Resumo

GUACANEME SUAREZ, Edgar Alberto. Euclidean Theory of Proportion in the Construction of Real Numbers: A Useful Subject for a Teacher?. Rev. Fac. Cienc. Tecnol. [online]. 2012, n.31, pp.113-131. ISSN 0121-3814.

From the Greek Golden Age, the Euclidean theory of proportion, stated in Book V of Elements, was established as an outline for the formulation of relations between magnitudes, were they or not measurable and, therefore, without resort to numerical values of its measurements to establish both the ratios of magnitudes as the proportion between ratios. Nearly twenty centuries later, this way of independent treatment of arithmetic strategy seems to be accurate and, paradoxically, the incentive and guidance for the establishment of the set of real numbers. Historians of mathematics have discussed the relationship between these theories and we conjecture that the study of their positions can bring benefits to the mathematics teacher education. These benefits relate with alternative visions of the mathematical study of a theory and the extension of the look on the mathematical objects involved in theories.

Palavras-chave : Ratio; proportion; real number; Euclid; Dedekind; Frege; teacher's knowledge.

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