This podcast delves into a fascinating mathematical discovery: a sequence of integrals that initially all equal π starts to diverge slightly after a certain number of iterations. The host illustrates this by likening it to a series of moving averages derived from a rectangular function, where the plateau length gradually diminishes until it vanishes completely at a specific iteration, reflecting the behavior of the integrals. The relationship between these integrals and moving averages hinges on Fourier transforms and convolutions, a link that is conceptually explained with promises of more detailed coverage in a future episode. This connection sheds light on the graceful relationships within seemingly unrelated mathematical ideas. Notably, the number 15 marks the moment when one sequence breaks from its pattern, while 113 indicates the turning point in a modified version of the sequence.
