Hoggatt sees Fibonacci everywhere. “The piano octave,” he notes with satisfaction, “has eight white keys—five black keys and 13 keys altogether,” all Fibonacci numbers. “I always use ...

Recent explorations of unique geometric worlds reveal perplexing patterns, including the Fibonacci sequence and the golden ratio.

Each number is the sum of the two preceding numbers. Fibonacci’s writings also include a wide variety of astute observations on numbers patterns and important results in number theory.