Recently, four students from Cohort 2021 of Guangdong Technion - Israel Institute of Technology (GTIIT) -- Fang Yiqi, Zeng Xianle, Fan Rongyu and Chen Zhu'an, published an academic paper entitled A Minimization Problem Based on Straight Lines in the international journal The Physics Teacher. Marcelo Fabián Ciappina, Associate Professor of the Department of Physics at GTIIT is the corresponding author of the paper. This article originated from the students who thought of the Brachistochrone curve problem when studying physics class. Since solving the problem requires mathematical knowledge that goes beyond the course content, the approach of "reduction" came up and eventually succeeded.

Have you ever wondered what trajectory an object would take to reach its destination in the shortest time possible when moving frictionless under the influence of gravity? Famous scientists such as Galileo Galilei, Isaac Newton, Gottfried Wilhelm Leibniz and others used to observe and think deeply about this fascinating problem. In this search for the shortest path, the mathematician Johann Bernoulli proposed the brachistochrone curve in 1696, and then, through the efforts of Leonhard Euler and others, the complex and interesting mathematical branch of the calculus of variations was gradually derived, in which the Euler-Lagrange equation gives the ordinary differential equation for solving the fastest path of a frictionless motion under the action of gravity.

"However, the popular solution isn't easily grasped without a solid foundation in advanced mathematics. As we ponder the path for the shortest time of an object moving frictionless under gravity, we bridge the observations of Galileo with modern mathematical tools. Our work presents a simple and elegant solution to this ancient problem, based on straight lines. Without the need of sophisticated tools and using very basic mathematics, taught in a Calculus 2 course, and physics concepts, taught in a Physics 1 course, we were able to find the brachistochrone curve and thus validate the solution obtained using more advanced approaches. Our method holds the promise of being applicable to other minimization problems." This innovative solution not only helps students consolidate relevant kinematics and dynamics concepts, but also leads them into the field of mathematical optimization.

Organized by The American Association of Physics Teachers (AAPT), The Physics Teacher is one of the most influential physics education journals internationally and the only SCI journal in the field of research on basic physics teaching. Focusing on topics such as the teaching of basic physics as well as contemporary physics, applied physics, and the history of physics, the journal is dedicated to enhancing physics teaching and learning at all levels of schooling, including secondary schools and universities, and to providing educators with practical ideas and solutions to improve their teaching methods and to make physics more engaging and comprehensible to students.

Notes of the Team Members

Fang Yiqi (21MCS)

The rigorous mathematics and physics education we received at GTIIT proved indispensable in our comprehension of the research. Armed with this foundation, we were able to discern potential and viable solutions. The application of theoretical knowledge in practical contexts has enriched our grasp of mathematics and physics, facilitating a more effective mastery of these subjects. A key lesson we've learned from this experience is that regardless of one's existing knowledge, there are always suitable projects awaiting exploration. This is a principle that Prof. Marcelo consistently emphasized, encouraging us even when we doubted our abilities to tackle complex problems. The message resonates: anyone can be a scientist as long as they remain curious and persistent in their inquiries. Under Prof. Marcelo's professional guidance, we gained insights into the entire research process—from formulating questions and analyzing problems to discovering solutions, culminating in this publication. This experience has not only enriched our academic journey but also laid a solid foundation for our future pursuits in academia.

Zeng Xianle (21ME)

In this process, I applied the knowledge I have acquired to explore uncharted territories and make my modest contributions. It marked my first experience of the joy of scientific research. Applying theoretical knowledge in practical scenarios has deepened my understanding of mathematics and physics, allowing me to master the subjects more effectively. Prof. Marcelo's rigorous approach to scientific research and his intense passion have left a lasting impression on me. The guidance and teachings regarding scholarly methods and scientific knowledge have been immensely beneficial.

Chen Zhu'an (21BFE)

The professional knowledge, which I learned at GTIIT plays a role for us to understand research. Through teamwork and joint thinking, we could have a wide view for question. And the question could be solved faster.

Marcelo Fabián Ciappina (Associate Professor of GTIIT Physics Department)

From the onset of the project, it was evident that each student approached their responsibilities with a high level of professionalism and a genuine passion for the subject matter. One notable aspect of their exceptional performance was their ability to work seamlessly as a cohesive team. The students exhibited strong communication skills, actively exchanging ideas, providing constructive feedback, and collectively problem-solving to overcome challenges. Their collaborative efforts not only enhanced the overall quality of the project but also fostered a positive and inclusive working environment.

Furthermore, the level of initiative and creativity displayed by them was truly remarkable. They demonstrated a keen ability to think critically, propose innovative solutions, and went above and beyond the project requirements. Their proactive approach and willingness to explore new ideas significantly enriched the project's depth and breadth. Their commitment to excellence, teamwork, and innovative thinking reflects not only their academic prowess but also their readiness to embrace challenges and contribute meaningfully to collaborative endeavors. I am confident that their remarkable achievements in this project foreshadow promising futures as aspiring professionals in their respective fields.

Text/Photos: Marcelo Fabián Ciappina, GTIIT News & Public Affairs