Beauty, which plays a central role in the practice of mathematics (Sinclair 2002), is almost absent in discussions of school mathematics (Dreyfus and Eisenberg 1986). This is problematic, because students will decide whether or not to continue their studies in mathematics without having an accurate picture of what the subject is about. In order to have a discussion about how to introduce beauty into the school mathematics curriculum, we need to have a clear idea about what beauty means. That is the aim of this study, with a focus on characterising beauty in mathematical proof. In this report we explore one particular metaphor for beauty, namely, beauty as fit. We focus on the Pythagorean theorem, providing two proofs, one that we claim fits the theorem and one that does not. This study provides some first steps towards exploring the metaphor of fit in mathematics. Many questions remain. Are there many types of fit? Does fit give rise to the sensation of beauty, or does it just accompany it? Is fit an objective quality or a subjective one? And what role could fit play in teaching? These are a few of the questions that are central to our ongoing work.