Volume VIII. Number 2. October 2018

This number of “Mathematical Thinking” Journal, presents some articles about different aspects related to Mathematics, not only from a formal o theorical point view but Maths applied to different areas such as engineering or physics.

Title: Créditos editoriales, Índice de artículos y Editorial del Número 2 (Vol. VIII)
Author: Equipo Editorial
Investigation Collections of objects, understood as groups of objects with its own right, are present all over the world. Despite of the fact that there is no formal mathematical definition of collection, collections are used in many applications of Science. In Computer Sciences, in particular, collections are represented by different data structures with different properties. This paper presents a new taxonomic classification of the most common types of collections organized according to four estructural properties: homogeneity, unity, order and cardinality. Based on this taxonomy we also present a catalog of similarity functions for comparing the different types of collections. This catalog is helpful to identify the most suitable similarity functions to compare two given collections and apply them automatically.
Title: Una nueva taxonomía de colecciones y de funciones de similitud para su comparación
Author: Alfredo Sánchez Alberca

Be-FAST is a computer program based on a time-spatial stochastic spread mathematical model for studying the transmission of infectious livestock diseases within and between farms. Through Monte Carlo methods, different scenarios are generated for disease risk of spread analysis. Livestock epidemics are financially severe damaging in the swine industry worldwide. The program can support epidemiological studies to identify areas at greatest risk and the most important routes of diffusion between farms, to evaluate and optimize the efficiency of control measures and to estimate the health and economic impacts of each scenario. Be-FAST is used here to analyze two diseases that directly affect the livestock industry: classical swine fever in Bulgaria, and foot-and-mouth disease in Peru.
Title: Evaluación del riesgo de propagación de epidemias ganaderas mediante simulación matemática
Authors: Eduardo Fernández-Carrión, Beatriz Martínez-López, Benjamín Ivorra, Ángel Manuel Ramos y José Manuel Sánchez Vizcaíno

Three years ago, leaders around the world adopted the ambitious 2030 Agenda for Sustainable Development, focusing on seventeen Sustainable Development Goals. The Agenda is a shared plan to transform the world in a decade and a half and, fundamentally, to encourage and ensure a dignified life for all. The Reports published for the ONU in the years 2016 and 2017 have served as a starting point for the realization of different quantitative studies. The application of mathematical tools has allowed drawing conclusions more than suggestive from the situation in which countries are, at present, and the measures to be taken to reach the levels of excellence.
Title: Una metodología matemática al servicio de los Objetivos de Desarrollo Sostenible para el 2030
Authors: Gabriela Fernández Barberis, María del Carmen Escribano Ródenas y María del Carmen García Centeno

The main goal of this work is to show some applications of a discrete mathematics result. Through this paper a simple and intuitive proof of Sperner’s Lemma is given. There are many different applications of this result; however, we are going to focus in a real experience of a concrete case. Moreover, we will set the bases in order to extend the use of this Lemma to other fields, as can be business management. The example that we are analyzing in this paper involves fair rent division. In particular, how to assign prices to rooms and those to tenants with a fix rent price. Using Sperner’s Lemma, we will find an objective solution based in the criteria of the tenants without negotiation involved.
Title: Toma de decisiones y el Lema de Sperner
Authors: Susana Merchán Rubira y José Samuel Rodríguez García
Teaching Experiences Our intention in this communication is to tell a story with three protagonists: Mathematics, Modernity and Fallas. Mathematics does not need presentation, although it is possible that after this story we discover a new facet of it. Modernity is our time. And with Fallas we mean the ephemeral monuments that are planted throughout the city of Valencia in mid-March, as a tribute to spring, and are burnt a few days later. What is the relationship between Mathematics, Modernity and Fallas? The objective of our work is to answer this question.
Title: Matemáticas, Modernidad y Fallas
Authors: Rafael Rivera Herráez y Macarena Trujillo Guillén

