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Noviembre 2008 revista sobre la enseñanza y el aprendizaje de las matemáticas SUMA. Revista sobre la enseñanza y el aprendizaje de las matemáticas. N.º 59 · Noviembre 2008 Federación Española de Sociedades de Profesores de Matemáticas 58 ISSN 1130-488X 9 771130 488006 0 0 0 5 8 ISSN 1130-488X ISSN 1130-488X 9 771130 488006 0 0 0 5 7 9 771130 488006 0 0 0 5 9 SUMA. Revista sobre la enseñanza y el aprendizaje de las Matemáticas Índice Directores Onofre Monzó del Olmo 59 Noviembre 2008 Tomás Queralt Llopis [email protected] Administrador Gregori García Ferri [email protected] Consejo de redacción Salvador Caballero Rubio (CEFIRE d’Alacant) Editorial 3-4 Marisa Fernández Villanueva (IES Veles e Vents, Torrent) Bernardo Gómez Alfonso (Universitat de València Estudi General) Floreal Gracia Alcaine (IES Politècnic, Castelló) José Antonio Mora Sánchez (IES San Blai, Alacant) Luis Puig Espinosa (Universitat de València Estudi General) Consejo Editorial Serapio García Cuesta artículos (Presidente de la FESPM) Francisco Martín Casalderrey (IES Juan de la Cierva, Madrid) Inmaculada Fuentes Gil Los números mórficos en secundaria (IES Ágora, Madrid) Antonia Redondo Buitrago 7-16 Ricardo Luengo González (Universidad de Extremadura) Matemáticas en la música Edita FEDERACIÓN ESPAÑOLA DE Angel Pastor Martín 17-21 SOCIEDADES DE PROFESORES DE MATEMÁTICAS (FESPM) El problema de la ruina del jugador Web J. Basulto, J. A. Camúñez, Mª D. Pérez 23-30 Antonio Alamillo Sánchez www.revistasuma.es Taller matemático de costura J. Galarreta, D. Acha, C. Barrio, A. Rodríguez, G. Sáez 31-42 Diseño de la portada: O. Monzó Fotografía de la portada: Las matemáticas del IRPF: ¿Por qué ganamos menos si ganamos más? Hielo antártico, Mayte Piera N. Plasencia, J. C. Pérez 43-49 Maquetación T. Queralt y O. Monzó Revista Suma poliedro Apartado 498 E-46900-Torrent (España) Fax:+(34) 912 911 879 Tirada: 6700 ejemplares JUEGOS: Doblar y cortar (kirigami geométrico) Depósito legal: Gr 752-1988 Grupo Alquerque de Sevilla 55-58 ISSN: 1130-488X 1 Asesores ELCLIP: El perímetro de Dubai y el área de Singapur Claudi Alsina 59-60 MATEMÁSTIC: Matemáticas lúdicas Mariano Real Pérez 61-66 Claudi Aguadé Bruix Amador Álvarez del Llano David Arnau Vera ARTE CON OJOS MATEMÁTICOS: El Greco en otra dimensión Carmen Azcárate Jiménez Francisco Martín Casalderrey 67-72 Luis M. Botella López Encarnación Castro Martínez EN LAS CIUDADES INVISIBLES VIII Abilio Corchete González Miquel Albertí 73-80 Manuel Díaz Regueiro Alejandro Fernández Lajusticia BIBLIOTECA: Mi biblioteca particular. Mª José Fuente Somavilla Escaparate 1: Matemáticas para todos.Enseñar en un aula multicultural Horacio Gutiérrez Álvarez Escaparate 2: Matemática inclusiva Arturo Mandly Manso Rafael Martínez Calafat Escaparate 3: Actividades matemáticas para Secundaria con Excel Ricardo Moreno Castillo Escaparate 4: FERMAT y los orígenes del cálculo diferencial Miguel Ángel Moreno Redondo Daniel Sierra (Coord.), Covadonga Rodriguez-Moldes 81-95 Maite Navarro Moncho Mª Jesús Palacios de Burgos EL HILO DE ARIADNA: Para la libertad Pascual Pérez Cuenca Xaro Nomdedeu Moreno 97-104 Antonio Pérez Sanz Ana Belén Petro Balaguer HISTORIAS: Historias de al-Khwārizmī (2ª entrega): los libros Luis Puig Mosquera Luis Puig 105-112 Mariano Real Pérez Francesc A. Rosselló Llompart Manuel José Sastre Álvarez LITERATURA Y MATEMÁTICAS: Matemáticas a medianoche 2ª parte Carlos Oswaldo Suarez Alemán Constantino de la Fuente 113-120 Francisco Villegas Martín CINEMATECA: Intriga y matemáticas José María Sorando 121-127 MUSYMÁTICAS: Las fracciones de la Música Vicente Liern Carrión 129-134 SUMA es una revista de didáctica de las matemáticas de periodicidad cua- trimestral, cuyo objetivo es tratar sobre aquellos aspectos relacionados actividades de la FESPM con su enseñanza y aprendizaje, des- tinada al profesorado que trabaja en educación infantil, primaria, secun- XIX Olimpiada Matemática Nacional daria y universitaria. Ascensión Fernández Vicente 135-139 La revista SUMA se edita en Torrent (Valencia) - ESPAÑA Convocatoria de las Secretarias de Relaciones Internacionales, Actividades con alumnos, Actividades y Formación del Profesorado y de Publicaciones de la FESPM 140 Convocatoria del Premio Gonzalo Sánchez Vázquez 141 Relación de Sociedades federadas 96 Normas de Publicación 143 Boletín de suscripción 144 no se identifica necesariamente con las opiniones vertidas en las colaboraciones firmadas. 