Temari balls are mathematical craft objects in which patterns of multicolored thread are wound around a spherical surface to create intriguing, sometimes remarkable patterns. In this paper, we demonstrate an interactive programming system, Math on a Sphere (MoS), that enables users to create and explore temari-like designs on a spherical surface represented on a computer screen. The programming language of MoS is based on the venerable “turtle graphics” elements characteristic of the traditional Logo language; unlike those traditional systems, however, in MoS the turtle does not draw lines on a plane, but on a representation of a sphere. Thus, MoS provides a medium in which to create striking patterns, and at the same time serves as an introduction to fundamental ideas in non-Euclidean geometry. We step through the creation of several temari designs based on the symmetries of Platonic solids, and show how the reader may access and play with the system on the Web. We conclude with a brief discussion of ongoing and future work related to the MoS system.