In 1972, Alfred Brousseau, a founding editor of the Fibonacci Quarterly, published an entertaining account of how geometric tilings can be used to generate identities involving Fibonacci numbers. In this article, we explain how there is a hidden formula in each of his tilings, discoverable by consideration of the tiling's geometeric centroid. To demonstrate the utility of this approach, we provide a simple derivation of a new formula for the sum of cubes of the first n Fibonacci numbers.
|Number of pages||8|
|Publication status||Published - 2016|