The period of oscillation of a simple pendulum ($T = 2\pi\sqrt{l/g}$) is a familiar formula to most first-year physics students. However, deriving this expression from first principles requires solving a nonlinear differential equation using the small-angle approximation. From our point of view, this method may seem obscure to students in the early stages of learning calculus and lacking in physical insight. Therefore, we propose an alternative approach to the derivation of this formula that relies on geometry, algebra, and physical intuition. Our method follows the ideas of the founders of calculus, replacing the circular path of the pendulum with a successive collection of infinitesimal inclined planes and summing the travel times along each plane as the number of planes becomes very large. Remarkably, the evaluation of this limit relies solely on geometry, making the approach accessible to any student, even those not yet familiar with calculus techniques.

It is often assumed that quantum mechanics and the theory of relativity were introduced in Mexico only after the Faculty of Sciences was established at the National Autonomous University of Mexico (UNAM) in 1938. In reality, before this, Mexican engineers were already teaching and disseminating these subjects using the limited scientific resources of the time, including the National School of Engineers, the National School of Higher Studies, and the “Antonio Alzate” Scientific Society. Manuel Sandoval Vallarta, a prominent scientist at the Massachusetts Institute of Technology (MIT) and a disciple of the founders of both theories, played a key role in this early dissemination of knowledge. At MIT, he mentored Alfredo Baños — the first director of the UNAM Institute of Physics —and Carlos Graef Fernández, who taught the first formal course on quantum mechanics in Mexico at the Faculty of Sciences. At UNAM, Sandoval Vallarta mentored Marcos Moshinsky, a leading theoretical physicist in Mexico. This paper highlights the introduction of quantum mechanics in Mexico, with Sandoval Vallarta as a central figure. His international standing allowed him to collaborate with leading scientists, promote theoretical physics, and inspire future generations.

Uno de los experimentos más populares en Óptica y Electromagnetismo es el de la medición de la velocidad de la luz, ya que reafirma la teoría electromagnética de Maxwell. Realizar este experimento en un salón de clases es bastante complejo debido a la dificultad para acceder a material adecuado y económico, así como por la falta de información en lo referente a la electrónica necesaria. En este trabajo describimos cómo implementar un sistema electrónico de láser pulsado y receptor rápido para realizar experimentos de medición de velocidad de la luz basados en el método de tiempo de vuelo, utilizando componentes de fácil acceso. El sistema es capaz de generar y detectar pulsos eléctricos y ópticos de $4.5\pm0.1$ns a frecuencias de repetición de decenas KHz, con lo cual fue posible medir una velocidad de la luz en el aire de $v=(2.99\pm0.05)\times10^8$m/s con una desviación menor al $1\%$ respecto del valor oficial, y el cual fue posible montarlo dentro de una longitud de 5m. Este sistema también es capaz de medir la velocidad de la luz en materiales translucidos como el acrílico y agua. Para usuarios sin acceso a herramientas, y/o experiencia, para la construcción de circuitos electrónicos, presentamos una alternativa basada en la plataforma Arduino, la cual permite realizar mediciones comparativas de la velocidad de la luz en materiales, aunque con una precisión limitada.
One of the most popular experiments in Optics and Electromagnetism is the measurement of the speed of light, because it reaffirms Maxwell's electromagnetic theory. Conducting this experiment in a classroom is quite complex due to the difficulty in accessing suitable and affordable materials, as well as the lack of information regarding the necessary electronics. In this work we describe how to implement a pulsed laser and fast receiver electronic system to perform light speed measurement experiments based on the time-of-flight method, using available components. The system is capable of generating and detecting electrical and optical pulses of $4.5\pm0.1$ns at repetition frequencies of tens of KHz, with which it was possible to measure a speed of light in air of $v=(2.99\pm0.05)\times10^8$m/s with a deviation of less than $1\%$ from the official value, and which was possible to implement within a length of 5m. This system is also capable of measuring the speed of light in translucent materials such as acrylic and in water. For users without access to the tools for building electronic circuits, we present an alternative based on the Arduino platform, which allows for comparative measurements of the speed of light in materials, albeit with limited accuracy.

Se presenta el diseño de una interfaz gráfica en Maple como recurso pedagógico para el análisis de integrales triples de tipo I y II en coordenadas rectangulares. La herramienta permite al usuario ingresar de forma sencilla el integrando y los límites de integración, generando como salida representaciones analíticas y gráficas. Entre ellas se incluyen las intersecciones que definen la región de integración, la visualización del sólido en 3D y su proyección en el plano XY, así como la evaluación de la integral. La interfaz ofrece además la opción de remover las caras del sólido, proporcionando una percepción detallada de sus superficies. Esta herramienta constituye un apoyo didáctico que complementa la resolución de problemas presentes en los textos clásicos asociados al cálculo de integrales triples, favoreciendo la comprensión geométrica de los sólidos y el proceso de integración.
We present the design of a graphical interface in Maple as a pedagogical resource for the analysis of type I and II triple integrals in rectangular coordinates. The tool allows the user to easily enter the integrand and the limits of integration, generating analytical and graphical representations as output. These include the intersections that define the region of integration, the visualization of the solid in 3D and its projection onto the XY plane, as well as the evaluation of the integral. The interface also offers the option of removing the faces of the solid, providing a detailed view of its surfaces. This tool is a teaching aid that complements the problem-solving exercises found in classical texts associated with the calculation of triple integrals, promoting a geometric understanding of solids and the integration process.

