On the role of kinesthetic thinking in computational geometry

Abstract

Computational geometry is a new (about 30 years) and rapidly growing branch of knowledge in computer science that deals with the analysis and design of algorithms for solving geometric problems. These problems typically arise in computer graphics, image processing, computer vision, robotics, manufacturing, knot theory, polymer physics and molecular biology. Since its inception many of the algorithms proposed for solving geometric problems, published in the literature, have been found to be incorrect. These incorrect algorithms rather than being ‘purely mathematical’ often contain a strong kinesthetic component. This paper explores the relationship between computational geometric thinking and kinesthetic thinking, the effect of the latter on the correctness and efficiency of the resulting algorithms, and their implications for education.