Visual Immersive Haptic Mathematics in Shared Virtual Spaces

When teaching subjects richly infused with mathematics, in particular geometry, topology and shape modeling, there is a frequent problem that the learners are not able to “visualize” the attendant theoretical concepts. It is important, therefore, to constantly illustrate the associated theories with practical visual exercises, which are preferably to be done in collaboration with other learners to allow them to discuss possible approaches to the problem and to consult with the instructor, virtually or face-to-face. We have proposed an approach that would allow for solving mathematical problems while being immersed within shared virtual 3D collaborative environments. Only mathematical formulas are used by the learners for immediate interactive definition of geometry, appearance and physical property of the shapes being created in the virtual environment. We target learners and educators who are studying subjects rich in mathematics and geometry, or teaching them at the secondary or tertiary level or doing research on these topics. The process allows the learners to see and feel the geometric meaning of mathematics, thus making it less abstract and more perceptual and tangible. We also see ways of incorporating beneficial uses of immersive virtual environments into traditional courses at Universities which might benefit from 3D visualization.