Volume V. Number 2. October 2015

We present the second number of the fifth volume of the “Mathematical Thinking´´ Journal. It includes some papers framed in the different sections of the Journal. The articles cover a wide range of the Mathematics topics and its applications.

Title: Créditos editoriales, Índice de artículos y Editorial del Número 2 (Vol. V)
Author: Equipo Editorial
Teaching Experiences

Fermat’s room is an interdisciplinary project based on experience, investigation and history of mathematics. It involves a lot of fields and takes us down many paths. It entertains us and motivates us and our students. That was started with the creation of a videogame has converted into a meeting point for teachers and students and is open to the participation of everyone.

Title: La habitación de Fermat: más que un juego…
Authors: José María Gallego, María Filomena Lara, María Azucena Leva, Fco. Javier Martín, Pilar del Pozo y Francisco Ramos

In this article we discuss a model used to introduce the concept of entropy with secondary school students. It can be used to discuss with students the reversibility of time, the tendency towards homogeneity and the link between probability theory and second law of thermodynamics. The model is useful to introduce crucial epistemological issues and helps students to understand the deep connection between the macroscopic and the microscopic.

Title: Un modelo para comprender la entropía
Author: Tommaso Castellani
History of Mathematics

Optimization problems have been studied recurrently since the time of the Greeks. In the beginning these problems arise from purely geometric issues such as the problem of Queen Dido. The demonstration techniques were very ingenious, but specific to each case. With the birth of differential and integral calculus tools to address such problems adopted a more general and analytical nature. However, geometrical thinking encloses results of unquestionable beauty and simplicity. In this article we will address some problems from a purely geometrical point of view, showing interesting demonstration tools, until a curious result related to the orthic triangle.

Title: Algunos problemas de optimización geométrica
Author: Federico Ruiz López

Considering the simultaneous occurrence of events that we consider highly improbable, the so called coincidences, we all get surprised. However the search for the explanation of this occurrence can be made by different approaches. From the standpoint of Diaconis and Mosteller, coincidences are not as unusual as we think. The birthday paradox illustrates the idea that something highly improbable from the individual point of view may, however, occur a considerable amount of times in general. To illustrate the validity of this paradox we will use the birthdays from FIFA´s official squad lists of 2014 World Cup.

Title: Un enfoque probabilístico para las coincidencias: la paradoja del cumpleaños Authors: Carla Santos y Cristina Dias

A counterexample is an example that proves the falsehood of a terms of reference. When the falsehood of an affirmation wants to be demonstrated it is sufficient in spite of finding an example that breaks the affirmation. A theorem needs often from several hypotheses, to understand since they work it is important to be sure of the need of each one of them. In this article we do a tour for some properties and mathematical theorems seeing the need of all the hypotheses.

Title: Contraejemplos en Matemáticas
Author: Antonio Rosales Góngora
Mathematical Stories

This story is the result of an innovative experience carried out with first year students of Polytechnic University of Madrid (UPM) who were attending the course of Calculus. The story is starring a secret agent, 00π who will try to save the world with the help of Mathematics.

Title: Misión Imposible
Authors: Humberto Nava y Mónica Martínez

Artificial Neural Networks, can be of great assistance to port planning. Poor planning, move to not use the resources and facilities available in the environment properly. The research focuses on the analysis of neural network performance in port planning in container terminals and – in particular – in the study of potential traffic growth and needs of facilities needed to move containers forecasted. This can be assessed without the need for new investment in infrastructure or minimum investment in facilities, that traffic can be managed in such terminals or investment grade would be necessary. The methodology indicates the grounds of the artificial neural networks (ANN) application, as well as the different steps for their use in a container terminal planning process, based on the ANN tools provided by the MATLAB software. Finally, it concludes that the proposed methodology tool and can be considered acceptable for this type of planning and forecasting future possible use.

Title: Previsiones de crecimiento y necesidades de infraestructuras en terminales portuarias mediante redes neuronales artificiales
Authors: Tomás Rodríguez García, Nicoletta González Cancelas y Francisco Soler-Flores

In this paper new manners of representing the Hurwitz zeta function in ordinary hypergeometric series is presented.

Title: Representaciones hipergeométricas de la función zeta de Hurwitz
Authors: Anier Soria Lorente, Eduardo Renato Moreno Roque y Raúl Recio Avilés
Games and Mathematical Oddities

We study the probabilities associated to the random choice of $n$ objects by their owners. Poisson´s law shows its accuracy in the description of such a situation.

Title: Una del Oeste
Author: Dionisio Pérez

This experiment is part of a series of lessons for introducing physics to laymen. The idea is that of presenting topics in physics as a kind of show, connecting them to topics in real life, trying to focus on the common principles that are beyond the variety of possible examples. This material can be also used in standard physics course as a way of convincing students that what they study in their course is actually acting in everyday life.

Title: Ciencia de cada día: El hundimiento del Titanic
Authors: Franco Bagnoli y Rosa M. Herrera
Cri­tics and Reviews

In last Volume III, Number 2 in October 2013, this magazine published the article “Laugh with Maths´´ Exhibition in the Teaching Experiences section. In June 2015 it has been published the book “Laugh with Maths´´, Math Comic Strips, which includes the contents of this exhibition extended with theoretical introductions on mathematical topics covered in it. This article makes a presentation of this work which we consider an entertaining, fun and suitable text for all lovers of mathematics and graphics text jokes.

Title: Informe sobre el libro: “Ríete con las Mates”. Viñetas Cómicas Matemáticas
Author: Equipo Editorial

José Ferreirós is a recognized expert in philosophy of mathematical practice, and in a broader sense in Philosophy and History of Mathematics. Professor Ferreirós is expert in some of the best names in Mathematics in the last centuries, such as Riemann, Cantor, Poincaré… His research and reflections on the mathematical experience show us a way forward in our understanding of mathematical thinking.

Title: José Ferreirós: Filósofo de la Matemática
Author: Rosa M. Herrera

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