Structural Geometric Topology 

 Welcome to Structural Geometric Topology for Artists

As a mathematical artist of 38 years, my journey has been one of joy and wonder born of a lifelong passion for structure, order, and harmony. When I began, I did not set out to create structural geometric topology, a form of mathematics where geometric components such as points, line segments, polygons, and polyhedra are used to construct topological structures including knots, links, braids, and weaves. Nor did I intend to invent STEAM CAD, a system that optimizes creative diversity, efficiency, and productivity and that can be used to design the mathematics, that inspires my art. That however, is where my path led me. 

If you're curious, I invite you to take a short walk through my art and practice. Along the way, you’ll encounter the systems I created to inspire my work and to make my creativity diverse, efficient, and productive.

Step 1. 

Topological Sculptures and Graphic Art

My works spans four mediums: 3D printed sculptures, paper sculptures, graphic art, and wooden sculptures (Figures 1a-d). They are inspired by structural geometric topology introduced in Step 2.

(Figure 1)

Step 2. 

Structural Geometric Topology

Structural geometric topology is the generative system I use to combine geometric components with topological structures that inspire my art (Figure 2). It is structural in the sense that geometric components like points, lines, polygons, and polyhedra are used to build topological structures such as knots, links, braids, and weaves. 

It is a system created with STEAM CAD introduced in Step 3.  

(Figure 2)

Step 3. 

STEAM CAD

STEAM CAD is the conceptual‑aided design system I developed to enhance my creativity and inspire my art using conceptual design tables — adapted from Leonardo da Vinci.  — to combine disciplines like geometry and topology (Figure 3). 

(Figure 3)

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