surlhommeetled00quet#page/n5/mode/2up
Rashed, Roshdi (2003). History of Science and Diversity at the Beginning of the 21st Century. En Proceedings of the XXI International Congress of History of Science, vol. I, 15-29. Ciudad de México: Universidad Nacional Autónoma de México, UNAM, Sociedad Mexicana de Historia de la Ciencia y la Tecnología.
Robson, Eleanor (2001). The Tablet House: A Scribal School in Old Babylonian Nippur. Revue d'assyriologie et d'archéologie orientale, 93 (1), 39-66.
Robson, Eleanor (2003). Tables and Tabular Formatting in Sumer, Babylonia, and Assyria, 2500 BCE-50 CE. En Martin Campbell-Kelly, Mary Croarken, Raymond Flood & Eleanor Robson (eds.). The History of Mathematical Tables. From Sumer to Spreadsheets, 19-48. Oxford: Oxford University Press.
Roegel, Denis (2010). A Reconstruction of the Tables of Briggs and Gellibrand's. Trigonometria Britannica (1633). En The LOCOMAT Project: Recomputing Mathematical and Astronomical Tables. Technical Report. Nancy, France: LOCOMAT, The LOria COllection of MAthematical Tables. Disponible en: http://locomat.loria.fr/briggs1633/briggs1633doc.pdf
Ross, Micah T. (2011). Survey of Graphical and Numerical Tables in Egypt. Oberwolfach Reports, 12, 650-652. Disponible en: http://www.academia.edu/7451497/Survey_of_Graphical_and_Numerical_Tables_in_Egypt
Schubring, Gert (2005). Conflicts between Generalization, Rigor and Intuition. Number Concepts Underlying the Development of Analysis in 17th19th Century France and Germany. New York: Springer. Sources and Studies in the History of Mathematics and Physical Sciences, SHMP.
Schubring, Gert (2011). Conceptions for Relating the Evolution of Mathematical Concepts to Mathematics Learning - Epistemology, History, and Semiotics Interacting. Educational Studies in Mathematics, 77 (1), 79-104.
Sidoli, Nathan (2014). Mathematical Tables in Ptolemy's Almagest. Historia Mathematica, 41 (1), 13-37. Disponible en: http://individual.utoronto.ca/acephalous/Sidoli_2014b.pdf
Tournès, Dominique (2000). Pour une histoire du calculgraphique. Revue d'Histoire des Mathématiques, 6, 127-161. Disponible en: http://www.numdam.org/article/RHM_2000__6_1_127_0.pdf
Tournès, Dominique (2011). What is a Numerical Table? Milestones for a Historical Research Project. Oberwolfach Reports, European Mathematical Society, 8 (1), Mini-Workshop: History of Numerical and Graphical Tables, 643-645. Disponible en: https://www.academia.edu/30940430/What_is_a_numerical_table_Milestones_for_a_historical_research_project
Tournès, Dominique (2014). Mathematics of Engineers: Elements for a New History of Numerical Analysis. En Proceedings of the International Congress of Mathematicians, Vol. 4, 1255-1273. Disponible en: https://hal.archives-ouvertes.fr/hal-01479456/document
Vergnaud, Gérard (1990). La théorie des champs conceptuels. Recherches en Didactique des Mathématiques, RDM, 10 (23), 133-170.
Vergnaud, Gérard (2013). Pourquoi la theorie des champs conceptuels? Infancia y Aprendizaje, 36 (2), 131-161. Disponible en: http://www.tandfonline.com/doi/pdf/10.1174/021037013806196283
Wiese, Heike (2003). Iconic and Non-iconic Stages in Number Development: the Role of Language. Trends in Cognitive Sciences, 7 (9), 385-390.
Wussing, Hans (1998). Lecciones de historia de las matemáticas. Madrid: Siglo XXI.
Youschkevitch, Adolph-Andrei Pavlovich (1976). The Concept of Function up to the Middle of the 19th Century. Archive for History of Exact Sciences, 16 (1), 37-85.
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Estrella, S., Mena-Lorca, A., & Olfos-Ayarza, R. (2017). Natureza do objeto matemático “tabela”. Revista Internacional De Pesquisa Em Educacao, 10(20), 105–122. https://doi.org/10.11144/Javeriana.m10-20.nomt
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