Volume IX. Number 1. April 2019

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 1 (Vol. IX)
Author: Equipo Editorial
Investigation We discuss how shadows associated to different mathematical classes of black holes are related to evidence in favour of tetradimensional classical General Relativity or in favour of higher dimensional scenaria.
Title: ¿Sombras en la Relatividad General?
Authors: José Rojo Montijano y Mª Carmen Escribano Ródenas

This paper develops a political competition game between two parties. The aim of the game is for each party to attract the greatest possible weight of a weighted set of voters located on the unit circumference.The Nash equilibrium is studied in the proposed game. Firstly, restricted equilibria are employed, and an analysis of which of them will give rise to Nash equilibria carried out. The study of Nash equilibrium raises the definition of a new type of equilibrium: minimum equilibrium. To conclude, necessary and sufficient conditions for the existence of minimum equilibrium positions are given.
Title: Estudio del equilibrio mínimo en un modelo circular de competición política
Authors: Javier Rodrigo, Mariló López y Sagrario Lantarón

In the paper, a review of the criteria that are necessary to identify in decision problem for the investment in a residential property is made. For this, the concept of metric spaces is used for the application of a methodology that provides a ranking of alternatives from measuring the distance of each alternative or possible solution to the ideal solution.
Title: Espacios métricos y métodos de decisión multicriterio
Authors: Belén Muñoz-Medina y Manuel Romana
Teaching Experiences When observing a complex geometric drawing, most people first distinguish two-dimensional figures. And then the three-dimensional figures. Here it is proposed a change in the teaching order of geometry to start with the third dimension. This way we will be able to improve the spatial vision.The Bafi Didactic Cube, with flexible vertices, is a very useful material to recognize and understand volumes, surfaces and lengths. Manipulating this educational resource, some mathematical concepts in which the students have difficulties are clearly visualized.
Title: Innovación educativa con un cubo flexible didáctico
Author: Mª Esperanza Teixidor Cadenas

Mathematics are present in all aspects of our life, but are we aware of it?The proposal is an innovative talk, which in a fun and entertaining way, allows to approach mathematics, to students and the general public, in a visual and attractive way.To achieve this goal, the talk has been designed combining two types of content. On the one hand, historical references on the evolution of mathematics from its origins as a mere tool to count to the current complexity, which makes them essential for the development of scientific knowledge and for the advancement of society. On the other hand the talk focuses on offering a vision of mathematics linked to our daily life based on striking correlations with our daily experiences. Thus, topics such as the link of mathematics with our perception of beauty, the use of statistics to win in games of chance, its importance in the search for love or how is the presence of mathematical patterns in pop music are discussed.Our intention is to awake the curiosity in mathematics, showing to the attendees their most unknown face and discovering the fascinating aspects hidden by this wonderful branch of knowledge.
Title: Math is in the air
Authors: Nerea Casas Bernas y David Ballesteros Álvarez
Mathematical Stories We live today the centenary of Eddington contribution to verify that gravity acts on light trajectories. This change of paradigm is reflected in the circle of ideas that evolves in the “science of vision” that underlies the history of painting.
Title: ¡La luz se curva!
Authors: Mª Carmen Escribano Ródenas, José Rojo Montijano, Juan Tarrés Freixenet y Susana Victoria Rodríguez

The relationship between art and mathematics does not appear evident at first, but the convergence between these two spheres of human culture has been numerous, profound and fruitful throughout history. Mathematics has been described as an art motivated by beauty, and it can be recognized in arts such as music, dance, painting, architecture, sculpture, and fashion. This article focuses, however, on the presence of mathematics in the visual arts.
Title: Matemáticas y Arte: una pincelada
Author: Danilo Magistrali

At present, there is very little presence of women in the list of winners in the different Mathematics Prizes that are granted, both nationally and internationally. It is true that one of them, Maryam Mirzhakani, has achieved the maximum distinction that a mathematician can obtain, the Fields Medal, but, in general, the proportion of women awarded against that of men is very small. This communication supplies an overview of this situation, showing the main existing Mathematical Prizes and short biographies of the women who have obtained them.
Title: Las mujeres y los Premios de Matemáticas
Author: Juan Núñez Valdés

In this survey, an historical journey along some problems of geometric dissections with some kind of paradoxical appearance is made. The principle of concealed distribution, conceived by Martin Gardner, to describing this type of problems is stated and some examples showing the relationship between these apparent geometric paradoxes and generalized Fibonacci sequences in the context of recreational mathematicas are studied.
Title: El principio de disposición engañosa
Author: Pedro Alegría
Games and Mathematical Oddities In this paper we present several challenges whose solutions are closely related to topology. The main idea of this work is to bring the geometry from a different perspective to the traditional one. The way to achieve this goal is through a discipline of the mathematics which, normally, is not in the classroom: the topology.These challenges have been made for a very wide audience. Indeed, the games have been carried out in front of public with different range of age and academic level; from primary to secondary school to university students. The solution we propose for each game is intuitive and for all audiences.
Title: Topología y juegos
Authors: Angélica Benito Sualdea y Susana Merchán Rubira

In this article we study some characteristics of polygonal numbers, which are the positive integers that can be ordered to form a regular polygon.The article ends, showing the relation of the polygonal numbers, with the combinatorial numbers when expressing any polygonal number, as a sum of combinatorial numbers.
Title: Números poligonales como suma de números combinatorios
Author: Alfredo Olmos Hernández
Mathematical Tales This paper shows one of the tales presented to the contest about tales with mathematical content organized by the Innovation Educative Group “Mathematical Thinking” in 2015. The tale introduces the integer numbers in a funny way.
Title: Riñas numéricas
Author: Paula Malara Saludes
Critics and Reviews We present in this communication an interdisciplinary experience in the School of Architecture of Valencia which has taken place in the subject Mathematics 2 of the Degree in Fundamentals of Architecture. The basis of this experience is the binomial function-form. The idea is that students were aware about the offer a wide geometric catalog which mathematics provide, even providing forms which escape our imagination, but we should not confuse this cast of curves and surfaces with the design itself. The function of the design is one of the most important characteristics that limit the use of some or other geometries. Throughout the 2017-2018 academic year we have carried out different activities to work on function and form, the most relevant being the exhibition we made with objects designed from Mathematica. In this communication we comment all these activities.
Title: Objetos con Matemáticas. Función con Forma
Authors: Rafael Rivera Herráez y Macarena Trujillo Guillén
Interview Luigi Montoro is a researcher and professor at the UNICAL. He teaches at University of Calabria, the most powerful university in southern Italy and he is a great researcher in the field of partial differential equations.
Title: Luigi Montoro: “De la ingeniería industrial a la matemática”
Author: Susana Merchán Rubira

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