Visual Proofs

LUMS Math Circles session held on May 10, 2024, which delved into the fascinating realm of "Visual Proofs." Facilitated by esteemed mathematicians Dr. Sarmad Abbasi and Dr. Imran Anwar, the session was an enlightening exploration of various theorems demonstrated through visual representations.

Dr. Sarmad Abbasi commenced the session with the renowned Gauss summation trick, captivating the attendees' attention as he unfolded how this trick serves as a gateway to comprehending diverse proofs. Through visual demonstrations, he elucidated how the sum of the first n odd numbers equates to n^2. Witnessing the simplicity and elegance of expressions like 1+3=2^2, 1+3+5=3^2, and beyond, underscored the beauty inherent in mathematical reasoning.

Moreover, Dr. Sarmad elaborated on the unexpected, inevitable, and economical nature of this theorem, echoing G. H. Hardy's assertion that these qualities elevate a theorem to greatness. Such insights provided a deeper appreciation for the mathematical constructs encountered.

One of the session's highlights was the visual "Two cake" proof of the Pythagoras theorem, masterfully presented by both Dr. Sarmad and Dr. Imran. The ingenuity of their approach left attendees in awe, showcasing how visualizations can illuminate complex concepts and foster intuitive understanding.

As the session drew to a close, certificates were distributed to all participants, recognizing their engagement and commitment to exploring the wonders of mathematics.

We extend our heartfelt gratitude to Dr. Sarmad Abbasi and Dr. Imran Anwar for their invaluable contributions in making this Math Circles session a resounding success. Their passion for mathematics and dedication to sharing knowledge are truly commendable.

Lastly, we want to thank each attendee and volunteers for their active participation and enthusiasm throughout the session. Your curiosity and eagerness to learn contribute immensely to the vibrant Math Circles community at LUMS.

Special thanks to Ms. Noreen Sohail and Mr. Qamar Hussain for their continued organizational support. 

Here are some highlights from the event: