LUMS Math Circle Holds Möbius Strips Session
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LUMS Math Circle, first launched in 2021 by Dr. Imran Anwar, Chair and Associate Professor, Department of Mathematics, Syed Babar Ali School of Science and Engineering (SBASSE), LUMS, aims to create a space where students can learn, practice and hone their understanding of mathematical sciences.
The recent Möbius Strip session, held on October 27, 2023, was graced by the presence of the esteemed visiting foreign faculty, Professor Abdelghani Zeghib, National Centre for Scientific Research (CNRS), and the ever-enthusiastic Dr. Waqas Ali Azhar, an Adjunct Faculty member at SBASSE. Professor Zeghib, a distinguished researcher known for his close association with the Preparatory School in Algeria, a training ground for gifted students in Olympiads and mathematical endeavours, brought a unique and enlightening perspective to the session.
The exploration commenced with the intriguing concept of dimensions. Professor Ghani initiated the journey by illustrating a line segment, extending it to a complete line on the board and posing a fascinating question: Can one traverse from the segment to the outer line without touching the endpoints of the segment? Initially, the unanimous response was "No." However, the brilliance of a student's suggestion to leap over one of the endpoints cracked open the door to a profound discussion on dimensions. Professor Ghani explained that to achieve this feat, an extra dimension was required, introducing the audience to the world of two dimensions.
Continuing on this enthralling path, Professor Ghani drew a 2D square on the board and posed another question: Could one move from inside the square to its outside without touching the boundary? This time, students, having encountered similar scenarios before, confidently responded, "Yes, but we need one more dimension." This experience provided an intuitive understanding of the concept of dimensions.
The session continued with an exploration of how a line can divide a plane into two components. Dr. Waqas introduced the concept of glueing in mathematics, explaining that equivalent points on an object can be identified and then glued together to create a new object. He elucidated how removing one point from the line segment separates it into two components, whereas the same isn't true for a circle. This intriguing property of glued objects continued to captivate the students.
The session progressed with the construction of the Möbius strip, achieved by twisting and glueing opposite sides of a rectangle. A moment of cinematic joy occurred as the room briefly plunged into darkness, with a clip from Avengers: End Game being shown, featuring Tony Stark working on time travel while modelling our universe as a Möbius strip.
The instructors then guided the participants through a hands-on activity, where they crafted cylinders and Möbius strips using paper and cut them along the centre lines, revealing surprising outcomes.
The session concluded on a high note, with Professor Zeghib receiving a memento from Dr. Haniya Azam, Assistant Professor, Department of Mathematics, SBASSE and the participants receiving certificates of participation from Professor Ghani.
For updates and information, visit the Math Circle website here.
