Geometer's Workbench: An active blackboard for geometrical exploration
The Geometer's Workbench is a digital blackboard used by mathematician to explain and explore aspect of differential geometry. It provides a new visual interface for Mathematica, which combines the casual interaction mode of a classical blackboard with the power of mathematical manipulation and graphic display. It uses FlowMenu, a new style of interaction that smoothly integrate noun selection, verb selection and parameter entry.
The mathematical workspace is divided into three sections. On the left is a 2D patch representing the mapping domain, on which the user can draw freely or select among a menu of simple forms such as circles, triangles, and rectangles. In the middle segment a user selects the mapping function and specifies parameters, using a technique of small multiples. On the right is a shaded 3-Dimensional model of the surface for the range of the mapping, produced by Mathematica.