Volume IV. Number 2. October 2014

We present the second 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 2 (Vol. IV)
Author: Equipo Editorial
Teaching Experiences

At the time we live in, teachers must consider how the development and the democratization of information technologies can help improve students´ learning. One option is the flipped classroom or reverse class, in which part of the work done in class is done by the student in advance using digital materials among others. After explaining briefly in what this methodology consists of and its background, we discuss our experience in one of our groups and the results and the opinions of the students about the applied methodology. This experience tells us that it has advantages in terms of a deeper learning, to the acquisition of generic skills and student motivation in the classroom but it also has aspects that may hinder its implementation as it requires a lot of preparatory work and planning by teacher and it is not always well accepted by students.

Title: Investigación del impacto en un aula de matemáticas al utilizar flip education
Authors: Cristina Jordán Lluch, María José Pérez Peñalver y Esther Sanabria Codesal

Do you believe that the Earth is a round Planet? Do you believe that number three is bigger than two? If you have said “yes´´ it´s hardly sure that you are right, but, why do you believe it?The Mathematical Science is a beautiful, arbitrary and artificial Human system. And it has become quite useful for data interpretation. The art of Magic is also based on the generation of ideas in the mind of the spectators according to an algorithm that has been previously taught to them. It is obvious that by interpreting the data presented with the algorithm taught, the conclusion, usually called `information´, will be unequivocal. (…)

Title: Magia y Matemáticas: más allá de los trucos
Authors: Carlos Pastor Paz y José María De La Torre Maroto
History of Mathematics

The mean curvature of a surface in a point is defined, for the first time, as the average value between the principal curvatures in Sophie Germain’s memoires. Presented in the Paris Academy of Sciences in 1811, 1813 and 1815 in order to obtain the award proposed by this institution, Sophie Germain won with her last memoire. She began to study elastic surfaces in 1809, motivated by the experiments with vibrating plates conducted by Chladni in Paris. Sophie Germain was self-educated, and passed away at the age of 55 as a result of breast cancer. She managed to both gain the esteem of Lagrange as a mathematician, as well as the appreciation of Gauss, with whom she exchanged several letters concerning these scientific matters.

Title: La curvatura media y Sophie Germain
Authors: Juan Tarrés Freixenet, Mª Carmen Escribano y José Rojo Montijano

Since the notion of mean curvature was first defined in the 19thC, this concept has impacted geometry, physics and mathematical cosmology in a fundamental way.In this paper we study the formation of singularities in the process of a surface moving in space, taking the vector of its mean curvature as its velocity. This flow is useful to illustrate the emergence of singularities such as the big-bang and the black holes in mathematical cosmology.We highlight, moreover, the role that mean curvature plays in some usual inequalities in General Relativity and its relation with the open problem of achieving a quasi-local description of the concept of mass.

Title: Curvatura media y Relatividad General
Authors: José Rojo Montijano, Mª Carmen Escribano y Juan Tarrés Freixenet
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: Dientes de serpiente
Authors: Blanca Martínez Kleiser, Beatriz Pascual Vegas e Irene De La Red García

The main features of complex structures emerging as a result of dynamical processes are reviewed and some examples of such structures are given. A simple mathematical model is used to illustrate some relevant aspects on the genesis and features of complex systems.

Title: Estructuras emergentes y órdenes intermedios: paradigmas para entender la complejidad en la naturaleza… y en la vida
Author: Miguel Ángel Martín Martín

From a basic structural model, defined by quadripartite nerves with cloister curvature and horizontal frame as the base, different numerical simulations are performed by using points discretization , considering the form factor of its geometry , variable. The method used allows confirming that the safety factor resulting from the comparison of the models is optimized when reducing gradually the ratio of the covered area and the volume enclosed by the spatial structure.The model is subjected to the action of permanent and wind loads, with prolonged effect in their quasistatic application. It is performed a behavioral analysis of the supporting structure both in isolation and considering the total loads , determining for every shape configuration the worst requested areas and evaluating prevailing loads. It is also considered when modeling the material cases for carbon steel structure in the lower horizontal part of the base, thus adopting the solution with aluminum metal alloy as glass fiber in the top of the quadripartite nerves.

Title: Evaluación de la influencia del factor de forma de una estructura de nervios cuatripartitos bajo solicitaciones cuasiestáticas
Authors: Juan Manuel Ros García, Roberto Alonso González Lezcano y Susana Hormigos Jiménez

The buildings sector represents 40% of the European Union’s (EU) total energy consumption. Reducing energy consumption in this area is therefore a priority under the “20-20-20” objectives on energy efficiency. The Department of Energy of the U.S.A. has been developing for many years the EnergyPlus : A simulation code to calculate the energy consumption of HVAC system of a buildings. However, the program does not cover items such as an IntelliGlass active window with water chamber. All these reasons make it necessary to develop parallel software to simulate energy systems. The objective of the simulation tool is to explore and to optimize different solutions. The effort to codify all these settings, even in the case of the EnergyPlus, is very large. It is shown a simulation code based on components or abstractions linked through graphs. It is also shown that the effort to simulate a new HVAC system is minimal. The HVAC system is created from a list of components or nodes and a different lists of arcs. These lists are automatically linked to form graphs which are automatically simulated.

Title: Simulador térmico para sistemas de climatización basado en componentes polimórficos conexionados mediante grafos
Authors: Juan A. Hernández Ramos y Fernando del Ama Gonzalo

The hospital emergency services receive a non insignificant proportion of patients who should have been attended in the primary attention services. Planning the emergency services of primary attention for them to improve their quality and to be attractive for the patients can clear the hospital emergencies influencing in an integral way on the whole sanitary emergency service. The reduced wait time is the main factor which the users identify with quality of service. In this article the problem is analysed from a mathematic and computer point of view designing a software which allows obtaining the assignment of doctors to an emergency service of primary attention fulfilling the objective of not surpassing a predetermined wait time as well as optimizing the resources consumption.

Title: Optimización de recursos y calidad de servicio en las consultas de urgencias de un centro de atención primaria
Authors: Sagrario Lantarón Sánchez y Mariló López González
Games and Mathematical Oddities

This work is done in order to understand how Benjamin Franklin, built an array of integers from 1 to 64, obtaining in this structure many curious features that have made this document an object of study, since it is a tribute to the special nature of the numbers.The paper has managed to uncover how it was possible this construction, then it used what has discovered under a process duly systematized to build larger structures that fit in a similar way the characteristics proposed in the original document, and in many cases achieve other interesting ones.

Title: Entendiendo el Cuadrado Matemático de Benjamín Franklin
Author: Marco Vinicio Vásquez Bernal
Cri­tics and Reviews

This paper presents a report of the book “El asesinato de Pitágoras” de Marcos Chicot. It was finalist for the Planeta prize. It is a text where history and fiction are together to offer a story of the Antigua Greece and the pitagoricos. The novel is based on real historical events and it is a combination of intrigue, romance, and action.

Title: Informe sobre el libro: “El Asesinato de Pitágoras´´, Marcos Chicot
Authors: Equipo Editorial

Franco Bagnoli develops his scientific activity as researcher, professor and communicator with a good sense of humor, intelligence, and efficiency. He transmits enthusiasm and interest to anyone who is fortunate enough to approach him. He knows how to combine scientific rigor with clarity of exposition, and his attentive humanity shortens distances. His admirable talent for making that complex things seem affordable attracts audiences of all ages. These notes are intended as an introduction to his exceptional personality.

Title: Franco Bagnoli: El físico cercano
Author: Rosa María Herrera

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