The emphasis on imagination is important, because Euclid wanted his mathematicians to think, to massage
their brains with possibilities.
For more about Euclid and some of his creative mathematical and philosophical buddies, Plato, and
Pythagoras, see Using and Understanding Mathematics: A Quantitative Reasoning Approach (2nd Edition),
by Jeffrey O. Bennett and William L. Briggs, Addison Wesley, 2001, ISBN 0201717115. Even better, try the very
readable Art & Physics: Parallel Visions in Space, Time & Light, by Leonard Shlain,William Morrow & Co, 1991,
ISBN: 0688097529. Shlain proposes that the development of art history actually presaged or coincided with
the evolution of math throughout history, and the connections he creates between two seemingly disparate
skillsets are brilliant.
What Euclid couldn't possibly imagine is the curvature of space/time, which was revealed by Einstein in the
twentieth century. This non-Euclidean geometry states that no line or plane can extend infinitely, because
there are, really, no straight lines except for our straight line of vision that uses the horizon as an orientation.
This horizon line is most useful for us when we create perspective.
You might wonder why Euclid and Einstein are important to our work as web designers. Both men were
mathematicians, but they were also designers. They created their realities, and the world agreed that what
they created was also real for them. Euclid merely crystallized practices used within his cultural space and
historical time. Since that era, architects, landscape artists, sculptors, and other three-dimensional designers
leaned on his principles to create our worlds. His ideas are even more important for typographers, fine artists,
and web designers, among many other two-dimensional artists, because we need his tools to create illusions
of depth, perspective, and proportion, among other visual optics. To learn more about the concepts of
geometry and its creative design processes, visit the
Geometry Junkyard.
Einstein's impact is seen in the works of
Salvador Dali, Man Ray, Pablo Picasso, and Rene Magritte, among
other artists and designers who utilized
surrealist techniques. After viewing some of these works, think about
what these artists might say about our ability to build visual environments with code and light AND
interactivity. Beyond surreal? You bet.
URU is one example that might blow the surrealists away. However,
even in URU, realism sets in when we begin to ponder how to utilize line to create boundaries, elicit emotions,
and direct the viewer's eye from one point to another.
The Element of Line Creates Other Design Elements
The following images illustrate how concepts of point, line, and plane are used to create visual illusions:
Ok, let's look at the first black square. The elements of design are in bold to show the impact of point here.
This simple yellow point represents colour, because it's a different hue from the background. It also creates
volume, because the point appears to either jut out from the background, or create a "light at the end of
the tunnel" effect. Value is represented by the lightness and darkness illustrated between the point and the
background. Space is represented by the lone point in the vast sea of black, or an element within an
element because this is a portion of line in space. Does it create texture or movement?