Zeckendorf's Theorem: The Unique Fibonacci Sum

Every positive integer has a unique representation as a sum of non-consecutive Fibonacci numbers, found by a simple greedy algorithm. In this episode we unpack the idea, the key lemma that guarantees uniqueness, a touch of history (Zeckendorf vs. Lekkerkerker), and connections to the golden ratio and real-world applications in coding and computing — plus a quick detour into negative Fibonacci representations.

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