Marriages Made in the Heavens: A Practical Application of Existence
Dan Kalman · Mathematics Magazine · 1999
Existence results are familiar to mathematicians, who understand their theoretical significance. But others, including students, are sometimes perplexed by existence results. What good is it to know something exists, they wonder, when you have no idea how to find it? The ultimate answer depends on some intrinsic appreciation of abstract mathematics-not all of mathematics can or should be justified on the basis of practical application. Still, abstract existence results sometimes have practical consequences, as this paper aims to demonstrate. Though the focus is on existence results, the demonstration itself is constructive: I will describe a problem I worked on in the aerospace industry that made thoroughly practical use of an existence result. Specifically, an existence theorem associated with the marriage problem for bipartite graphs was applied to a satellite communications network, matching orbiting satellites with ground stations. A briefer account, which omits most of the mathematical details, can be found in [2].