Volume I. Number 2. October 2011

In October 2011, the Grupo de Innovación Educativa Pensamiento Matemático published a new issue with a multitude of articles directly oriented to teaching professionals, as well as to our students and the general public. Our goal is to facilitate and support the pedagogical and educational work through content suitable for different levels of demand.

Title: Editorial Número 1
Author: Equipo Editorial
Teaching Experiences This article reports the experience of the Educational Innovation Group (GIE) Mathematical Thinking of the Polytechnic University of Madrid (UPM) in the realization of a Mathematical Gymkhana for the Moncloa campus in the University City of Madrid that took place on September 30, 2011.
Title: Gymkhana Matemática para estudiantes universitarios por la Ciudad Universitaria de Madrid
Authors: Mª Dolores López González y Javier Rodrigo Hitos

The use of new information and communication technologies, commonly known as ICT’s, is currently a fundamental support in our work as teachers. This article is aimed at both teachers and students in the last years of high school and first years of science and engineering careers. The main purpose is to integrate the use of the dynamic geometry software Geogebra with the resolution of practical cases to obtain some famous geometric places.
Title: Visualización de Lugares Geométricos mediante el uso de Software de Geometría Dinámica Geogebra
Author: José Manuel Sánchez Muñoz

The computer as a calculus tool in the application of numerical analysis techniques to find possible solutions to the use of computerized resources. The objective of this research was to develop didactic strategies based on the use of the computer for the teaching of polynomials in the second year of elementary school.
Title: Estrategia Didáctica Lúdica basada en el Computador para Enseñanza de Polinomios en Segundo Año de Educación Básica
Author: María Celeste Urbano
History of Mathematics This article shows a historical evolution of Fractional Calculus, from its merely theoretical and intuitive birth at the end of the 17th century, through the formalists of the 19th century where there was a vertiginous race to establish and define a consistent theory in a definitive way, to the present day, giving an account of the scientific advances achieved by different disciplines due to its application during the 20th century.
Title: Génesis y desarrollo del Cálculo Fraccional
Author: José Manuel Sánchez Muñoz

This article aims to give an overview of what are today considered the first two modern Greek mathematical schools. A review is made of both schools, the Ionian School personified in Thales of Miletus and the Pythagorean School personified in Pythagoras of Samos. Both characters were a reference for other later philosophers and mathematicians.
Title: Las Escuelas Jónica y Pitagórica
Author: José Manuel Sánchez Muñoz

This article aims to offer a vision from the mathematical point of view of the fundamental concepts on which Albert Einstein built his Special Theory of Relativity, which would be published in Annals of Physics, directed by the prestigious physicist Max Planck, in 1905, and which meant a revolution in the scientific community, since it was able to make James Maxwell’s Electromagnetic Theory compatible with Newtonian Classical Mechanics. Later the theory would be polished, making use of the pseudoeuclidean tetradimensional space-time spaces proposed by the German mathematician Hermann Minkowski.
Title: El Álgebra de la Teoría Especial de la Relatividad
Author: José Manuel Sánchez Muñoz

This article aims to give an overview of the discovery of the so-called quaternions by the Irish mathematician William Rowan Hamilton. It is intended to give the reader some details of the birth of the imaginary numbers in the 16th century, their geometrical interpretation in the early 19th century, and the extension of the complex plane to the three dimensions through the quaternions, which would open the way to the study and development of the new non-commutative algebras and a new three-dimensional interpretation of physical reality.
Title: Hamilton y el descubrimiento de los Cuaterniones
Author: José Manuel Sánchez Muñoz

This article offers in its last section, an annotated translation of the memoir that Niels Henrik Abel published in 1824, to demonstrate the impossibility of solving the fifth degree equation by means of radicals (Abel-Ruffini Theorem). In addition, an overview is given of the difficulties he must have suffered throughout his life, always longing for a place of privilege among the scientific community of his time, which systematically denied him the place that the history of mathematics ended up reserving for him.
Title: Abel y la imposibilidad de resolver la “quíntica” por radicales
Author: José Manuel Sánchez Muñoz

