Note on Archimedes’ quadrature of the parabola

• Dusan Vallo ^[1] ; Jozef Fulier ^[1] ; Lucia Rumanova ^[1]
  1. [1] Constantine the Philosopher University in Nitra

     Constantine the Philosopher University in Nitra

     Eslovaquia

     
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 53, Nº. 4, 2022, págs. 1025-1036
• Idioma: inglés
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• Resumen

  • In this paper, we present a novel solution of the quadrature of a parabola based on application of Ramanujan’s formula for the partial sum of the square roots of the first n natural numbers. We also derive a new formula for calculating of area of a parabolic segment and we apply the result to a generalization of some classical theorems related to this problem.