Presentamos el proyecto educativo de la construcción de un telescopio óptico, que se caracterizó por ser económico, fácil de ensamblar y construido con materiales accesibles para cualquier escuela pública de nivel educativo medio o medio superior. Este proyecto se describe como multidisciplinario, constructivista y en el ámbito STEM, que se adapta fácilmente como proyecto transversal al currículo de educación media superior. El documento presenta los preliminares de su elaboración, optimización y calibración, así como la evaluación del aparato didáctico frente a un grupo de estudiantes quienes lo ensamblaron. Los resultados de la evaluación son positivos en el aprendizaje del tema de telescopio y lentes, así como en la facilidad de armado y materiales para el usuario. Para su uso didáctico, se proponen proyectos STEM con los que el estudiante estimule su creatividad para agregar aditamentos sencillos al telescopio, lo que le permite alcanzar objetivos avanzados como fotografía de animales sin perturbarlos, objetos celestes como el Sol y la Luna, o en paisajismo. Estos retos, y otros que se pueden abordar, van dirigidos tanto al profesor frente a grupo, así como a estudiantes de educación media superior e independientes, y con el objetivo de que hagan suyo el proyecto desarrollando la creatividad basada en física y tecnologías accesibles.
We present the educational project for the construction of an optical telescope, which was characterized by being inexpensive, easy to assemble, and built with materials accessible to any public school at the middle or high school level. This project is described as multidisciplinary, constructivist, and within the STEM field, easily adaptable as a cross-curricular project within the middle school curriculum. The document presents the preliminary stages of its development, optimization, and calibration, as well as the evaluation of the teaching device in front of a group of students who assembled it. The evaluation results are positive in terms of learning about telescopes and lenses, as well as ease of assembly and materials for the user. For educational purposes, STEM projects are proposed that stimulate students' creativity by adding simple attachments to the telescope, allowing them to achieve advanced objectives such as photographing animals without disturbing them, celestial objects like the Sun and Moon, or landscaping. These challenges, and others that can be addressed, are aimed at both teachers in front of groups, as well as middle or high school and independent students, and are intended to encourage them to embrace the project and develop creativity based on physics and accessible technologies.

This paper presents a study of vertical circular motion with friction, modelled by a first-order nonlinear differential equation. It is obtained an analytical solution for the original model, and, additionally, the same problem is solved semi-analytically using the Adomian Decomposition Method. The results are experimentally compared through video analysis using Tracker software, An acceptable agreement between the experiment and the theoretical solutions is reported.

Obtaining exact solutions to the time-dependent Schrödinger equation in complex quantum systems presents significant challenges. In this context, numerical methods offer powerful alternatives for exploring the dynamics of such systems. This work introduces a numerical approach based on the fourth-order Runge-Kutta method, implemented in Python, for the simulation of radiation-matter interaction models. As an example, the methodology is applied to the well-known Jaynes-Cummings model, and the accuracy of the numerical results is verified by comparison with its exact analytical solution. Although only this model is explicitly solved, the same numerical framework can be readily extended to more complex Hamiltonians for which analytical solutions are not available. This makes the approach a practical and accessible tool for studying a wide range of quantum systems.

We present two examples where the Schrödinger equation admits R -separable solutions. In one of them (a particle in a uniform force field) the Schrödinger equation admits separable and R -separable solutions.

Physics learning can be designed with a contextual approach and is relevant to students' daily lives. Physics is very relevant in various fields, one of which is the field of technology. The aim of this research is to create a simulation of the use of video analysis tracker software in kinematics material as an alternative to distance learning. This research uses descriptive methods. The kinematics material that will be discussed in this research includes rectilinear motion, parabolic motion and circular motion. This research uses video analysis tracker software to obtain information from the movement of an object. The results of this research have produced a simulation of the use of video analysis tracker software as an alternative to distance learning. The use of video analysis tracker software can be used to carry out experiments on motion and optical phenomena. From investigative activities, students are able to prove physical theory with the results of investigations or experiments using video analysis tracker software. Researchers suggest that simulations using video analysis tracker software can be applied in classroom learning, especially in kinematics material. The use of video analysis tracker software in the classroom learning process can improve students' problem solving skills and learning independence

SpaceMath v.2.0 with Machine Learning is an extension of the previous version which we implement observables related with LHC Higgs boson data and their projections for the High Luminosity and High Energy Large Hadron Collider. In this version we implemented processes with Flavor-Changing Neutral Currents at tree and one-loop level, namely, i) Radiative decays ℓi → ℓjγ, ii) ℓi → ℓjℓk ￣ℓk decays (ℓi = τ, μ, ℓj, k = μ, e, with ℓi ̸= ℓj ̸= ℓk) and iii) anomalous magnetic dipole
moment of the muon δaμ. SpaceMath v.2.0 is able to find allowed regions for free parameters of
models with both real and complex singlets and real and complex doublets using the processes
previously mentioned within a friendly interface and an intuitive environment in which the user
enters the couplings symbolically, sets parameters and execute Mathematica in the traditional way.
As result, both tables as plots with values and areas agree with experimental data are generated.
We present examples using SpaceMath v.2.0 to analyze the free Two-Higgs Doublet Model of type
III parameter space, step by step, in order to start new users in a fast and efficient way. Finally,
we have implemented in this version of SpaceMath algorithms of Machine Learning to generate
specific Benchmark Points to be used directly in numerical evaluations of calculations of physical
observables.

We show that in the framework of special or general relativity, the invariance of an electromagnetic field (with or without sources) under a one-parameter family of space-time transformations leads to a constant of motion for a charged test particle if the transformations also leave the space-time metric invariant. We also show that if the electromagnetic field and the space-time metric are invariant under a one-parameter family of space-time transformations, then one can find four-potentials that are also invariant under this family of transformations.