kasprzyckiart presents

In The Geometry Of Form

Remember how the geometrical "unit" was portrayed in classical
geometry? Depending on its power, it is either a line of unit length; a
square area with unit edge-lengths; or, a cube having one unit volume
and edges one unit in length. One of the problems with this rendering of
the three powers of the unit is that the line and area forms have no
capabilities for meaningful modeling in a three-dimensional space frame
(the line having no breath or thickness, the area has no thickness...). My
image, titled "The Fundamental Unit", shows how The Geometry Of Form
beautifully models the three powers of the unit commensurately in a
three-D framework.

          The yellow square dominating the image represents one face of a
cube with a volume equal to 1. Of course this would make its' edge equal
to one; and, each one of its' six faces equal to 1 (with the yellow square
being one of its' six faces). This is identical to the classical expression of
the unit in 3-D. But in the Geometry of Form, the 2nd power of the unit is
modeled by the red cube, the visible square being but one of its six sides.
And likewise, the lineal unit in The Geometry of Form, is any of the three
smaller tetrahedrons since the combined length of any one of the
tetrahedron's six edges equal 1 unit. Now, all three powers of the "unit"
have "spatial extension" and are compatible with modeling in 3-D space.

          We know geometry likes this modeling because the three forms of
the same unit, its' three powers, are absolutely perfectly commensurate
to one another.Three forms of the first power of the unit, as
tetrahedrons, stacked atop one another delineate the edge or height of
the unit in its' second power form, its' areal expression. Geometry likes
this arrangement. Repeated in "fractal" form, the three larger
tetrahedrons having edges equal to the edges of the red one-areal-unit
cube, together perfectly delineate the height or edge of the one-
volumetric cube.