Cartesian Lace Drawings

The past few months I have been developing a new type of drawing process based on Set Theory and the concept of mapping. Using the Cartesian coordinate system, I started by plotting sets of points on the x, y and z axes. To create a visual metaphor for the 4th dimension, I added one more axis perpendicular to the z axis. Using different mapping procedures I connect points from one axis to point on another. I utilize bijective (one point to one point) mapping, as well as non-bijective (one point to many points ) mapping patterns.

These new drawings use mathematics to create intricate patterns that relate to technological network maps, neurological phenomena, but also to hand-made lace.
Susan Happersett

The Armory Show

The largest of all of the Art Fairs in New York City last week was the Armory Show that was on two huge piers (92 and 94) on the Hudson river. A wide  range of work was exhibited, I have just chosen a sampling of more recent work with Mathematical themes.

Bernar Venet, “11 Acute Unequal Angles”, 2015
Courtesy of Paul Kasmin Gallery

I was still in line to check my coat when I spotted Bernar Venet’s  steel sculptures across the aisle. The title of the work above, “11 Acute Unequal Angles”, is a perfect description of the geometric theme of the work. It is always exciting to see work that so directly embraces the mathematics.

Shannon Bool, “Untitled”, 2017
Courtesy of Daniel Faria Gallery

This next work, by Shannon Bool, is a large- scale oil and batik on silk. The fabric is slightly transparent and backed with a mirror which creates an interesting repetition of the design, as well as a slight ghost of the reflection of the viewer. Through the use of grids and diagonals, there is a reference to the geometry of architecture.

Brandon Lattu, “Columns, White, Natural Progression”, 2016
Courtesy of Koenig & Clinton Gallery

This eight foot tall painted plywood column by Brandon Lattu consists of 12 stacked prisms. Each prism has a regular polygon as its base. The top form has is triangular, the second is square. The third one has a pentagonal base, and so on. Each subsequent prism has bases with one extra side. The prisms are stacked in such a way that a vertex from each prism lines up to create a vertical line.

Brandon Lattu, “Columns, White, Natural Progression”, 2016 (detail)
Courtesy of Koenig & Clinton Gallery

When you walk around the structure you can see the different angles. This work is a great visual example of a numeric progression in terms of the number of sides in each section. It also compares the different angles found in regular polygons.

Jim Iserman, “Untitled” , 2013-2014
Courtesy of The Breeder Gallery

Jim Iserman’s acrylic painting is a pulsating homage to hexagons. This work is made like a tiling. Each hexagon is created using three rhombi. By situating the yellow bands to meet at the center, Iserman creates a Y-pattern. The forms take on the presence of cubes jumping off the surface.

Jim Iserman, “Untitled” , 2013-2014 (detail)
Courtesy of The Breeder Gallery

The Armory show is an overwhelming experience. It takes hours to even get a superficial overview. There were a myriad of other works of art that relate to mathematics at this venue. It was difficult to chose just a few.

Susan Happersett

Art on Paper Fair

It is the first week of March, time for galleries from all over the world to display art at one of the half dozen large fairs in New York City. Since a lot of my own work involves paper, it makes sense that my first stop this year was the Art on Paper Fair. Here is just a quick overview of some of the work I thought had interesting mathematical connections.

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As you walk into the large venue, you are greeted by Tahiti Pehrson‘s three monumental paper towers titled “The Fates” , presented by Art at Viacom.
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This closer look shows the intricate paper cuts. Pehrson has used the Fibonacci sequence – obviously a favorite of mine – to develop a pattern of concentric circles.
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I found these two watercolor and pencil in the Cindy Lisica Gallery booth. They are the work of Chun Hui Pak. The top painting is titled “Iris Fold Watercolor 19”, the bottom painting is titled “Iris Fold Watercolor 13”. These works are 2-dimensional representations of a 3-dimensional origami sculptures. The square format is placed on a diagonal, emphasizing the order-4 rotational symmetry of the form. The geometry of origami folding is of great interest to mathematicians using shading techniques. Chun Hui Pak has given us a type of portrait of the paper folding.
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Anita Groener has made a series of pen and ink drawings that incorporate grid  structures. The Gibbons & Nicholas Art Gallery has the drawing “Units 3” on display. The underlying squares of the grid anchor parallel sets of straight lines that create the illusion of volume in the rectangular cage, like a prism.
Although the focus of this fair is more specific to the materials used to make the art, there was a diverse  selections of themes and forms represented. Art on Paper is open till Sunday March 5 2017.
Susan Happersett

Holger Hadrich – by Sarah Stengle

Holger Hadrich makes complex, collapsible geometric structures out of steel wire, and then photographs them in a way that dissolves the pure determination of the geometry into a feeling of a fleeting memory. The context chosen is often an ordinary place that implies motion, or transition. Sidewalks, asphalt and rivers recur with the superimposition of a delicate geometric structure.

