Skip to main navigation menu Skip to main content Skip to site footer

Artículos

Vol. 16 No. 3 (2013): Noviembre

THE HISTORICAL GENESIS OF THE CONCEPTS RATIO AND PROPORTION AND LATER ARITHMETIZATION

DOI
https://doi.org/10.12802/relime.13.1632
Submitted
July 13, 2023
Published
2023-07-13

Abstract

The importance of the arithmetical proportion is unquestionable from two points of view: school mathematics and its practical application. Its importance is reflected in a series of works in the Mathematics Education field, which is our main topic. In this article we show an historical review of some of the main concepts related to the arithmetical proportion, such as ratio and proportion. Besides its importance, as an historical study, we believe that the conclusions that follow this research may be useful in order to improve the teaching of ideas, concepts and techniques involved.

References

  1. Anzola, M., Bujanda, M.P., Mansilla, S. y Vizmanos, J.R. (2009). Esfera. Matemáticas 1º ESO. Madrid, España: S.M.
  2. Baratech, B. (1966). Matemáticas 2º de Bachillerato. Zaragoza, España: Edición del autor.
  3. Benoit, P., Chemla, K. y Ritter, J. (Coords.) (1992). Histoire de fractions, fractions d’histoire. Basel, Suiza: Birkhäuser Verlag.
  4. Caveing, M. (1994). La proportionalité des grandeurs dans la doctrine de la nature d’Aristote. Revue d’Histoire des Sciences, 47 (2), 163-188.
  5. Chace, A.B. (1979). The Rhind Mathematical Papyrus. Reston, EEUU: National Council of Teachers of Mathematics.
  6. Chemla, K. (2005). The interplay between proof and algorithm in 3rd century China: The operation as prescription of computation and the operation as argument. En P. Mancosu, K. F. Jorgensen y S.A. Pedersen (Eds.) Visualization, Explanation and Reasoning Styles in Mathematics, (pp. 123-145). Dordrecht, Holanda: Springer.
  7. Crespo, C., Farfán, R.M. y Lezama, J. (2009). Algunas características de las argumentaciones y la matemática en escenarios sin inf luencia aristotélica. Revista Latinoamericana de Investigación en Matemática Educativa, 12 (1), 29-66.
  8. Cullen, C. (2007). The Suàn shù shű, “Writings on reckoning’”: rewriting the history of early Chinese mathematics in the light of an excavated manuscript. Historia Mathematica, 34 (1), 10-44.
  9. Dauben, J.W. (1998). Ancient Chinese mathematics: the Jiu Zhang Suan Shu vs Euclid’s Elements. Aspects of proof and the linguistic limits of knowledge. International Journal of Engineering Science, 36 (12-14), 1339-1359.
  10. Djebbar, A. (1997). La rédaction de L’istikmal d’al-Mu’taman (XI e s.) par Ibn Sartaq, un mathématicien de XIIIe -XIVe siècles. Historia Mathematica, 24 (2), 185-192.
  11. Euclides (1994). Elementos. Libros V-IX. Madrid, España: Gredos.
  12. Filep, L. (2003). Proportion theory in Greek mathematics. Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, 19 (2), 167-174.
  13. Fine, H.B. (1917). Ratio, proportion and measurement in the Elements of Euclid. Annals of Mathematics, 19 (1), 70-76.
  14. Fowler, D.H. (1979). Ratio in early Greek mathematics. Bulletin of the American Mathematical Society, 1 (6), 807-846.
  15. Fowler, D.H. (1980). Book II of Euclid’s Elements and a pre-Eudoxan theory of ratio. Archive for History of Exact Sciences, 22 (1-2), 5-36.
  16. Fowler, D.H. (1982). Book II of Euclid’s Elements and a pre-Eudoxan theory of ratio. II. Sides and diameters. Archive for History of Exact Sciences, 26 (3), 193-209.
  17. Freudenthal, H. (1983). Didactical phenomenology of mathematical structures. Dordrecht: D. Reidel Publishing Company.
