The present study details an investigation into the provision of opportunities for secondary school students to develop an understanding of visual aesthetics by manipulating a single mathematical curve: the parabola. The study documents the establishment of a robust cross-curricular relationship between Mathematics and Visual Design by providing a pedagogical model for learning that relies on the conduit between the two subject areas being explicitly linked. Although the central concept is the marriage of disparate themes, it was operationalised by the development and delivery of activities sequenced to grow appreciation and understanding of the links between unrelated curricula. While this account aims to foster cross-curricular discourse and action, the product output simultaneously provided avenues for the presentation and exhibition of student work; a gallery of which is included in the study. Documenting the inter-disciplinary approach to learning and teaching has resulted in an exploration of the complexities we employ to discover meaning in a range of contexts not singularly reliant on art or language. A convergence is presented in that mathematical rules unite with the rules of art and design in the attempt to project new concepts into new situations where a space for originality exists. Here, the students have been encouraged to imagine new, effective ways of bringing ideas to form (Richmond, 2009). Naturally, developing explicit appreciation/action situations required critical and creative thinking to coincide with lateral and literal approaches to gaining knowledge and understanding of aesthetics. The study presents a reflexive account of the delivery of coursework entitled The Possibilities of the Parabola, from concept to completion.