17-08-01These objects rarely obscure their backdrop but rather hover like an apparition. One can see right through them, as one could see through a ghost. In his hands, the timeless geometry of the Archimedean solids are presented as movable objects that we pass by in a fleeting world. The context for his creations underscore the idea of passage and form a sequence of ordinary by-ways transformed by an ongoing internal conversation with mathematical form.

17-08-02The objects themselves are based on polyhedra, which are usually conceived of as solid. In his hands, however, they are rendered flexible and collapsible. Their web-like delicacy show precision and immense patience. One can almost imagine the object being turned in hand as careful attention is paid to the vertices. In many cases they are punctuated by small brass washers or carefully formed loops, which form a secured but collapsible hub. A different aspect of the work is made apparent when the objects are held in the hands. They are designed to be collapsible. Many are collapsible along more than one axis. To understand the collapsibility of his constructs it is best to handle them or see them in motion. His video Medusa Tower below shows one of his structures expanding from a depth of about three inches to nearly five meters.

Art historians from Vasari to Wöfflin have debated the supremacy of linear versus painter pictorial devices in art.  These works are both simultaneously linear and painterly (malerisch). The absolute clarity of the mathematic constructs is intentionally obscured to become integral to the partially dissolved, or transient clarity of the object as photographed.  These linear forms become painterly through Hadrich’s lens. The geometric forms are pulled out of the originating mathematical abstractions and into our ordinary life, where they seem to hover on the brink of collapsing and disappearing.

17-08-03To quote Wölfflin: “Composition, light and color no longer merely serve to define the form, but have their own life absolute clarity has been partly abandoned to enhance the effect.” The resolutely normal sidewalks and fragments of asphalt are also transformed when viewed through the orderly but complex web of geometric construction of wire. One immediately intuits a precise order that stands against our own transience and feels patient, quiet and timeless.
You can find more about Hadrich’s work on his Facebook page.

This is Sarah Stengle’s first contribution to this blog. Sarah is an artist and writer based in St Paul, Minnesota.

College Art Association Conference Math Art Lecture

This Saturday, February 18 at 12 Noon EST, I will be speaking about mathematical art at the CAA’s annual conference at the Hilton Midtown in New York. I will be focusing on the works I have made in collaboration with Purgatory Pie press, which will be on display (and for sale).

College Art Association Conference
Hilton Hotel, 1335 6th Ave) at 53rd St
Second Floor – Rhinelander Gallery – Table 219
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Susan Happersett

Picturing Math at the MET

The Metropolitan Museum of Art is current exhibiting a show titled “Picturing Math: Selections from the Department of Drawings and Prints”. The  exhibit features work from the 15th to the 21st Century. It presents  a cornucopia of beautiful work, and it was very difficult for me to choose just a few to discuss in this blog. Some of the most historically significant work was in the form of books that were opened to show prints.

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This first image is a page from Durer’s “Treatise on Measurement” from 1525.  This particular print Is “Construction of a Spiral Line”. Although the aesthetic significance of this work is undeniable, it is a technical diagram complete with measurements.
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This next page is “Dodecahedron and Variants”, from “Perspectiva corporum regularium” (Perspective of Regular Bodies). This is a 1568 treatise by Jost Amman based on the work of Wenzel Jamnitzer.  This work offers a progression of depictions of increasingly complex 3-D solids. Both of these books were created for the purpose of visualizing Mathematics as an expository tool, but because they are such gorgeous images they also highlight the beauty of the Mathematics.

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This exhibition also include contemporary art. A great example is Mel Bochner’s 1991 lithographs in the series “Counting Alternatives: The Wittgenstein Illustrations”. This particular print is titled “Eight Branch”. Referencing Bochner’s drawings from the 1970’s, this 1991 portfolio relates to the philosopher Ludwig Wittgenstein and his ideas about certainty. The print features two different lines of counting series, both starting with 0 in the top left corner. One line of digits goes horizontally across to the top right corner with 23 and the other goes diagonally across the page to the lower right corner with 33. Both routes end in the bottom left corner with 54.

Unlike the historical texts Bochner’s work is not about presenting mathematical principles to educate. Instead, he is using mathematics to express ideas. This is truly an excellent exhibit it will be up through April and I suggest that if you are in NYC, go see for yourself.

Susan Happersett

Roy Colmer at Lisson Gallery

Although Roy Colmer was well known for his photographic work, in the late 1960’s and early 1970’s he produced a series of paintings on canvas. Currently on display at Lisson Gallery, this work was created by using tape to make bright horizontal bands of color, that where then painted over using a spray gun.