2 59 Noviembre 2008 Que veinte años no es nada Editorial L a revista SUMA acaba de cumplir el pasado mes de octubre veinte años de su primera aparición, y aunque en el contexto de una clásica melo- día embriagada de nostalgia o de un capítulo de la historia universal este tiempo es insignificante, para nosotros ha sido relevante. No he podido resistir la tentación de revisar aquel primer ejemplar, que daba carta de naturaleza a una incipiente Federación Española de Sociedades de Profesores de Matemáticas, gracias al empuje de un equipo de entusias- tas y bajo la dirección de Rafael Pérez Gómez en Granada, que asumió el reto e inició la tarea de su edición. A la vista de aquel primer ejemplar, puedo apreciar que grandes cambios se han producido en SUMA, tanto en la forma como en el fondo. Gracias a los avances tecnológicos que nos facilitan la tarea de edición, vamos obte- niendo unos resultados cada vez mejores. Los programas informáticos de maquetación y edición gráfica, así como la incorporación del color, pro- porcionan un resultado muy alejado de la imagen inicial de nuestra revis- ta. Nuestro mayor reconocimiento a los que empezaron a trabajar para que la revista llegara a lo que ahora tenemos en nuestras manos, así como a los que después la continuaron. Tras Rafael Pérez, Sixto Romero en Huelva, Julio Sancho y Emilio Palacián en Zaragoza, y Francisco Martín e Inmaculada Fuentes en Madrid, han puesto su trabajo y esfuerzo al servi- cio de todos para que SUMA sea útil e interesante para el profesorado de matemáticas. 3 También en el fondo SUMA ha ido evolucionando, adquiendo en el tiempo la forma en la que actualmente se distribuye en las secciones de artículos, poliedro y actividades de la Federación. Pero no ha perdido su voluntad de ser: ...una revista sobre la enseñanza y el aprendizaje de las Matemáticas, órgano de expresión de la Federación de Sociedades que la edita, útil para la clase, plural y participativa, dedicada a todos los niveles educativos y que recoja ideas, sugerencias, informaciones, innovaciones,... agrupadas en las distintas secciones, tal y como se apuntaba en el editorial del número 1. Sin embargo, hay ciertas cosas que observo no han cambiado: el entusias- mo por nuestro trabajo, la voluntad de mejorar en el proceso de enseñanza y aprendizaje en el que participamos con nuestros alumnos, el interés por conocer todos los aspectos que nos pueden ayudar a ser mejores profesio- nales, y como no, mejores personas. Esperemos que este espíritu se man- tenga e incluso se incremente con las nuevas generaciones de profesores y profesoras de Matemáticas. Quiero aprovechar para elogiar la labor abnegada, silenciosa las más de las veces, equilibrada y brillante de todos los que han contribuido con su aportación, a construir SUMA a lo largo de estos veinte años, y agradecer en nombre de todos su colaboración para conseguir que la revista SUMA disponga actualmente de un prestigio reconocido a nivel internacional. Estos veinte años serán dentro de otros veinte aquellos primeros años de supervivencia, afianzamiento y lucha por la conquista del respeto y el reco- nocimiento del profesorado de matemáticas como un grupo profesional que puede aportar a la Sociedad su experiencia y conocimiento. A todos, ¡muchas felicidades!. 4 Manuscrito de Pedro Puig Adam Manuscrito de Pedro LOS NÚMEROS MÓRFICOS EN SECUNDARIA A. Redondo MATEMÁTICAS EN LA MÚSICA A. Pastor EL PROBLEMA DE LA RUINA DEL JUGADOR J. Basulto, J.A. Camúñez, Mª D. Pérez TALLER MATEMÁTICO DE COSTURA J. Galarreta, D. Acha, C. Barrio, A.Rodríguez, G. Sáez LAS MATEMÁTICAS DEL IRPF. ¿POR QUÉ GANAMOS MENOS SI GANAMOS MÁS? N. Plasencia, J.A. Pérez artículos 59 Noviembre 2008, pp. 7-16 Los números mórficos en secundaria El número de oro y el número plástico pertenecen a la clase de los números mórficos. En este artículo revisamos algunos aspec- tos históricos, presentamos algunas de sus propiedades y proponemos actividades sobre ellos, que permitirán trabajar transver- salmente Álgebra y Geometría. Usando el lenguaje funcional como modelo de representación, los alumnos podrán conjeturar, de forma intuitiva, un resultado fundamental: Solo existen dos números mórficos, el número de oro y el número plástico. The golden mean and the plastic number belong to the class of morphic numbers. In this paper we recall some historical aspects and we show some properties of them and we present some activities, which will allow us to work transversely Algebra and Geometry. By means of use of the functional language as a representational model, our students will can to conjecture the most fundamental result: There exist only two morphic numbers, namely the golden mean and the plastic number. U na de las manifestaciones más fructíferas de la actividad con el problema de la búsqueda de un “sólido armonioso”. En matemática es la generalización. Cuando generalizamos cons- la segunda intentaremos ir mas lejos... truimos matemáticas, pues definimos y relacionamos con- ceptos, descubrimos propiedades, confirmamos intuicio- Como sabemos que el estudio de la belleza y armonía en las nes,… y tanto en el “resultado
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