From Pigeonholes to Frequencies: How the Pigeonhole Principle Powers FFT Efficiency—And Frozen Fruit’s Hidden Math
The Pigeonhole Principle, a cornerstone of combinatorics, states simply yet powerfully: if more than *n* items are placed into *n* or fewer bins, at least one bin must hold multiple items. This idea—though elementary—underpins profound insights in signal processing, especially in the Fast Fourier Transform (FFT). Its elegance lies in turning abstract counting into computational …