Happy New Year!
I decided to start 2016 with a big show and the Frank Stella exhibition at the Whitney Museum definitely qualifies as a really big exhibition. When the elevator door opens into the first gallery,the viewer is met by two very different canvases: a large, geometric, consecutive squares painting, and a huge abstract that is exuberant to the point of being Baroque. The dichotomy of these two works highlights the the range of styles and themes explored throughout the galleries. On display are the all black paintings from the late 1950’s, as well as the colorful geometric square-and-shape canvases from the 1960’s. Also included are the wall sculptures from the 1980’s and the more recent work created using 3-D printing.
For the purposes of this entry I decided to concentrate on Stella’s paintings from the 1960’s. These works are clearly about geometry. Some of the artist’s sketches and schematic diagrams are on display as a group. I highly recommend taking a close look at these plans, they really highlight the mathematical processes involved in the paintings.
Stella – “Jasper’s Dilemma” – 1962
The two canvases of “Jasper’s Dilemma” each have the same spiral geometric structure, but the left canvas features a system of the color spectrum, while the right canvas is composed of shades of gray. Stella has built these spirals within the squares by creating two sets of isosceles triangles. The set with vertical bases are slightly larger than the triangles with the horizontal bases. This results in only one diagonal line on each canvas and the four triangles do not all meet at the same point.
Stella – “Empress of India” -1965 – Metallic powder in polymer emulsion on canvas
“Empress of India” is a monumental shaped canvas featuring a series of four V-shaped sections, each featuring a line of reflection symmetry and a 60 degree angle at the point of the “V”. There is also an interesting line of order-2 rotational symmetry running diagonally through the center section of the work.
Both “Jasper’s Dilemma” and “Empress of India” spotlight Frank Stella’s dedication to developing complex geometric structures in his work during the 1960’s.
Keep posted for many more observations on Mathematics and Art in 2016
“Geometrics: Waves, Roads, Etc”, Mary Heilmann’s current solo show at 303 Gallery in Chelsea, features work with an emphasis, as the title suggests, Geometry. My favorite pieces were two shaped canvases, “Geometry Right’ and Geometry Left” both acrylic on canvas from 2015.
Each painting consists of two squares that overlap on a diagonal so that they share a corner quarter square. The top square of each pair is divided horizontally in half to create two congruent rectangles. The top rectangle is bright blue and the bottom rectangle is matte white. The two canvases are displayed in the gallery in a symmetrical fashion. The installation creates a reflection symmetry with the vertical axis of symmetry running midway between the works.
Although I was first drawn to these two canvases because of the geometry they represented. When I stood back to observe their placement in the gallery space, I realized the intriguing perspective of positive and negative space within the parameters of reflection symmetry.
The Andrea Rosen gallery in NYC is exhibiting the work of Matt Keegan. I found two of the powder coated steel wall sculptures of particular interest. These structures originate as folded paper cut-outs that are then fabricated in steel. The type of fold that is used to make the paper forms is called a French fold. To make a French fold you take a sheet of paper and fold it in half. Then without opening the paper you fold it in half again perpendicularly to the first fold. When you unfold the paper you have two types of folds: valley folds, which are concave, and hills folds that are convex.
In the sculptures Untitled (Navy) and Untitled (Neon) the French fold technique creates horizontal valley folds running through the centers. The top portion of each sculpture shows a vertical hill fold through the center, and the bottom half has a vertical valley fold through the center. Disregarding the fold directions both sculptures have two lines of reflection symmetry, vertical and horizontal.
Keegan celebrates the simplicity of the folded and cut paper by transforming the patterns into substantial steel structures .
Dikko Faust is the printer and co-owner of Purgatory Pie Press, a letter press publishing company in Tribeca, Manhattan that he runs together with Esther K. Smith. Faust also teaches a course on Non-Western Art History at the City University of NY. It was his experience in looking at Non-Western patterning that has lead to his recent series of prints called Tesselations. The prints are made by hand setting bits of lead to create the pattern, using only red and black ink. Each patterned print has its own set of distinct symmetries. Today, I will discuss two prints from the series.
The first one is “Tesselation 4 -Nessonis 1: Pyrassos”. Printed on the back of the card is the following descriptive text: “A serving suggestion for a Middle Neolithic stamp seal design found in three sites in Northern Greece”:
Dikko Faust – Nessonis 1: Pyrassos – Hand set block print – 2012
I see this print as a fragment of a wallpaper symmetry, because the repetition in the pattern is based on the symmetries between the shapes. The white figures with the black outlines that resemble a $ or an S and the 8 red squares around them have order 2 rotational symmetry. If you rotate the figure 180 degrees, you have the same figure again. Each of the $ or s shapes has glide reflection symmetry with the upside down $ or S in the rows above and beneath it. In a glide reflection symmetry we see the mirror image of the original shape, but then it is glided or moved along the plane (in this case, along the paper).
The second print is “Tesselation 6- Magnified Basketweave”. The text on the back of the print states “aka Monk’s Cloth or Roman Square Quilt As seen on NYC sewer covers”:
Dikko Faust – Magnified Basketweave – Hand set block print – 2013
This print is a great example of reflection symmetry. It has two lines of symmetry: one horizontal though the center, and one vertical through the center. Another interesting mathematical feature of this print is the similarity between the larger sets of black or red bars and the smaller sets. Two figures are similar if they have the same shape and are only different in size. Both the large set of bars and the small set of bars form two sides of a square: all squares are similar. The inner rectangle of larger bars measure 5 sets by 7 sets. It requires a rectangle of 11 sets by 15 sets of the smaller squares of bars to frame the large rectangle. There is a border with the width of one small square, so after subtracting 1 set from each dimension, we have the inner rectangle of 5 by 7 surrounded by a 10 by 14 rectangle of smaller sets of bars. The ratio of the dimensions of the larger to the smaller is 2:1.
Faust has made a whole series of these striking Tesselation prints. He has been inspired by what he has encountered teaching art history, and what he sees all around him looking at art, and in the case of Tesselation 6, the streets of New York City. The mathematics in these prints go beyond the patterns themselves and connect the viewer with distant times and cultures, and links us all in a visual aesthetic.