Recopilación de resoluciones del problema de Basilea

• Vicent Navarro Arroyo ^[1]
  1. [1] Universitat Politècnica de Catalunya

     Universitat Politècnica de Catalunya

     Barcelona, España

     
• Localización: TEMat: Divulgación de trabajos de estudiantes de matemáticas, ISSN-e 2530-9633, Nº. 7, 2023, págs. 27-40
• Idioma: español
• Enlaces
  • Texto completo  1    2  
• Resumen
  • español

    El problema de Basilea se basa en hallar si, en efecto, la suma de los inversos de los cuadrados naturales converge y, en caso afirmativo, a qué valor. Este problema fue resuelto, primero, por Euler, pero se han conseguido numerosas pruebas tras él. Recopilaremos algunas de sus demostraciones más importantes y mostraremos la versatilidad de los enfoques hacia este problema señalando el potencial de determinadas teorías (en particular, la teoría de series de Fourier), las demostraciones más insospechadas y directas, así como los puentes que se tienden entre varias áreas de las matemáticas

  • English

    The Basel Problem consists in finding if, actually, the sum of inverse squares of the natural numbers converges and to what value. This problem was first solved by Euler but numerous proofs have been obtained later. We compile some of its most important proofs and show the versatility of approaches to the Basel Problem by pointing out the potential of certain theories (particularly, the Fourier series theory), the most direct and unsuspected proofs, as well as the bridges that are built between various areas of Mathematics.

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