A visual approach to proofs and limits
Abstract: In this session, we start with exploring the connections between physics and mathematics via approximations, and then dive into several visual proofs spanning concepts in trigonometry and geometry. We will explore an unusual way to prove the ‘squeeze’ theorem and apply it to a pendulum to solve for the time period (sans calculus!) as well as a geometric derivative. Moving on, we will explore how pictures can encode elegant mathematical proofs, as we uncover clues hidden within pictures. These will range from arc(ane!) tangent identities to three-dimensional solids, as we ponder the question: as we slice out a pyramid from up a prism, we are left with a third of the original volume, but why just a third?
About the Speaker:
Kaushik Basu is an instructor in Mathematics and Physics at the Graduate School of Education, University of California, Berkeley. He designs and teaches enrichment and accelerated summer courses for San Francisco Bay Area students and visiting students from South Korea and Singapore. Additionally, he mentors undergraduate teaching interns pursuing careers in STEM education and supports fellow instructors in curriculum development. Kaushik also teaches physics and art at Proof School in San Francisco, develops workshops for the Pacific Pinball Museum, and is a speaker at the Marin Math Circle.