A friendly engineer recently sent me a version of Figure 1 below, and asked me to explain the connection between it and the well-known Fibonacci Problem (FP) about calculating a population of rabbits. He knew that Figure 1 was related to the ‘Divine Proportion’ or ‘Golden Ratio’ ϕ ( = ½(√5 - l), which also occurs in the solution to FP, and wondered how such different problems could be related by such a number. (He unfortunately regarded ϕ as 0.618 exactly, thus missing a lot of stuff to arouse curiosity.) I knew of various references that I could recommend, but none covered all the things my engineer mentioned, so I constructed the following mathematical development, leaving the relations with biology and architecture to be explained in the books referenced later, see for example [1]. A matrix approach is used here, and may be new to those readers of the Gazette who may be quite familiar with the other material.