Number 2. April 2012

With this new issue, the journal Pensamiento Matemático celebrates its first year. After this year we have managed to disseminate our publication, which is included in numerous national and international databases. This, together with the enthusiasm with which day after day we try to disseminate mathematics, teaching experiences in this subject and research in all its areas, means that we are receiving numerous contributions from many parts of Spain and Latin America.

Title: Editorial Número 2
Author: Equipo Editorial
Teaching Experiences During the 2010-2011 academic year, the Miguel de Guzmán Chair of the Complutense University of Madrid organized the Seminar on Mathematical Ideas and Visualizations. The material used in this seminar, including the recordings of the sixteen lectures given, was compiled in a DVD whose structure and content are described in this article.
Title: Ideas y Visualizaciones Matemáticas
Author: Antonio Díaz-Cano Ocaña
Mathematical Stories Certain hydraulic problems raised by the engineer Baliani in 1630 culminated in the barometric experiment carried out by the mathematician Torricelli in 1644. The latter, a fervent Galilean, thought of mathematics as the language with which nature speaks to men. With this theoretical support of the world, he performed a physical experiment with which he calibrated the atmospheric pressure and proved the existence of the vacuum.
Title: Historia del Experimento Barométrico
Author: Rosa María Herrera

This article presents a brief biography of María Capdevila D’Oriola, professor of high school mathematics and the first Spanish woman university professor, obtained from the scarce existing written documentation and from conversations with direct relatives.
Title: María Capdevila D’oriola, pionera de la Matemática española
Authors: Juan Núñez Valdés, María Arroyo Castilleja y María Luisa Rodríguez Arévalo

In this article we present an evolutionary journey through the history of Geodesy, with special emphasis on the achievements obtained as well as the people who wrote with golden letters the development of this science.
Title: Introducción histórica a la Geodesia
Author: Miguel J. Sevilla de Lerma

Torricelli considered the calculation of the volume of the acute hyperbolic solid as the best achievement in his work with ‘curved indivisibles’. It was published in the Opera geometrica. It is presented here as a sample of the style of mathematical (geometrical) demonstrations carried out in the 17th century, and for its value as a precursor of infinitesimal calculus. It is a significant example for approaching Torricellian thought.
Title: El sólido hiperbólico agudo
Author: Rosa María Herrera
Mathematical Tales Mi media conjetura muestra la paradoja subyacente en la conjetura de Collatz y en general en muchas conjeturas matemáticas, especialmente en el área de la teoría de números: su enunciado puede ser entendido por un niño, su demostración se resiste a matemáticos de todas las épocas.
Title: Mi media conjetura (basado en un hecho irreal)
Author: Javier Rodrigo Hitos
Investigation In this paper we will model the electricity market auction as a two person game with incomplete information under the assumption that bidders are asymmetric in units production, risk neutral and with unknown values.
We characterize the strictly monotone bayesian Nash equilibrium and we rank a family of auction models which contains the classic models Uniform, Discriminatory and Vickrey auction models.
Title: A Revenue Equivalence Result in a Duopolistic Electricity Market where one of the suppliers has two production units
Authors: Estrella Alonso y Juan A. Tejada

This paper presents two contributions to applied combinatorics, the first one is the equivalence relation of the Ford-Fulkerson, Menger, Köning, Dilworth and Hall Theorems, and also presents a new proof of Hall’s Theorem that serves as an algorithm to detect systems of different representatives, in each section generalities of the mentioned theorems are established and finally the algorithm with its respective justification.
Title: Teorema de Hall y un algoritmo para detectar sistemas de representantes distintos
Author: Edwin Carranza Vargas

An application of generalized least squares data fitting for vector functions to the modeling of Space Geophysics parameters f0 F2 and Dst is presented, with the objective of forecasting them. A model with delay and two algorithms that were created, one for fitting and the other for estimating the covariance matrix, both implemented in MATLAB Version 7.3, are employed.
Title: Mínimos cuadrados generalizados para funciones vectoriales en la Geofísica Espacial
Authors: Jorge Lemagne Pérez y Alexander Calzadilla Méndez

A theoretical and numerical framework to model the foundation of marine offshore structures is presented. The theoretical model is composed by a system of partial differential equations describing coupling between seabed solid skeleton and pore fluids (water, air, oil,…) combined with a system of ordinary differential equations describing the specific constitutive relation of the seabed soil skeleton. Once the theoretical model is described, the finite element numerical procedure to achieve an approximate solution of the governing equations is outlined. In order to validate the proposed theoretical and numerical framework the seaward tilt mechanism induced by the action of breaking waves over a vertical breakwater is numerically reproduced. The results numerically attained are in agreement with the main conclusions drawn from the literature associated with this failure mechanism.
Title: Mathematical and Numerical Modeling in Maritime Geomechanics
Authors: Miguel Martín Stickle, Manuel Pastor y Paola Dutto
Games and Mathematical Oddities Henry Ernest Dudeney (1857-1930) was an English author, known for the mathematical challenges and puzzles that he published throughout his life in different magazines and that have been later compiled in different books. Some of his more than 200 challenges have interesting geometric properties that can be explored and shown clearly, using current computer tools. This article presents and analyzes two puzzles (dissections) of great geometric appeal: the transformation of an equilateral triangle into a square, and the transformation of a curious cross into a square.
Title: Triángulos cuadrados y cruces cuadradas: algunos puzzles geométricos de H. E. Dudeney
Author: Francisco Pérez Arribas
Critics and Reviews The editorial team wanted to review this book, even though it does not have mathematical content, because they consider that quality scientific dissemination is very important and necessary.
Title: La Puerta de Los Tres Cerrojos (Una Aventura Cuántica) – Sonia Fernández Vidal
Author: Equipo Editorial

The CD-ROM “Dynamic Modeling in Mathematics. Uses of GeoGebra” is a material intended for teachers of Mathematics in Secondary Education and High School. It consists of eleven different projects on mathematical modeling, in which, using GeoGebra software, mathematical problems based on real-world situations are solved.
Title: Modelizaciones Dinámicas en Matemáticas. Usos del Geogebra
Author: Isabel Álvarez García-Mon
Interviews In this article we present an interview with Juan Tarrés Freixenet, to review his professional and vital trajectory on the occasion of his retirement.
Title: Juan Tarrés Freixenet, Profesor Titular de la Universidad Complutense de Madrid
Author: Equipo Editorial


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