Mètodes de demostració

• Autores: Armengol Gasull i Embid
• Localización: Materials matemàtics, ISSN-e 1887-1097, Nº. 0, 2023
• Idioma: catalán
• Enlaces
  • Texto completo
• Referencias bibliográficas
  • M. Aigner, G. M. Ziegler, EL LIBRO de las demostraciones. Nivola Libros y Ediciones, S.L., 2005.
  • A. Alonso T. Bermúdez, De conejos y números. La sorprendente sucesión de Fibonacci. Gaceta de la Real Sociedad Matemática Española 5 (2002),...
  • C. Alsina, R. B. Nelsen, Charming Proofs: A Journey into Elegant Mathematics, Dolciani Mathematical Expositions 42, 2010. AMS/MAA Press.
  • T. Andreescu, R. Gelca, Mathematical Olympiad Challenges. Birkhäuser Boston, MA, 2009.
  • N. D. Baruah, B. C. Berndt, H. H. Chan, Ramanujan’s series for 1/π : a survey, Amer. Math. Monthly 116 (2009), 567–587.
  • A. Bogomolny, Cut The Knot. https://www.cut-the-knot.org/ front.shtml
  • M. Chamberland, Single digits. In praise of small numbers. Princeton University Press, Princeton, NJ, 2015.
  • E. Chen, Euclidean geometry in mathematical Olympiads. With 248 illustrations. MAA Problem Books Series. Washington, DC: Mathematical Association...
  • K. Conrad, The Gaussian integral. http://www.math.uconn.edu/ ~kconrad/blurbs/analysis/gaussianintegral.pdf
  • H. S. M. Coxeter, S. L. Greitzer, Geometry Revisited, Math. Assoc. Amer. 1967.
  • H. T. Croft, K. J. Falconer, R. K. Guy, Unsolved problems in geometry. Problem Books in Mathematics. Unsolved Problems in Intuitive Mathematics,...
  • D. R. Curtiss, Recent extensions of Descartes’ rule of signs. Annals of Mathematics 19 (1918), 251–278.
  • B. A. Davey, Maths delivers! Proofs by induction. The University of Melbourne on behalf of the Australian Mathematical Sciences Institute (AMSI),...
  • W. Dunham, El universo de las matemáticas: un recorrido alfabético por los grandes teoremas, enigmas y controversias, Ed. Pirámide, 1995.
  • W. Dunham, Viaje a través de los genios. Biografías y teoremas de los grandes matemáticos. Ed. Pirámide, 2002.
  • T. Edgar, Sums of Powers of 4/9. Math. Mag. 89 (2016) 191.
  • A. Engel, Problem-solving strategies, Springer, 1998.
  • P. Eymard, J-P. Lafon, The number π. Traduït de la versió francesa de 1999 per S. S. Wilson. American Mathematical Society, Providence, RI,...
  • D. Fomin, S. Genkin, I. Itenberg, Mathematical circles (Russian experience). Providence, Rhode Island: Americal Mathematical Society, 1996.
  • A. Gasull, Gemmes matemàtiques. Mat. Mat. 2019, treball no. 2, pp. 88, 2019.
  • A. Gasull, 55 proves sense paraules. Mat. Mat. 2022, treball no. 2, pp. 61, 2022.
  • A. Gasull, J. T. Lázaro, J. Torregrosa, Rational parameterizations approach for solving equations in some dynamical systems problems. Qual....
  • A. Gasull, F. Luca, J. L. Varona, Three essays on Machin’s type formulas. Pendent de publicació a Indag. Math. DOI: 10.1016/j.indag.2023.07.002
  • J. Grané (Editor), Sessions de Preparació per a l’Olimpíada Matemàtica. Publicacions Electròniques de la Societat Catalana de Matemàtiques,...
  • S. L. Greitzer, Olimpiadas matemáticas internacionales. La Totuga de Aquiles 2, Ed. DLS-EULER, Madrid, 1994.
  • M. de Guzmán, Aventuras matemáticas. Una ventana hacia el caos y otros episodios. Ed. Pirámide, Madrid 2004.
  • R. Hammack, BOOK OF PROOF, 2003. Disponible a https://www. people.vcu.edu/~rhammack/BookOfProof/BookOfProof.pdf
  • R. Honsberger, Mathematical gems from elementary combinatorics, number theory, and geometry. The Dolciani Mathematical Expositions, 1. The...
  • R. Honsberger, Mathematical gems. II. Dolciani Mathematical Expositions, 2. The Mathematical Association of America, Washington, D.C. 1976.
  • R. Honsberger, Mathematical gems. III. The Dolciani Mathematical Expositions, 9. Mathematical Association of America, Washington, D.C. 1985.
  • D. J. Jeffrey, A. D. Rich, Computer Algebra Systems: A Practical Guide. Chapter: Simplifying square roots of square roots by denesting, John...
  • E. Key, Disks, Shells, and Integrals of Inverse Functions. The College Mathematics Journal 25 (1994) 136–138.
  • S. G. Krantz, The History and Concept of Mathematical Proof, 2007
  • C. A. Laisant, Intégration des fonctions inverses. Nouvelles Annales de Mathématiques, Journal des candidats aux Écoles Polytechnique et Normale...
  • M. Macho Stadler, Mapas, colores y números, Descubrir las matemáticas hoy: Sociedad, Ciencia, Tecnología y Matemáticas 2006 (2008) 41–68
  • J. Neunhäuserer, 122 beautiful mathematical theorems with short proofs. Preprint.
  • F. D. Parker, Integrals of inverse functions. The American Mathematical Monthly. 62 (1955) 439–440.
  • G. Polya, Mathematical Discovery. On Understanding, Learning, and Teaching Problem Solving. Combined Edition. John Wiley & Sons, 1981.
  • H. Rademacher, O. Toeplitz, Números y figuras. Alianza Editorial. Madrid 1970.
  • C. H. Raifaizen, A Simpler Proof of Heron’s Formula. Mathematics Magazine. 44 (1971), 27–28.
  • J. Ramírez Alfonsín, The Diophantine Frobenius problem. Oxford Univ. Press., 2005.
  • M. A. Rincón Ortega, E. Letón Molina, Tipos de demostraciones, http://www.minixmodular.ia.uned.es, Madrid, 2021
  • D. O. Shklarsky, N. N. Chentzov, I .M. Yaglom, The USSR Olympiad problem book: selected problems and theorems of elementary mathematics, 3a...
  • J. H. Silverman, Taxicabs and sums of two cubes. Am. Math. Monthly 100 (1993) 331–340.
  • T. B. Soulami, Les olympiades de mathématiques: Réflexes et stratégies. Ed. Ellipses, Paris, 1999.
  • P. Zeitz, The art and craft of problem solving. 3rd edition. John Wiley & Sons, 2017. Hi ha una traducció en castellà “El arte y el oficio...
  • A Collection of Algebraic Identities, https://www.scribd.com/document/ 72611415/A-Collection-of-Algebraic-Identities