page_title: Robert Williams (geometer)
section_title: Catenatic Geometry
hierarchical_section_title: Robert Williams (geometer) / Catenatic Geometry and Sacred Geometry / Catenatic Geometry
caption_attribution_description: English: photo of intersecting circles
context_page_description: Robert Edward Williams is an American designer, mathematician, and architect. He is noted for books on the geometry of natural structure, the discovery of a new space-filling polyhedron, the development of theoretical principles of Catenatic Geometry, and the invention of the Ars-Vivant Wild-life Protector System for repopulating the Western Mojave Desert in California, USA with desert tortoises.
context_section_description: Following the lead of mathematicians L. Fejes Tóth and C. A. Rogers, Williams formalized the concepts underlying Catenatic Geometry. In The Kiss Catenatic he expanded the concept of small circles covering a sphere to include interconnected platen circuits that model multi-level linked units of the 3-dimensional matrix chain. He presented examples of the use of Catenatic Geometry in discussions of dark matter and dark energy, red-shift, fundamental forces, discrete units of space, and the expansion of the universe.
caption: Photo of intersecting small circuit boundaries that form the conceptual basis for Catenatic Geometry.
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