geometry of the parabola, and along with it trigonometry.
The cloth on the table forms saddle shapes, waves, and similar interesting forms. This is a tribute to the non-Euclidean geometry of Lobachevsky and Bolyai. This new geometry has led to geometry beyond three dimensions, which brings back our two planes intersecting at right angles. In the painting, the plane formed by the table top looks like it goes out away from us in space. It doesn't, of course. This is a painting, and what looks like depth is an illusion. What we see of the table top is part of the flat surface of the painting. The same is true of the plane marked out by the three pears. In mathematical models of say, a universe of seven dimensions, two planes can be perpendicular as well as parallel.
This brings us to new theories of the universe, to relativity and string theory. Those theories were built with the geometric concepts that first took form when we worked our way from Euclidean to non-Euclidean geometry. The space we now live in is united with time, and this unitary time/space is malleable, with space wrapping around forms to create gravity, and time which changes in proportion to the speed at which you travel. Our study of the universe continues, as string theory maps the energy that forms the universe we know.
All of this got started with lines planes, triangles. While the painting points to bigger thoughts about cosmic realities, this is still a painting. So you are invited to enjoy the view of some fruit on a table. You are also invited to relax in your place in time/space and contemplate vast realities, such as the way space wraps around you and the earth, keeping you from flying off through the cosmos.
and went with the idea as I continued painting. In particular, I handled the painting of the fabric in ways that fit these ideas.
As a result, the painting is a meditation on the mathematical principals that shape the universe. Here I have a square table, arranged so one of the points is toward us, making it a diamond as well as a square. On top, three pears form a line, and around them three peaches form the points of a triangle. All of this is straightforward Euclidean geometry, which to most is quite familiar.
So, what happens if we add a third dimension? The plane that the pears mark out intersects at right angles with the plane that the table top gives us. If the triangle takes on three dimensions, then it can be a cone, which has the plane intersecting it at an angle. That brings in the
Geometry
One thing to bear in mind as I tell you about my paintings is that I don't plan them ahead of time. I paint a still life, and as I do I sort out my thoughts about the subject of the painting. Out of those thoughts I develop a list of words to point in the direction of my thoughts, map out the texts, and paint the remaining details.
This piece started out from a desire to set up a composition that was different from the arrangements I had been painting in previous works. So I put some fabric on the table, put three pears in a row, and three peaches like three points in a triangle. It was not long before I realized that I had set up an arrangement of compositional elements that summarized geometric theory from points on a line to the most advanced geometries that are in use today. So I adjusted the arrangement of fruit slightly,
Text © 2008 Roberta Morgan, all rights reserved Image © 2002 Roberta Morgan, all rights reserved
On Geometry