Volume IX. Number 2. October 2019

This number of the “Mathematical Thinking” Journal, presents some articles about different aspects related to Mathematics, not only from a formal o theoretical point of view but Maths applied to different areas such as engineering or physics. Some articles were presented to the 55th “Matemáticas Everywhere” Congress, celebrated in the CIEM from Castro Urdiales on the 18th, 19th and 20th of june, 2018.

Title: Créditos editoriales, Índice de artículos y Editorial del Número 2 (Vol. IX)
Author: Equipo Editorial
Investigation This paper presents a simple approach to obtaining a unified polynomial formula accounting for the sums of powers of the first n odd integers, Tk(n) = 1k + 3k + 5k + · · · + (2n − 1)k, where n and k are nonnegative integers. Our polynomial formula for Tk(n) applies to any k ≥ 0, in contrast with other polynomial representations specialized to the case where k is odd or even.
Title: Fórmula polinómica para la suma de potencias de los primeros n enteros positivos impares
Author: José Luis Cereceda Berdiel
Teaching Experiences This work presents an extracurricular experience carried out in Jaranda High School (Jarandilla de la Vera – Cáceres) where an exhibition of an activity of initiation of students to the encryption and decryption of messages is made. The experience highlights the importance of transversability as a methodological tool for content from different pedagogical areas, without undermining its appeal to a completely profane student body.
Title: Iniciación a la Criptología: una actividad extracurricular transversal
Author: José Manuel Sánchez Muñoz

The following paper aims to show a set of educational material that let us to decorate the classroom with maths contents. A small survey, made on secondary school education, get allows obtain conclusions about their preferences. The main advantages are indicated, which have already been analyzed in different methodological studies. The paper ends with a collection of examples and links to start working with them.
Title: Estrategias de motivación con la decoración en el aula de Matemáticas en distintos niveles de Secundaria
Author: Óscar Jesús Falcón Ganfornina
Mathematical Stories Engineering and mathematics have been fed back since its inception. Engineering as the application of scientific knowledge to practical invention and mathematics as scientific knowledge itself. This article is placed in the germ of the development of mathematical physics as a key tool in engineering, through the vibrating string problem, with an end wrapped in “harmonies”.
Title: Ingeniería y Matemática: armonías
Authors: Marco Castrillón López, Omar Gil Álvarez, y María Jesús Vázquez-Gallo

Maryam Mirzakhani’s brief personal contextualized biography and a succint approach to concepts involved in her research, creditor of the first Fields Medal obtained by a woman. The contextualization is done in line with the film Persepolis, and the approach to her work has the support of dynamic objects built with the Surfer software.
Title: Maryam Mirzakhani en Surfer
Author: Xaro Nomdedeu Moreno

The voyage of discovery of October 1492 was one of the most important historical feats of humanity. It is considered that started the historical period called the Modern Age. It was not the individual adventure of a visionary, as some claim, there were necessary men, media, knowledge and scientific-technical preparation, essential to make it possible. This article deals with some considerations about the state of scientific knowledge in which the trip was developed.
Title: Aspectos científicos del viaje del Descubrimiento
Author: Santiago Higuera de Frutos
Games and Mathematical Oddities In this article we will use the properties of the inscribed and circumscribed polygons, to obtain the approximated value of π as limit of a sequence involving the function sin (x). To do this, the perimeter and the area of the polygons inscribed and circumscribed to a circumference are calculated in function on their sides.
Title: El valor de π como límite de perímetros y áreas de polígonos regulares
Authors: Alfredo Olmos Hernández y Reyna Romyna Olmos Hernández

This paper presents an alternative way to find the singular solution of Clairaut ́s differential equation, using algebraic reasoning. With this method the solution is given in implicit form, avoiding the resolution by removing the parameter that appears in the system of parametric equations that results when this equation is solved by the classical method.
Title: Ecuación de Clairaut, un desarrollo algebraico
Authors: José Albeiro Sánchez Cano y Orlando García Jaimes
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: La aparición de los números de dos cifras
Author: Malena Durán González
Critics and Reviews Writing a review of a book is possibly a useless task, because it is not likely that whoever is tempted to read it will give up due to the contrary opinion, nor will anyone who is not inclined to open the book do so, driven by the opinion of an unknown critic. However, I am here to record my impressions on the work cited in the title, and I do it willingly, that reading and writing are two pleasurable activities.
Title: Crítica del libro “Los crímenes de Alicia” de Guillermo Martínez
Author: Dionisio Pérez Esteban


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