We present in this paper a methodology for geometric concepts learning in high school students, using the hologram as a tool. To do this, the foundations are first established to make the hologram a means in the teaching-learning process to continue with the description of the development of this methodology.
Title: Uso del holograma como herramienta para trabajar contenidos de geometría en Educación Secundaria
Authors: Lara Orcos Palma, Cristina Jordán Lluch y Ángel Alberto Magreñán Ruiz

It has created an easily replicable system consisting of a set of boxes, one into the other, closed by padlocks, keys, etc. in which clues are hidden. Only the resolution of the previous hint allows access to the next one. To achieve these challenges the students should collaborate promoting, on the way, cooperative learning. Thus, they must decode messages using ancient techniques, solving systems of equations whose solutions will be the key that will open the next lock, match some colors with their respective wavelengths and reveal hidden messages by ultraviolet light, so that progress is made on this knowledge adventure. The maximum available time to reach the goal will be one session- class.
Title: Math Mystery Box: Gamificando el aprendizaje de las matemáticas
Authors: Nerea Casas Bernas, David Ballesteros Álvarez y Egoitz Etxeandia Romero
Mathematical Stories How about if we calculate the sum of the 1000 first powers of 10 natural numbers? That if, with pencil and paper or pen, they were the tools our beloved teacher Bernoulli had in those days. This article discusses some of the key ideas that led him to make such purpose and who were also the origin of numbers that now bear his name: Bernoulli numbers.
Title: Sobre las sumas de Bernoulli
Author: Federico Ruiz López

This paper offers teachers of Secondary Compulsory Education a glossary of the life and work of mathematicians from Extremadura born between the fiftieth and twentieth century, with the objective of using the history of Mathematics as a methodological resource in the classroom. To provide data to be used as models in workshops and panels which can be treated with in the cultural weeks in their centers is also pretended.
Title: Matemáticos extremeños nacidos entre los siglos XV y XIX
Author: Juan Núñez Valdés
Games and Mathematical Oddities In Uruguay, it is common to observe the participation of people in raffles of services or products through social networks such as Facebook, indicating only the last four digits of the identity document number. Is there a person identified unequivocally in this way? If not, how many people have a termination of these characteristics in their identity document number?
Title: La Cédula de Identidad y los sorteos en Facebook
Author: Duberly González Molinari

The members of the Innovative Education Group “Pensamiento Matemático”, participants of the Museum of the Mathematics “π-ensa” are preparing a collection of videos to include in the web page of the Museum. The aim of the videos is to show the relation of sciences such as the engineering and the architecture with the dance. The videos express how to “dance architecture, engineering or mathematics” and give a way to approach the science to the people by means of the dance.
Title: Danza, Ciencia e Ingeniería
Authors: Mariló López y Javier Rodrigo
Mathematical Tales This issue continues with the publication of the awarded tales in the First Mathematical Short Tales Contest “π-ensa” organized by the Mathematics Museum Workshop Classroom “π-ensa” during the 2015-2016 course. This tale awarded a special jury award in the highschool and college student category. All information on the contest is available on the website of the Classroom: http:/innovacioneducativa.upm.es/museomatematicas/
Title: 1993
Author: Rosa Moncayo Cazorla
Critics and Reviews This article presents a review of the film “The Imitation Game” directed by Morten Tyldum. It is a biographical adaptation of British mathematician Alan Turing’s life, father of modern computing and artificial intelligence among other achievements, focusing mainly on the decryption of the German ENIGMA during World War II.
Title: Informe sobre la película “Descifrando Enigma”
Author: José Manuel Sánchez Muñoz
Interview Andrea Guazzini is a psychologist at the University of Florence, his work ranges between complex systems and psychology. So he sets up his original and funny thinking. In our conversation we approach to his interesting vision and his knowledge on Mathematics and Physics inserted in Psychology.
Title: Andrea Guazzini: “Un psicólogo entre teoremas”
Author: Rosa María Herrera


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