Volume XIV. April 2024

This is the number of Mathematical Thought of the year 2024. Very varied articles are presented by authors from different countries that you will find of great interest. The open nature of all applications and works related to Mathematics, as well as the varied origin of the authors who participate in the issue, enriches the contribution of the Journal and is its hallmark.

As usual, the works are distributed in each of the sections of the publication:

Título: Editorial credits, Table of Contents and Editorial of Issue 1 (Vol. XIII)
Autor: Equipo Editorial

This article aims to illustrate the internal computation details of binary classification algorithms using Support Vector Machines (SVM). Specifically, a detailed example of the algorithm’s usage and the precise computation of parameters associated with the training system using a quadratic kernel are presented. The computations and definitions p resented in this work may be of benefit to students of computer science, engineering, mathematics, and anyone interested in learning about artificial intelligence.

Título: A detailed example of binary classification by quadratic kernel and its associated decision function
Autor: Yeisson Alexis Acevedo Agudelo & Oscar Mario Londoño Duque

In this research, we analysed the activities proposed for learning probability in the textbooks of seventh and eighth grade of Basic Education in Chile of two editions (public and private), comparing and categorising them according to their meaning, cognitive demand and context. The qualitative methodology was based on content analysis. The results show the predominance of the classical meaning of probability, procedural tasks with connection and activities without context.

Título: Probability in Chilean mathematics textbooks for 7th and 8th grade of Primary Education
Autor: Matías Beltrán-Rodríguez, María José General-Leiva, Tamara Torres-Aravena & Danilo Díaz-Levicoy
Teaching Experiences

The objective of this work is to analyze the evaluations of a group of students on a data collection and analysis project in a Statistics and Probability course. For this objective, a questionnaire was applied to 34 students of the course. It was obtained that most students reported that the activity helped them improve their knowledge of the subject, the management of the software used, the perception of the importance of statistics and some skills in didactics and research. The article provides evidence that the projects are relevant in learning Statistics.

Título: Student evaluations of an experience about data collection and analysis
Autor: Luis Rojas-Torres
History of Mathematics

Mathematics is distinguished from philosophy and the other sciences fundamentally by the use of rigorous proofs. The demonstration concept makes the difference and gives cohesion as well as timelessness. Our goal is to tell its story and explain its importance.

What distinguishes theoretical mathematics from other disciplines is the chain of reasoning that, following logical rules, leads to certain conclusions. That is why we can trust Euclid’s mathematics of 2300 years ago as much as we believe in today’s mathematics.

Título: Mathematical proof through history
Autor: Antonio Rosales Góngora
Games and Mathematical Oddities

Since 2018 the Universidad Politécnica de Madrid (UPM) has an annual appointment with Pi Day, which is celebrated on March 14 (3/14 in the calendar of Anglo-Saxon countries). In this article, we review the two problems and some questions of the Quiz contest proposed to all UPM students in the 2022 edition.

Título: Celebration of Pi Day 2022 at the UPM
Autor: Pedro M. G. Manchón, Ernesto Nungesser, Andrea Tellini

This work arises from the curiosity to look for relationships between perfect square numbers, understanding that they mold square-shaped areas, which can be joined together and at the same time generate other square areas of greater value, where the sides of those resulting areas may or may not be exact values.

Thus, taking into account the results of the famous Pythagorean theorem, where the resulting square side does have an integer value as its magnitude, it was proposed to look for a similar property by joining more than two squares.

With a very clear mathematical analysis it is possible to establish identities based on integer variables, two of which are then proposed as independent to propose a relationship with the third that would become dependent to propose the identity in the whole numbers.

Then delving somewhat into these identities and their structure it is demonstrated that the Pythagorean ternas arise as results of the ESPERANZA identities and allow us to understand the construction of these ternas in a very simple and orderly way.

It is also observed how manipulating these identities yields striking results of relationships between several perfect square numbers, showing that the characteristics of the numbers will always keep results that will surprise us positively.

This work arises from an individual research developed by the author as a member of the institutional research group EUREKA 4i of the UNAE and is dedicated to my granddaughter Luciana Elisabeth ARAUJO VÁSQUEZ, who just brought hope in difficult times and whose light coincided with finding these results

Título: Hope Identities
Autor: Marco Vinicio Vásquez Bernal
Mathematical Tales

This tale took part of the literary and mathematical contest organized by the Innovation Educative Group “Pensamiento Matemático”. The mathematical content of the tale is centered in two topics: the code theory and the numerical basis (decimal and binary), as a mean to find and defeat a fugitive.

Título: Penal Code
Autor: Celia García Ramírez
Critics and Reviews

AJUST3 de CU3NTOS is an attempt to discover the day-to-day mathematics through stories. It is true that it is not a novelty, several books have been written about it, however this book has a different approach since tries to explain it from the own experience of the authors that is told through stories. Because in AJUST3 de CU3NTOS the main characters are the stories that orbit around mathematical concepts and that are framed in three scenarios: the children’s world, daily life and university life. Stories with the common denominator of bringing mathematics closer to all audiences.

Título: AJUST3 de CU3NTOS
Autor: Rafael Rivera y Macarena Trujillo

This article reviews the books Ilusiones Matemáticas (Mathematical Illusions). It is an informative work published in two volumes, that aims to convey a close and accessible vision of mathematics. Many principles and curiosities related to different branches of mathematics are presented throughout its pages, as well as how they are used to create magic tricks, riddles, puzzles and optical illusions, among other ways of artistic expression.

Título: Mathematical Illusions
Autor: Aurelio Sánchez Estévez

You can download the full issue here:

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