Volume V. Number 1. April 2015

We present the first number of the fourth 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 1 (Vol. V)
Author: Equipo Editorial
Teaching Experiences

In this paper, the authors present a brief theoretical content on the teaching of students with high abilities and indicate their reflections on the teaching of any discipline in general, and mathematics in particular, that can be done with these students in any educational levels. To do this, they use experience gained by themselves in a private school devoted to teaching these students.

Title: Aprendiendo de al tiempo que enseñando a alumnos de altas capacidades
Authors: Irene Araujo Guijo, María Teresa Fernández Reyes, Juan Núñez Valdés y Fco. Javier Sanz Gil

It tools are immensely helpful when teaching mathematics to UPM engineering and architecture students because of the convenience and speed with which a wide variety of images can be obtained. But, wherefore this need to depict formulas? Is it a student demand? The analysis of knowledge visualization-based learning discussed in this article addresses the following items:

  1. The type of students concerned, born in a cultural age in which the visual component prevails over any other form of communication.
  2. The importance of visualizing mathematical knowledge.
  3. The connection between mathematical concept and students’ immediate realities.
  4. Mathematics as a language for communication between idea and form.
Title: Visualizar el conocimiento
Authors: Ascensión Moratalla, Juana María Sánchez y Mª Agripina Sanz
History of Mathematics

Usually, the proving of an open mathematical problem does not mean metaphorically the closing of a door, but the birth of new theories and fields to research. The Basel Problem meant not only a springboard in the career of a young Leonhard Euler, but the germ of one of the fundamental tools in Number Theory such as the Zeta Function.

Title: Euler y el Problema de Basilea
Author: José Manuel Sánchez Muñoz
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 Police Inspector, Mr.Barreda, who will be able to discover and catch the murderer of an investigated crime with the help of Mathematics.

Title: El Observatorio Astronómico
Authors: Alejandro López, Sergio Rodríguez y Ramón Sost

Traffic Engineering is a part of transportation engineering and civil engineering and it is the planning, design and operation of traffic on the streets, roads and highways, their networks, infrastructure, adjoining land and its relationship with the different modes of transport to get thi safe, efficient and convenient for people and goods.Traffic engineering studies the traffic accidents, these are very low probability events and can be considered rare events. Thus, this paper presents a summary of results from the application of Naive-Poisson model to the Traffic Engineering focused, by estimating traffic accidents, suggestions for improvements in the design of some Spanish roads.

Title: Sucesos raros en Ingeniería de Tráfico
Authors: Francisco Soler Flores, José Ángel Olivas Varela y María Dolores López González

The story of Adam and Eve has served for millennia as the canonical model of a long-term love relationship in the Western culture. Its influence on the design and expectations of individuals about lasting love has been tremendous. Inadvertently or not, romantic couples have tried to follow the pattern of the early fathers of the Bible. However, current data on couple breakup tells a massive failure of the model, which it is not well understood and it poses a substantial problem for society and also for the social sciences. A recent mathematical model has unveiled a mechanism that may explain the intrinsic difficulty to sustain a relationship projected to endure. In this note some ideas of the mathematical model and its implications are explored, in particular, to predict the final outcome of the couple in the model of love of Adam and Eve.

Title: ¿Qué fue de la historia de amor de Adán y Eva?
Author: José Manuel Rey Simó

In the slot machines type Bingo, in which the player bets some money trying to obtain more, there are two problems that must be controlled to satisfy both the trader and player: 1) Having the player on the machine a reasonable amount of time so that the games are neither too short nor too long, discouraging the player and 2) Having a percentage of return around 90-95% for the machine to give benefits. It is desirable to maintain these two items in reasonable figures in the statistical pay cycle, i.e. for a long time interval. But it is more difficult to have these two items under control for short time intervals. The aim of this work is to examine how the percentage of return of the money that a Bingo type machine gives to the players can be controlled by perturbing the price of the extra balls the machine offers.

Title: Una aplicación de las matemáticas al estudio de una máquina electrónica de Bingo
Authors: Raquel Caro Carretero y Javier Rodrigo Hitos
Games and Mathematical Oddities

Through a collection of comic books of the writer and cartoonist Marc Antoine Mathieu, we will discover how mathematics can also be disseminated through the comic. In fact, the visual and playful component of a comic book, make it an exceptional tool to explain mathematics to all kinds of audiences.

Title: Julius Corentin Acquefacques, prisionero de los sueños
Author: Marta Macho Stadler
Cri­tics and Reviews

The Museum Workshop Classroom Mathematics “π-ensa” was born as an educative project that the Educative Innovation Group “Pensamiento Matemático´´ proposed to the Polytechnic University of Madrid (UPM in spanish) with the main objective to approach mathematics to general public. It was opened the last week of September 2014 to mark the Apprentice Engineers Fair organized by UPM. From that date provides a space to enjoy mathematics.’

Title: Aula Taller Museo de las Matemáticas “π-ensa”
Author: Equipo Editorial

Contagious joy of living, I evoke Vicente, a scientist as a musician. Knower of the mathematical aspects of tuning, a studious of the physical techniques of building tools and of their history. Creator of scientific and musical groups. These lines are only an approximative sketch.

Title: Vicente Liern: “El arpa y la luz”
Author: Rosa María Herrera

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