Geometric Modeling: An advanced guide to creating models in three dimensions

Geometric patterns, abstracted and idealized from forms in nature, are like an alphabet. Their varied and often beautiful shapes can inform and inspire the architect, the designer, the engineer, the inventor, the student and the artist/scientist. Useful geometric forms (like structures applicable to architecture for instance) can also be discovered through logic, visualization and modeling.

Geometric models provide a unique way to explore many of these patterns - they provide hands-on learning opportunities which cannot be replaced by books and proofs. Structural models provide a demonstration (a different kind of “proof”) that they are in fact stable configurations. Transformable models tend to demonstrate some basic principles of dynamic interactions, useful for understanding how things with moving parts articulate with various levels of constraint (or degrees of freedom). They also allow one to explore multiple geometric shapes with one model.

Spending time with geometric models tends to promote the ability to visualize geometric forms. Said another way, they help to develop spatial intelligence. And they can make learning geometry fun and interesting.

The modeling techniques to follow allow for the creation of various types of structural, static and transformable models, based on concepts of polygons, polyhedra, tensegrity, and generally simple ratios between edge-lengths.

Some of the geometric models and modeling techniques that are presented in this booklet are ideally suited to teaching in mainstream classroom settings. Furthermore, this booklet provides some innovative model categories that are presumed to be completely new to the educational field in general, such as the transformable fractal models and hybrid linear/circular models (model classes developed and explored by the author, who is unaware of any other comparable body of work).

The modeling systems presented herein are the most versatile systems explored to date by the author. The systems were also developed around the idea of low-cost components, so as to be affordable for widespread use. Therefore, it is hoped that this booklet will be appreciated for what it is attempting: to provide new and better ways of teaching and learning.