Fibonacci numerical integration on a sphere

For elementary numerical integration on a sphere, there is a distinct advantage in using an oblique array of integration sampling points based on a chosen pair of successive Fibonacci numbers. The pattern has a familiar appearance of intersecting spirals, avoiding the local anisotropy of a conventional latitude-longitude array. Besides the oblique Fibonacci array, the prescription we give is also based on a non-uniform scaling used for one-dimensional numerical integration, and indeed achieves the same order of accuracy as for one dimension: error ∼N-6 for N points. This benefit of Fibonacci is not shared by domains of integration with boundaries (e.g., a square, for which it was originally proposed); with non-uniform scaling the error goes as N-3, with or without Fibonacci. For experimental measurements over a sphere our prescription is realized by a non-uniform Fibonacci array of weighted sampling points