Lahore, The LUMS Math Circle, a platform for fostering understanding of mathematical sciences among students, hosted a Möbius Strips session on October 27, emphasizing the concept of dimensions with contributions from esteemed visiting scholars.

According to Lahore University of Management Sciences, the session featured Professor Abdelghani Zeghib from the National Centre for Scientific Research (CNRS) and Dr. Waqas Ali Azhar, an Adjunct Faculty member at LUMS. Professor Zeghib is recognized for his work with the Preparatory School in Algeria, which focuses on training Olympiad-level students.

The event began with Professor Ghani engaging participants with the puzzling nature of dimensions. A simple line segment led to an interactive discussion, encouraging students to think beyond conventional boundaries and consider the role of an additional dimension in traversing from a segment to a line.

This interaction set the tone for further explorations into the complexity of dimensions, with Professor Ghani illustrating with a 2D square and challenging students to think about the transition from the inside to the outside without crossing its boundary. The exercise provided students with a tangible grasp of the concept.

Dr. Waqas introduced the mathematics of glueing, a method of creating new objects by identifying and joining equivalent points. He demonstrated how removing a point from a line segment creates two distinct components, unlike with a circle, fostering a deeper curiosity among students about the properties of geometric shapes.

A practical demonstration of the Möbius strip was the session’s highlight, involving twisting and glueing a rectangle’s ends and a popular culture reference to Avengers: End Game, which showcased the strip as a model of the universe.

Participants engaged in constructing cylinders and Möbius strips and observed the unexpected results of cutting these objects, enhancing their understanding through hands-on experience.

The session concluded with Professor Zeghib being honored with a memento by Dr. Haniya Azam, Assistant Professor at LUMS, and students receiving certificates of participation from Professor Ghani.