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Roy Colmer, “Untitled #57”, 1970
Picture courtesy of Lisson Gallery

The practice of spraying a mist of paint applied a gradient of opacities over the hard-edge parallel lines. The resulting optical quality of the work relates to Colmer’s use of – what he referred to as –  “feedback” in his film and video work. These techniques seem to bend and distort the canvas plane altering the nature of the parallel line.

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Roy Colmer, “Untitled #133”, 1971
Picture courtesy of Lisson Gallery

Susan Happersett

James Siena at Pace

James Siena artistic practice incorporates the use of rules to create art. I have written about his type writer work, as well as his sculptures, in earlier posts. Obviously I am a fan, and I was very excited to be able to see some of his recent drawings at the Pace Gallery on 24th st. This exhibition features work from three different series; “Manifolds,”, “Wanderers” , and “Nihilism”. All of the drawings are hand-drawn, geometric studies but the the series I feel that  has the most Mathematical implications is “Manifolds”.
James Siena Manifold X, 2015 No. 61220 Format of original photography: digital Photographer: Tom Barratt

James Siena
Manifold X, 2015
No. 61220
Format of original photography: digital
Photographer: Tom Barratt

“Manifold X” from 2015 addresses the artist’s interest in the field of Topology. Topology studies the properties of surfaces allowing them to change through the manipulations of bending growing and shrinking without being cut or broken or having attachments added. In “Manifold X” the orange, yellow and blue surfaces are homeomorphic, they each have nine holes within their shapes . The green surface is different because it ha sixteen holes. The four surface are woven together but each individual shape does not intersect itself.  Siena has managed to take a fairly complex field in mathematics and develop a system of rules to create work that aesthetically beautiful and also expresses his affinity for the subject matter from which it is derived.
Susan Happersett

Dan Walsh at Paula Cooper Gallery

Dan Walsh is known for his large-scale geometric work. I was introduced to his paintings at the 2014 Whitney Biennial. At his solo exhibition at the Paula Cooper gallery I was immediately drawn to his large scale square paintings. Not only do they feature geometry, they also present the theme of counting. In the painting “Fin” from 2016 the canvas is divided in to four horizontal rows of varying widths.  Thickest on the top with 3 sections divided by black and white parenthesis and narrowest on the bottom divided into six segments.

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Fin – 2016
[copyright] Dan Walsh. Courtesy Paula Cooper Gallery, New York. Photo: Steven Probert

Since the width of each row is the same the progression 3, 4, 5, 6 segments presents a visual comparison of the fractions 1/3, 1/4, 1/5, 1/6.

“Debut” from  2016 the artist uses the same 3, 4, 5, 6 divisions in horizontal rows but this time groupings of thin lozenge shapes make up the pattern.

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Debut, 2016
[copyright] Dan Walsh. Courtesy Paula Cooper Gallery, New York. Photo: Steven Probert

There is a stack of 8 lozenges in the rows of three, 6 lozenges in the rows of four, 5 in the rows of five across, and 4 in the rows of six. Instead of having all of the shapes the same base color like in “Fin”, Walsh has created a scale with the more intense blues in the bottom row, grounding the picture space, almost like a landscape.

The painting “Circus”, also from 2106, presents a more architectural form. Working once again with rows of varying width this has seems to have more of a subject and background.

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Circus, 2016
[copyright] Dan Walsh. Courtesy Paula Cooper Gallery, New York. Photo: Steven Probert

The alternating black and white coloring of the vertical thin lozenge-like strips create a tower. The rows grow from 13 to 15 to 17 to 19. Each row gaining one strip on both the left and the right sides.

Dan Walsh’s painting style is both precise and systematic, but his choice of numerical subject matter that everyone can relate to creates a joyful imagery.

Susan Happersett

A Million

I never planned to use this blog to discuss my political leanings but …

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My sister Laura and I participated in the Woman’s March in Washington this past weekend. The size of the crowd was of a magnitude I have never experienced before. Anyone who has seen my work knows i have a predisposition for counting. Years ago, I developed a system of creating counted mark-making drawings. One project – from 1999 – titled “A Million Markings for the Millennium features 125 prints, each with a 40 by 20 square grid. Each grid square contains 10 markings. The number one million is thrown around freely in rhetoric and dialog, causing it to loose its gravitas. This work is my visual answer to the question “Just How many is a million?”

EPSON MFP image

Standing on Indepence Avenue on Jan 21 I was overwhelmed by the sea of people all walking together. The societal effects of very large number was palatable. I had not planned on discussing these emotions in this forum but when the concept of counting becomes an issue with regards the Presidential inauguration crowd, I could not stop myself.

Artists, even Math artists, do not work in a bubble (although I have attempted to crawl under a rock for the last two months). Objective counting and measuring has become a source of political existential angst. There is really no such thing as “alternative accuracy”. Sometimes numbers speak louder than words.

I guess I will always be a Nasty Number Geek

Susan Happersett