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Artículos

Vol. 3 N.º 1 (2000): Marzo

LA CREACIÓN DE EXPONENTES CONTINUOS: UN ESTUDIO SOBRE LOS MÉTODOS Y LA EPISTEMOLOGÍA DE JOHN WALLIS

Enviado
março 22, 2025
Publicado
2001-03-31

Resumo

Este é um trabalho de pesquisa histórica que é enfocado em momentos matemáticos especí-ficos, onde os métodos, conceitos e definições passaram por profundas mudanças. Há duas principais metas: Primeiro, esboçar a história do desenvolvimento do conceito contínuo de expoentes e o segundo, examinar cuidadosamente o cenario epistemológico onde desen-volveuse o mesmo. Colocado de forma mais simple, que foi o que convenceu a alguns matemáticos de que seus conceitos eram viáveis. Não pretende ser uma discusão histórica completa, e sim uma serie de discusões instantâneas. Os detalhes matemáticos desses mo-mentos ocurrem na medida que sejam necesarios para compreender a epistemologia.

Referências

  1. Baron, M. (1969). The Origins of Infinitesimal Calculus, Pergamon. London.
  2. Boyer, C.B. (1968). A History of Mathematics, Willey, New York.
  3. Boyer, C.B. (1956). History of Analytic Geometry, Chapters III-V. Scripta Mathematica, New York.
  4. Boyer, C.B. (1943). Pascal's formula for the sums of powers of integers, en: Scripta Mathematica 9,237-244.
  5. Cajori, F. (1913). History of exponential and logarithmic concepts, en: American Mathematical Monthly 20.
  6. Cajori, F. (1929). Controverses on mathematics between Wallis, Hobbes, and Barrow, en: The Mathematics Teacher XXII(3), 146-151.
  7. Calinger, R. (1982). Classics of Mathematics. Moore, Oak Park. IL.
  8. Confrey, J. (1988). Multiplication and splitting: their role in understandig exponential func-tions. en: Proceedings of the Tenth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA), DeKalb. IL.
  9. Confrey, J. (1992). Using computers to promote students' inventions on the function concept. This Year in School Science 1991. en: Malcom, Roberts & Sheingold, (Eds.). American Association for the Advancement of Science. Washington DC, 131-161.
  10. Confrey, J. (1993). Learning to see children's mathematics: crucial challenges in construc-tivist reform. The Practice of Constructivism in Science Education. Tobin, K. (Ed.), en: American Association for the Advancement of Science. Washington DC, 299-321.
  11. Confrey, J. (1994). Splitting, similarity, and range of change: New aproaches to multiplica-tion and exponential functions, en: The Development of Multiplicative Reasoning in the Learning of Mathematics (Harel. G. And Confrey, J., eds.), State University of New York Press, Albany NY, 293-332.
  12. Confrey, J. & Smith, E. (en prensa). Applying and epistemology of multiple representations to histoical analysis: A review of "democratizing the access to calculus: New routes to old roots" by James Kaput, Mathematical Thinking and Problem Solving (Schoenfeld, A., ed.), Lawrence Erlbaum Assoc. Inc., Hillsdale NJ.
  13. Courant, R. (1984). Gauss and the present situation of the exact sciences, en: Mathematics: People, Problems, Results (Campbell, D. And Higgins, J., ed.), vol.I, Wadsworth International, Belmont CA, 125-133.
  14. Dennis, D. (1995). Historical perspectives for the reform of mathematics curriculum: geo-metric curve drawing devices and their role in the tansition to an algebraic description of functions (unpublished doctoral dissertartation), Cornell University, Ithaca, NY.
  15. Descartes, R. (1952). The Geometry, (Translated by D.E. Smith and M.L., Latham), Open Court, LaSalle, IL.
  16. Edwards, C.H. (1979). The Historical Developtment of Calculus, Springer-Verlag, New York.
  17. Euler, L. (1988). Introduction to Analisys of the Infinite, (Translated by J.D. Blanton), Springer-Verlag, New York.
  18. Fowler, D. H. (1987). The Mathematics of Plato's Academy: A New Reconstruction, Clarendon Press, Oxford.
  19. Katz, V. (1993). A History of Mathematics; An Introduction, Harper Collins, New York.
  20. Lakatos, 1. (1976). Proofs and Refutations, The Logic of Mathematical Discovery, Cambridge University Press, New York.
  21. Mahoney, M.S. (1973). The Mathematical Career of Pierre de Fermat, Princetown University Press, Princeton NJ.
  22. Newton, L. (1967). The Mathematical Papers of Isaac Newton, Volume I: 1664-1666, Cambridge University Press, Cambridge.
  23. Nunn, T.P. (1909-1911). The arithmetic of infinites, en: Mathematics Gazete 5, 345-356 y 377-386.
  24. Scott, J.F. (1981). The Mathematical Work of John Wallis, Chelsea Publishing Co., New York
  25. Smith, E., Dennis, D. & Confrey, J. (1992). Rethinking functions, cartesian constructions, en: The History and Philosophy of Science in Science Education, Proceedings of the Second International Conference on the History and Philosophy of Science and Science Education (S.Hills,ed.). The Mathematics, Science, Technology and Teacher Education Group; Queens University, Kingston, Ontario.
  26. Struik, D.J. (1969). A Source Book in Mathematics: 1200-1800, Harvard University Press, Cambridge MA.
  27. Unguru, S. (1976). On the need to rewrite the history of Greek mathematics, en: Archive for History of Exact Sciences 15(2), 67-114.
  28. Wallis, J. (1972). Arithmetica Infinitorum, Opera Mathematica, vol.I, Georg Olms Verlag, New York, 355-478.
  29. Wittgestein, L. (1967). Remarks on the Foundations of Mathematics, (translated by G.E.M. Anscombe). MIT Press, Cambridge MA.
  30. Whiteside, D.T. (1961). Newton and discovery of the general binomial theorem, en: Mathematics Gazette 45, 175-180.
  31. Whiteside, D.T. (1960-1962). Patterns of mathematical thought in the later 17th century, en: Archive for History of Exact Sciences, vol. I, 179-388.

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