Quita Brodhead. Whence and Where To. 2000. Oil on canvas. 36-1/4 x 48 inches. Courtesy of Hollis Taggart Galleries, New York, and the Estate of Quita Brodhead I'd like to offer something from the realm of projective geometry, with respect to infinity, that is (believe it or not) very practical.  I have found that projective geometry...

This article was recently written for the Science to Sage International eMagazine. It introduces the work of Frank Chester, artist, sculptor, and geometrician, and explores how the special seven-sided volume with faces of equal area -- the Chestahedron -- relates to the traditional Platonic Solids. Download a high quality PDF here: The New Sacred Geometry...

If you don't know about the discovery of the Chestahedron, a volume with seven faces of equal area, you should check it out at New Forms Technology (shameless plug: I'm the webmaster). I have been experimenting with the form in its sculptural capacity, and have come up with some interesting designs that are featured on...

PDF: Goethean Studies Notebook (40mb) PDF: Higher quality, print version (180mb) This notebook was created as a personal record of the 1999-2000 Goethean Studies program at Rudolf Steiner College. This unique course, conceived of and taught primarily by Dennis Klocek, is still being offered -- it is now called Consciousness Studies. When I took the course,...

A golden section is a geometric form constructed in a particular ratio of 1:1.618... (it's an irrational number that goes on forever without repeating... I like the idea that the golden ratio is irrational).  Technically, the golden section is defined as the relation between two sections (a short and a long) on a line...

A response to the question: "How is chaos theory non-determinant?" This is an interesting question, because I think it might normally be asked in the opposite way: "How is chaos theory DETERMINANT?", because chaos theory is, well, chaotic, so it seems more logical to connect chaos with non-determinancy than with determinancy. So to explore the question that wasn't...

4. I don't understand how the butterfly effect looks like the structures seen in the book...a butterfly looking pattern. The butterfly effect is just the name, slightly arbitrary, of the idea that complex systems exhibit the characteristic by which tiny tiny tiny (infintesimally tiny) changes in one part of the system have the potential (not...

3. And so, there's all this talk about 'deterministic chaotic systems'... What exactly, is the stunning significance of this? I think I get that every shape in nature is ultimately created by patterns of itself within itself, but I'm confused as a biologist or physiologist or biochemist because things like continents are made of...

2. Does the fractal model also work for dynamic, fluid or changing shapes? Yes, in fact this is it's most 'natural home' I think.  The reason is that fractals are about processes, not things, and processes are just that: descriptions of changes, not of things, and changes have a way of, well, being DIFFERENT the...

The following four questions (one per post) were posed in a recent class. My edited responses follow. 1. So I understand that any shape in nature can be converted to a mathematical formula, right? Then you take that formula and plug in the variable related to that shape and feed the answer into the variable...

Trust me, YOU DON'T WANT TO MISS THIS!!! Frank Chester (find out about his initial work here, and read reviews of his work here) has just returned from a very well received presentation of his research on the Chestahedron at Sunbridge College in Spring Valley, New York. Many in the audience expressed disappointment afterwards that...