Analogy formulation and modification in geometry ANALOGY FORMULATION AND MODIFICATION IN GEOMETRY

We assume that the processes of analogy formulation and modification comprise some combination of finding and representing a fruitful source domain, forming appropriate associations, making predictions and inferences, verifying these new ideas, and learning (not necessarily in this order). We argue that these processes are as ubiquitous and fundamental in mathematics as they are elsewhere in empirical science, and therefore ideas in analogy research apply equally to mathematics. As a case study, we explore the origin and evolution of the Descartes–Euler conjecture, and discuss how geometry has developed via analogies which were used to invent and analyse this conjecture.