Securing a
Smooth Transition from 2D to 3D using Dynamic Software
Douglas Butler debutler@argonet.co.uk
iCT Training Centre Oundle School UK
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 dotproduct definition of the 3D plane is the same as a dotproduct 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 moviemakers), 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.autographmath.com
