Volume XI. Number 2. October 2021

This is the second issue of Volume XI of the 2021 Journal. It seems that we are beginning to see the end of the tunnel generated by the pandemic. This expected end is getting on track thanks to science which, with the vaccine, is allowing us to return little by little to the life to which we are accustomed. Pensamiento Matemático continues its task by publishing interesting papers distributed in its different sections.

Título: Créditos editoriales, Índice de artículos y Editorial del Número 2 (Vol. XI)
Autor: Equipo Editorial

In the present work, besides recreating the history and connections of the Basel problem, we offer a different view of the problem, in its relation with the theory of numbers and probabilities, which could avoid frequent errors related to independence in probability. In addition, we give a new elementary proof that the sum of the inverses of the inverses of the squares of the natural numbers is (π^2)/6. The above results allow an approach to students, even at the intermediate level.

Título: El problema de Basilea: un paradigma para enseñar a través de la resolución de problemas
Autor: Carlos M. Falcón-Rodríguez, Jarlyn J. Díaz Peralta, Ribelly Estrella Salazar y Marileidy Bonilla Núñez

The purpose of this study is to analyze the game statistics in the main European leagues and to see which factors are more determinant in predicting the outcome of a match. To do this we will use multivariate statistical techniques including principal component analysis and logistic regression. The first two principal components explain about 70% of the accuracy obtained when predicting away wins taking the components themselves as predictor variables. This study also shows that in the English league matches are less balanced.

Título: Estadística multivariante aplicada al análisis y predicción de partidos de fútbol en las principales ligas europeas
Autor: Pedro J. Chocano Feito y Elena Castilla González

Landslide cones are a very common form of relief in temperate high mountains, being one of the most representative periglacial and snow processes. In this paper we analyze two landslide cones (Cono A and Cono B) located in the area of “La Vueltona” in Picos de Europa. The scree cones have a dynamic behavior and their evolution has been measured uninterruptedly in the months of August during a period of 10 years (2009-2018) applying the Terrestrial Laser Scanning (TLS) technique. To understand the linear evolution of the two scree cones, profiles have been made following the maximum slope lines of the Digital Elevation Model (DEM) of the year 2009, and these profile lines have been extrapolated for the rest of the measurement years. For the same planimetric position (X, Y) along the profiles, and their altimetric evolution during the years (2009-2017), the position (Z) of those points for the year 2018 has been calculated by statistical methods. This statistical value has been compared with the information from the field data collection for the year 2018. The results of both coordinates (Z), i.e. the real field coordinate and the statistical coordinate, are consistent, within the margin of error inherent to the data collection. As an interpretation of this study, it can be indicated that the behavior of the two landslide cones of La Vueltona has an undulatory dynamic following the line of maximum slope, which allows calculating its evolution in a short period of time by means of statistics.

Título: Aplicación del Láser Escáner Terrestre (TLS) y de modelos matemáticos para la modelización de conos de derrubios en la alta montaña templada.
Autor: José Juan de Sanjosé Blasco, Mariló López-González, Estrella Alonso-Pérez y Enrique Serrano


Teaching Experiences

In the data-driven society of the 21st century, the use of graphical representations is widespread in the media, commercial advertisements, technical and business reports, and scientific research. Although the information in statistical graphs is often considered clear to the intended audience, the literature provides ample evidence that understanding graphs is a complex task.

In a task consisting of reading and interpreting a bar graph with the ordinate axis truncated, most students had difficulty interpreting the content of the graph, reaching only the first of the three levels of Curcio’s taxonomy of graphic comprehension.

Título: Lectura e interpretación de una representación gráfica engañosa
Autor: Carla Santos y Cristina Dias

In this paper we present an activity included in the evaluation of an internship,
whose contents are related to graph theory and its multiple applications to
real problems. We include some statements of the problems delivered, which
demonstrate the learning and skills achieved by the students in this field.

Título: Aprendiendo a modelizar con grafos
Autor: Cristina Jordán Lluch y Esther Sanabria Codesal
History of Mathematics

This article outlines a profile of Newton as a man and as a scientist. In particular, some of his major contributions to the field of mathematics are described.

Título: La sonrisa de Newton
Autor: Danilo Magistrali

This paper presents the results obtained from a literature review of research on the teaching and learning of elements of Fractal Geometry (FG) for secondary education (12 to 17 years of age). It was concluded that it is necessary to work on its adequacy to be teachable, focusing on the intrinsic properties of fractals such as infinite recursion and self-similarity. It is proposed to recover the mathematical essence of this geometry, exploring the possibility of linking it with other knowledge and using forms of validation specific to geometry in high school.

Título: Estado del arte sobre la enseñanza y el aprendizaje de la Geometría Fractal en la escuela secundaria
Autor: María Victoria Artigue, María de los Ángeles Fanaro, Eduardo Lacués
Games and Mathematical Oddities

In this communication we present SudokUrbano, a game that mainly combines mathematics and urban planning, but also includes other disciplines. SudokUrbano is designed for architecture students who have studied, or are studying, mathematics and urban planning. The main advantages of sudokUrbano are: to value interdisciplinarity and transversality between subjects, to promote group work, to allow to practice theoretical concepts of the different subjects, to be a versatile proposal that allows to cover many contents and, above all, to be a game with all that it implies (creativity, fun, participation, motivation, etc.).

Título: SudokUrbano
Autor: Rafael Rivera Herráez, Macarena Trujillo Guillén
Mathematical Tales

In this dramatized story (it can be seen as the libretto of a play), two methods of problem solving are compared: the arithmetic method, which is more intuitive, and the algebraic method, which is more systematic and allows automatic generalization. The synthesis of the two methods is proposed as the ideal way to deal with mathematical problems.

Título: El valor de la x
Autor: Luis Balbuena Castellano
Critics and Reviews

The year 2020 marked the 300th anniversary of the creation of the Royal and Military Academy of Mathematics of Barcelona. Mateo Calabro was the first director and General Jorge Próspero de Verboom its promoter. This Academy is considered a precursor of certain current Military Academies, especially the Academies of Engineers and Artillery of the Army, as well as the Higher Technical Schools of Civil Engineers. This exhibition has been one of the actions carried out for this anniversary.

Título: Exposición 300 aniversario de la Academia de Matemáticas de Barcelona
Autor: Equipo Editorial

On September 6, a new degree program opened its doors to students at the Universidad Politécnica de Madrid. It is the degree in Mathematics at the UPM. We talked to Alejandro Zarzo and Fernando San José, both directors of two of the five Departments of Applied Mathematics of the UPM and president of the conference of directors of mathematics of the UPM and responsible for the coordination of the new degree, respectively.

Título: Alejandro Zarzo y Fernando San José. Grado en Matemáticas por la UPM
Autor: Equipo editorial

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