FIG. 2.

(Color online) The simple, self-similar geometric movements that Grosseteste describes as the basis for vowel categorization. We have interpreted his categories of simple movements—straight movement, circular movement, and dilating and constricting movement—as the three fundamental classes of linear geometric transformation: translation, rotation, and uniform scaling. Points (shown in black) embedded in planes undergoing these transformations trace out movements that agree well with Grosseteste's descriptions of simple movements, shown in grey. Videos are provided in the online version of this paper.