In the month of November 1859, during the monthly presentation of the reports of the Berlin Academy, the German Bernhard Riemann presented a paper that would change the future designs of mathematical science. The central theme of his report centered on prime numbers, presenting what today, once Poincaré’s Conjecture has been proved, may be considered the most important open mathematical problem. The present article shows in its third section a translation of this work into Spanish.
Title: Riemann y los Números Primos
Author: José Manuel Sánchez Muñoz
Mathematical Tales The Club de la Señora Matemática metaphorically shows the enormous diversity and richness from the analytical point of view in which functions can be classified, carrying out a brief review of some of the most unique ones.
Title: El Club de la señora Matemática
Author: Javier Rodrigo Hitos

In a technified future in which mathematics has fallen into disuse, a young number enthusiast named Unita is faced with the problem of approximating a fraction by a prettier one. In her search for the solution, she visits the office of a mathematician, a kind of fortune teller with the reputation of a necromancer who offers personal teachings.
Title: Fracciones Bonitas
Authors: Fernando Chamizo Lorente y Dulcinea Raboso Paniagua
Investigation Causality is a fundamental notion in every field of science. Since the times of Aristotle, causal relationships have been a matter of study as a way to generate knowledge and provide for explanations. In this paper I review the notion of causality through different scientific areas such as physics, biology, engineering, etc. In the scientific area, causality is usually seen as a precise relation: the same cause provokes always the same effect. But in the everyday world, the links between cause and effect are frequently imprecise or imperfect in nature. Fuzzy logic offers an adequate framework for dealing with imperfect causality, so a few notions of fuzzy causality are introduced.
Title: Causality in Science
Author: Cristina Puente Águeda

This paper presents the theoretical and numerical bases necessary to analyze the contact phenomenon between deformable bodies. After describing the theoretical model necessary for the correct reproduction of the contact phenomenon between deformable bodies, based on adequate kinematic and constitutive relationships, the fundamental aspects for a correct numerical resolution, through the finite element method, of the associated boundary problems are addressed. To validate the proposed numerical-theoretical framework, it is applied to the soil-structure interaction phenomenon. The numerical results obtained are in agreement with existing experimental data.
Title: Mecánica de contacto de cuerpos deformables. Interacción suelo-estructura
Authors: Miguel Martín Stickle, Pablo de la Fuente y Carlos Oteo
Games and Mathematical Oddities The Tower of Hanoi is one of the most ingenious mathematical discoveries in recreational mathematics. Thanks to an oriental-tinged legend, it is now universally known. This article describes the relations between the solutions of the puzzle and the Hamiltonian cycles in the Qn graphs.

Title: La Torre de Hanói y los Qn Grafos
Author: Mª Milagros Latasa Asso
Texto Solución Q4 Solución Q5

To a greater or lesser extent, we all associate the name Lewis Carrol with literature, especially with children’s literature, with titles such as Alicia in Wonderland, Alicia Through the Looking Glass, or The Hunting of the Snark. But in addition to literary, Lewis Carrol was a man with quite a few concerns around mathematics, logic and philosophical thought. But not everyone is aware of his facet as a creative in the field of games. Rendezvous is one of his most surprising inventions, an intelligence game for all audiences, whose guidelines make it a quite original game.
Title: Rendezvous, un juego de Lewis Carrol
Author: José Manuel Sánchez Muñoz
Critics and Reviews This article reports on a book about prime numbers belonging to the informative collection The world is mathematical. This collection includes other books that will be commented soon.
Title: Los Números Primos. Un largo camino al infinito – Enrique Gracián
Author: Javier Rodrigo Hitos

Bletchley Park is a museum located one hour from London dedicated to cryptography and computer science. It was the headquarters of the British Intelligence Services during World War II, and also where the mathematician Alan Turing worked, designing a computer to read messages encrypted with the Enigma machine.
Title: Bletchley Park, un museo de informática y criptografía
Author: Susana Mataix
Interviews Mariano Soler Dorda is University Professor at the School of Civil Engineering of the Polytechnic University of Madrid and has been teaching Mathematics for more than 35 years. He has just received the award for the best teacher of the past academic year 2010-2011. He is a person committed to the teaching of Mathematics and with great experience in this subject. We have talked with him about the teaching of Mathematics at the University.
Title: Mariano Soler Dorda – Catedrático del Departamento de Matemática e Informática Aplicadas a la Ingeniería Civil de la Universidad Politécnica de Madrid
Author: Equipo Editorial


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