Pieces of Pi

Oil, acrylic, charcoal, and Galkyd on canvas

12" x 12" (each)

2008

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This triptych shows fractions of pies over fractions of pi.  Or rather, fractions of 2*pi.  

The first piece is called "Pie for Three" and it shows 4*pi/3 written out in decimal form to about 35 digits in the background.  The pie is missing one third.

The second piece, "Pie," has 2*pi in approximate decimal form and shows a full pie.

The third piece, "Pie for 8," has pi/4 in approximate decimal form and shows an eighth of a pie.

Though it doesn't photograph well, each pie has a thick coating of dripped Galkyd over the red part, making it look like pie filling.

27 is Not a Prime Number

Oil and conte crayon on masonite

36" x 42"

2008

$500

This piece includes the ordered numbers 1 through 90 with the prime numbers highlighted in white.  There is an abstracted rock wall superimposed over the number line.  The piece speaks to the unpredictable nature of the occurrence of primes and relates it to the unpredictability of natural forces. 

Beta Birds

Oil, acrylic, charcoal, and conte on canvas

24" x 30"

2008

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This piece substitutes birds on a wire for gammas and betas in an equation.

Mathematics of Aesthetics

Oil, acrylic, charcoal, conte, and ink on canvas

32" x 45"

2007

$200

There is an essay called "The Mathematics of Aesthetics" by George David Birkhoff.  The essay asserts that aesthetic mass is order over complexity, and that the  more aesthetic mass something has, the more beautiful it is.  This piece is a reaction to that formula, and actually to all formulas for what is beautiful and what isn't.  

When I first discovered the essay, I was determined to make a painting which maximized aesthetic mass according to the equation.  But when I thought about how to maximize order and minimize complexity visually, I ended up with an image that I found incredibly boring.  This piece shows the space that I was working in while studying the essay.  The blank book and the clean equations contrast with the disorder of the studio, but I think both look beautiful in their opposition.

2.3-D

Oil, graphite, and collage on masonite

24" x 48"

2008

$150

This piece is about transformations between 2 and 3 dimensions.  The maps collaged into the background show a 2-D representation of a 3-D world.  Paper airplanes show how a 3-D object can be created from a 2-D one.  Some of the paper airplanes in this piece are painted (another 2-D representation of 3 dimensions) and some are made out of maps and attached.

The ways that objects and properties change when transferred between spaces of different dimensions is under constant scrutiny by mathematicians.  By studying the changes between 2 and 3 dimensions, they can often infer how changes in higher level dimensions may act.  In this way, they are able to study spaces that cannot be comprehended without math.  

Pythagorean Theorem Series-Part II (Pieces 5-8)

Pythagorean Theorem V: Moving Up
Oil, mylar, nails, fishing line, and wire on board
11" x 11"
2008
$150

Pythagorean Theorem VI: You Too?
Oil, mylar, nails, fishing line, and wire on board
11" x 11"
2008
$150

Pythagorean Theorem VII: Close
Oil, mylar, nails, fishing line, and wire on board
11" x 11"
2008
$150

Pythagorean Theorem VIII: Q.E.D.
Oil, mylar, nails, fishing line, and wire on board
11" x 11"
2008
$150

Pythagorean Theorem Series - Part I (Pieces 1-4)

Pythagorean Theorem I: The Set Up
Oil, mylar, nails, fishing line, and wire on board
11" x 11"
2008
$150



Pythagorean Theorem II: First Steps
Oil, mylar, nails, fishing line, and wire on board
11" x 11"
2008
$150



Pythagorean Theorem III: Shadow of My Former Self
Oil, mylar, nails, fishing line, and wire on board
11" x 11"
2008
$150



Pythagorean Theorem IV: Self Aware
Oil, mylar, nails, fishing line, and wire on board
11" x 11"
2008
$150


The Pythagorean Theorem Series shows the geometric proof of the Pythagorean Theorem (a^2 + b^2 = c^2) in eight steps. The proof begins with two squares; one has sides of length a and the other has sides of length b. These two squares have areas of a^2 and b^2, respectively, and the proof essentially manipulates these areas until we see that when they are combined, they equal the area of a third square with sides of length c and area c^2. The proof manipulates the areas of the squares by cutting them into triangles, so you'll see triangles in most of the works. Circles are also visible to show the equality or inequality of certain lengths. The coordinate axes appear so that viewers can orient the shapes, and other geometric shapes that I found important to the proof are painted in high gloss.

To me, the way that the proof maneuvered the areas of the triangles seemed to relate to cross culturalism- the triangles looked different, they interacted differently, but they essentially were all triangles of the same area (area as a basic element of their identity, and area as in the space that they live). Furthermore, after being translated (in a non-mathematical sense) all over the place, they achieved unity and accomplished a profound goal! It's a pretty cheesy personification, but the analogy inspired me...

I related the two ideas by illustrating each step of the proof with a stage of life that seems fairly universal. The first stage is being a fragile infant, the second is as a young child gaining independence, third is realization of growth and impending maturity, fourth is the self aware feeling that comes with the physical ability to reproduce, fifth is "striking out to seek your fortune" or to have a role in society, sixth is the desire to find others similar to yourself and to bond with them, seventh is to forge loving relationships, and last is to restart the cycle. (The last four images will be in next week's post!) The title of each piece refers to the life stage that is illustrated as well as to the actual movement of the triangles in the proof. For example, in Shadow of My Former Self, the triangles have been elongated so that they look like shadows of the two original triangles, but the title also refers to the feeling of having left one's childhood.

Limits

Charcoal, conte crayon, and oil on masonite

52" x 47"

2006

$550

In math, a function is said to have a limit as it approaches infinity if it yields the same value regardless of the way the input approaches infinity. The boxes in this piece represent that notion. They represent views from different perspectives and their sides converge in unexpected ways, yet they all show the same blue on the far side.

My initial sketch for this piece consisted solely of boxes; there was no portrait involved. Upon painting it, however, I realized that the boxes alone didn’t make for a very interesting piece. I added the portrait in a moment of frustration, thinking that I would just forego the box idea completely and turn the whole piece into a sour looking self portrait. When I returned to the studio, I decided to merge the two images, and I eventually ended up with a portrait painted within the boxes.

I feel that the portrait represents a limit in a human sense - It came about as a response to having reached a limit, and it’s confined within certain boundaries. This piece ended up being a representation of a mathematical limit with a representation of a human limit superimposed on top of it.

Optimization

Ink, charcoal, gesso, and graphite on paper

14" x 34"

2007

$150

Soap bubbles are used in mathematics to represent the container of minimal surface area which encloses a specific volume.  Given two volumes to be enclosed separately in a single container, the double bubble (think of two bubbles joined together) is the container of minimal surface area.  Of course, the more volumes one is given, the more complex the problem gets, but the imagery of intersecting bubbles spawned this piece.  

Undetermined Coefficients

Oil & charcoal on canvas

36" x 48"

2006

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This was the first of many ventures into using concrete mathematic imagery in my work.  This piece uses the solving of a first order differential equation as a backdrop.  The concept behind this piece is that numbers are symbols defined by what surrounds them.  I represented this by painting the space between the numbers rather than the numbers themselves.