The iconic Flatiron building on 23rd street in Manhattan is home to the Sprint Flatiron Prow Art Space, a bright triangular room of windows, that can be viewed from the sidewalks of both Fifth avenue and Broadway. In coordination with Cheryl McGinnis Gallery, artists fill the space with interesting, temporary projects. This winter, Chelsea Hrynick Browne’s exhibition “Flakes” consists of vertical strings suspended with a multitude paper shapes.
Each two-sided shape is created by cutting and layering pieces origami paper. Browne’s intricate paper cutting relies on Mathematics to create the symmetrical patterns. These two examples each feature order-4 rotational symmetry. The use of contrasting colored papers affords an interesting expression of positive and negative space.
Each of the flakes is two-sided. Some flakes are circular and others are square, but my favorite flakes have 16 sides. These extra special flakes are formed by two back-to-back square paper cuts with a 45 degree rotation.
“Flakes” is a terrific installation for Winter in NYC. Each of the paper cut outs is different and they colorfully beckon to pedestrians navigating the snow and grey slush. I stumbled across this display and it made my whole day better. I am always amazed and happy to be able to find so many great examples of Mathematical art as I go about town.
Glenn Horowitz Bookseller’s gallery Rare is currently showing the work of Sjoerd Hofstra with Karen O’hearn. On display are some of their artist’s books, featuring finely engineered kinetic elements. The subject matter of these books is directly mathematical. “A study in Averages” is a schematic treatise on the relationship between averages and society.
“Elements of Geometry by Euclid” includes pop-ups of the geometric solids. The mathematical texts have been blurred and instructional line drawings have been added.
“6 Empty Bookcases” is more architectural, but each of the bookcases presents interesting geometric 3 dimensional properties as it folds off the page.
What I find refreshing about Hofstra’s and O’hearn’s books is the clear unabashed connection to the mathematics. Whether addressing the societal implications of the use of averages, or creating their own interpretation on the historical Euclidean text, or using sophisticated calculations to build their geometric bookcases, the artists embrace mathematics.
I realize how difficult it is to see the true interactive nature of these books through my inadequate photos. The artists have provided a video link so you can see their work in action.
The use of repetitive geometric patterns is a prevalent theme in abstract art. Lori Ellison’s paintings and drawings celebrate the hand of the artist, featuring a lyrical, hand drawn quality. Through the use of basic geometric shapes Ellison created lively compositions that hum, buzz and pulsate. The current exhibition at the McKenzie Fine Art gallery include small scale paintings on wood panels and drawings on notebook paper. All of this ambitious work was completed the year or so before the artist’s death in 2015.
This gouache on wood panel from 2015 measures 14 x 11 inches. Its compact format holds a profusion of triangles. The almost parallel columns of almost isosceles triangles are packed tightly on the plane. Alternating the the red and pink shapes, all of the red triangles seem to point right and all pink ones point left. This forms an interesting dialogue between positive and negative space.
In this close up of the same panel we can see more clearly that this work is not about the accurate measurement of pure clean geometry. It is some ways more complicated, more human. This is definitely a painting about lines, triangles, positive and negative, but it is also about the artist. The personal scale makes the viewer stand close to the work and be drawn into the patterning. Art can be about mathematics with out having to use a ruler or striving for perfection.
The current exhibition in the North gallery room of the Klein Sun Gallery is called “The Simple Line”. The show features the work of Beijing artist Gao Rong. Each of Gao Rong’s installation pieces is based on a circular hoop framework. Threads are stretched across the circle from evenly placed locations around the circumference. Although the basis of her subject matter is circular, through careful placement of the threads Gao Rong is able to create geometric arrangements featuring straight lines and angles.
This work contains a square grid of nine squares with the center square darkened with the overlapping of many lines of thread. this work at first appears to have two axis of reflection symmetry but this is only superficial. Upon closer inspection we see that some of the corners of the of the squares are much darker than others and taking that into consideration there is an order-2 rotational symmetry.
The next work is based on triangles. Starting at the bottom with single unit isosceles triangle, then moving up the structure, this single unit is overlapped by a triangle with a base twice as long. The next overlapping triangle has a base three times the length of the initial triangle Each subsequent triangle gets larger but also lighter in color. The shape seems to fade into the top of the circular frame.
There are two sets of theoretical juxtapositions in Gao Rong’s work. First and most is obviously the fact that the work illustrates linear structures within a curvilinear environment. Second, there is also the social statement of the use of colored thread, traditionally seen in women’s decorative needle work, to create very structured geometric diagrams that are heavily influenced by Mathematics.
