Securing a Smooth Transition from 2D to 3D using Dynamic Software

Abstract

Securing a smooth transition from 2D to 3D using dynamic software Douglas Butler iCT Training Centre, Oundle School, Peterborough, UK Douglas.Butler@btinternet.com Autograph now has a comprehensive selection of 2D and 3D coordinate geometry tools available, and this presentation will argue that the transition from 2D to 3D can be made easier if 3D methods are anticipated in 2D. For example the straight line: there are many forms for the straight line, but the vector form commonly used in 3D also works in 2D. The implicit form for a 2D line ax + by = c and its normal vector [a, b], has an immediate parallel with the plane ax + by + cz = d and its normal vector [a, b, c]. This can be nicely illustrated with dynamic objects. Also the dot-product definition of the 3D plane is the same as a dot-product definition of a straight line in 2D. Common transformations in 2D, such as enlargement, rotation (about a point), reflection (in a line) become in 3D: enlargement (often used by movie-makers), rotation (about a line) and reflection (in a plane). The gradient (slope) of a curve in 2D (defined by the tangent and its normal vector) becomes the slope of a surface, defined by the tangent plane and its normal vector. Many school curricula have dropped the study of 3D coordinate geometry on the pretext that it is hard to visualise. This presentation will argue that the tools are available now and that this important topic area should be restored into mainstream mathematics teaching in schools. http://www.autograph-math.com