  18. Gairín, J.M. y Oller, A.M. (2012). Análisis histórico sobre la enseñanza de la razón y la proporción. En A. Estepa, Á. Contreras, J. Deulofeu, M.C. Penalva, F.J. García y L. Ordóñez (Eds.) Investigación en Educación Matemática XVI (pp. 249-259). Jaén, España: SEIEM.
  19. Gardies, J.L. (1988). L’Héritage épistémologique d’Eudoxe de Cnide. Paris, Francia: Librairie Philosophique J. Vrin.
  20. Gardies, J.L. (1997). L’organisation des mathématiques grecques: de Théétète à Archimède. Paris, Francia: Librairie Philosophique J. Vrin.
  21. Grattan-Guinness, I. (1996). Numbers, magnitudes, ratios and proportions in Euclid’s Elements: how did he handle them? Historia Mathematica, 23 (4), 355-375.
  22. Grattan-Guinness, I. (2004). The mathematics of the past: distinguishing its history from our heritage. Historia Mathematica, 31 (2), 163-185.
  23. Heath, T.L. (1957). The thirteen books of the Elements. 3 Volúmenes. New York, EEUU: Dover.
  24. Jankvist, U.T. (2009). On empirical research in the field of using history in Mathematics Education. Revista Latinoamericana de Investigación en Matemática Educativa, 12 (1), 67-101.
  25. Kangshen, S.; Crossley, J.N. y Lun, A.W.-C. (1999). The nine chapters on the mathematical art. Beijing, China: Oxford University Press.
  26. Lam, L.Y. (1994). Jiu zhang suanshu (Nine chapters on the mathematical art): an overview. Archive for History of Exact Sciences, 47 (1), 1-51.
  27. Mansilla,S. y Bujanda, M. P. (1984). Pitágoras.Matemáticas 7º E.G.B. Madrid, España: S.M.
  28. Modestou, M., Elia, I., Gagatsis, A. y Spanoudis, G. (2008). Behind the scenes of pseudoproportionality. International Journal of Mathematics Education in Science and Technology, 39 (3), 313-324.
  29. Needham, J. (1995). Science and Civilisation in China Volume III. Cambridge, Inglaterra: Cambridge University Press.
  30. Patwardan, K.S.; Naimpally, S.A. y Singh, A.L. (2001). Lilavati of Bhaskaracarya. A treatise of mathematics of vedic tradition. Delhi, India: Motilal Banarsidass Publishers.
  31. Rashed, R. (1997). Historie des sciences arabes, tome 2: Mathématique et physique. Paris: Seuil.
  32. Rashed, R. y Vahabzadeh, B. (1999). Al-Khayyam mathématicien. Paris, Francia: Librairie Scientifique et Technique Albert Blanchard.
  33. Robins, G. y Shute, C. (1987). The Rhind mathematical papyrus. An ancient Egypcian text. London, Inglaterra: British Museum Publications.
  34. Rommevaux, S. (1999). La proportionalité numérique dans le Libre VII del Éléments de Campanus. Revue d’Histoire des Mathématiques, 5 (1), 83-126.
  35. Rusnock, P. y Thagard, P. (1995). Strategies for conceptual change: ratio and proportion in classical Greek mathematics. Studies in History and Philosophy of Science, 26 (1), 107-131.
  36. Sigler, L.E. (2002). Fibonacci’s Liber Abaci. A translation into modern English of Leonardo Pisano’s Book of Calculation. New York, EEUU: Springer Verlag.
  37. Thorup, A. (1992). A pre-Euclidean theory of proportions. Archive for History of Exact Sciences, 45 (1), 1-16.
  38. Valverde, A.G. y Castro, E. (2009). Razonamiento proporcional: un análisis de las actuaciones de maestros en formación. Indivisa, Boletín de Estudios e Investigación, Monografía XII, 121-137.
  39. Van Dooren, W., De Bock, D., Hessels, A., Janssens, D. y Verschaffel, L. (2004). Remedying secondary school students’ illusion of linearity: a teaching experiment aiming at conceptual change. Learning and Instruction, 14 (5), 485-501.
  40. Youschkevitch, A.P. (1976). Les mathématiques arabes (VIIIe-XVe siècles). Paris, Francia: Librairie Philosophique J. Vrin.

Downloads

Download data is not yet available.

Similar Articles

<< < 1 2 3 4 > >> 

You may also start an advanced similarity search for this article.

Most read articles by the same author(s)