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
The exhibition “LARRY ZOX: Master of Color and Form” is currently on display at the STUX + HALLER located at 57th street in Midtown Manhattan. This neighborhood has a number of blue chip galleries that show the work of established and often historically significant artists. Zox’s acrylic paintings from the late 1960’s are all about hard edge geometry on a flat plane.
“Untitled” from the “Double Gemini Series”, 1969
Picture courtesy of the gallery
This large scale rectangular canvas has adjacent sides in a 2:1, ratio creating a format consisting of two equal squares. From each side of the squares an obtuse isosceles triangle has bee drawn. An obtuse isosceles triangle has two sides and two angles of equal measure, and the third angle measures over over 90 degrees. All Isosceles triangle have a line of reflection symmetry. The triangles with vertical bases have a greater height than the triangles with horizontal bases. This gives the illusion of stretching the plan across the canvas. All but one of the triangles have been painted a different color than the central form. The left central vertical triangle is only defined by a white line outline. This painting is a very important piece, MOMA owns a similar work from this series. It is quite gratifying to be able to enjoy it in an intimate gallery setting.
“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.
Pino Manos’ solo show titled “Synchronicity” is currently on view at the Unix Gallery. His Monochrome paintings feature vertical strips of canvas layered over the stretched canvases, creating three dimensional works that come off the wall. The strips are of varying widths and have a twist. This act of twisting the canvas creates shadows. The work appears to have lighter and darker sections but the works are all actually the same exact tone and shade allover. By changing the width of the strips the twists also vary. The thinner the strip, the more of the strip stays closer to the vertical lines.
In this red canvas the direction of the twist is not uniform resulting in lines that seem to cross. A side way view reveals the both the width of the strips and the vertical length of the each twist.
Involved in the Rigorismo movement in Italy, Pino has created a new type of geometric space on canvas by challenging our preconceived ideas about painting.
This week there are numerous art fairs in NYC that emphasize prints and artist’s books. I am participating in the E/AB fair with the letterpress publisher Purgatory Pie Press. We are exhibiting the first of series of three prints based on my Fibonacci Spiral drawings.
“Fibonacci Spiral 1” – 2015
Using an algorithmic process of folding and tearing double-sided prints, we have made an edition of a book called “Galactic Collision, Fibonacci Spiral”. This book breaks up the spiral patterns into small segments of the curves.
“Galactic Collision” – 2015
Bernard Chauveau Editeur brought some very interesting work from Paris including “Mineral Skin”, a limited edition cut and folded paper sculpture by Arik Levy.
Mineral Skin – 2013
“Mineral Skin” is a single sheet of paper that has been cut and folded to create a surface of pentagons and hexagons.
At the Wingatestudio booth Sebastian Black’s large scale accordion books are on display .
“Period Piece, Simple Sequence” 2014-2015
“Period Piece, Simple Sequence” is a series of two sets of counting books. The first starts with one randomly placed black square on the first page. Each subsequent page has one more square, up to ten squares. The second set begins at eleven square marks and continues up to twenty.
There is a very diverse collection of work at the E/AB fair and I was quite pleased to find some work with mathematical themes.
Currently on display Museum of Modern Art, “Scenes for a New Heritage” is a fresh reinstallation of the Museum’s collection of contemporary art. The first work you encounter as you enter the gallery is On Kawara’s “One Million Years (Past and Future)”. A limited edition Artist Book published in 1999 by Editions Micheline Szwajcer and Michele Didier, Brussels. Situated on a white pedestal in a clear vitrine the book features rows and columns of numerical years in sequence from 998,031 BC to 1.001,992 AD.
As you get close to the vitrine to study the book, a voice reads out the numbers of a year. There is a speaker in the front of the stand. If you stand close to the pedestal another year in consecutive order is read out. The voice on the recording alternates between male and female. The audio recording was produced by the David Zwirner Gallery NY in 2000. This installation at the MOMA is really two works of art, the visual component in the form of a book and a poetic component in the reading of the dates.
On Kawara is very famous for his paintings of single dates on canvas. I feel this installation reflects a deeper connection to Mathematics. The emphasis on the listing of numbers makes the viewer think about how we mark time using digits and order. The act of counting to this huge number of one million creates an extremely emotionally charged audio experience. The number are just as poignant as any other words in expressing the vastness and continuity of time.