Math Unmeasured

Summertime is a time to relax the rules. During most of the year my drawings require the use of grids and calculated templates. In the warmer months, when I am away from my studio, I continue to draw, but using a more organic approach. I have created two new types of small scale drawings based on the Fibonacci Sequence. These works are more about counted iterations then measuring. This allows the patterns to grow and develop more freely across the paper.

The first type of drawing I am calling Fibonacci Fruit. This type of drawing features pod-like forms with internal structures based on the consecutive terms of the Fibonacci Sequence. Here are two examples using the numbers 5 and 8.

In the first drawing there are 13 pods each divided into 8 segments and each segment contains 5 seeds.

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The second drawing has 21 pods and again each pod has 8 segments with 5 seeds each.

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Another type of new drawing I am calling Fibonacci Branches. In these drawings one branch divides into two new branches. Those branches each divide into three branches, then those branches each get five branches, then each of those gets eight branches until finally each of these branches gets thirteen new branches.1, 2, 3, 5, 8, 13. This creates a treelike arrangement.

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In the next example, five sets of branches are scattered across the page. Each branch formation starts with one branch and grow in a similar fashion to the other drawing but in this case the final branch count is eight.

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I am always interested in the negative space in my drawings. A good way to explore this is to make a white on black drawing.

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There are still a multitude of possibilities for the continuation of these two drawing series. It will be exciting for me to see where the Fibonacci Sequence will take me next.

 

Susan

Mathematics and Fashion: Charles James at The Metropolitan Museum of Art

When you think about evening gowns, mathematics may not be the first think that comes to mind, but Charles James used geometry and engineering to design his stunning sculptural creations. In 1944, Vogue Magazine referred to his “Mathematical tailoring”.
The Metropolitan Museum has devised an exhibition that celebrates the mathematical structures of James’ work using technology to enhance the viewer experience. Robotic arms with cameras and video recorders present close-up details of structural elements of the gowns. X-rays provide an inside glimpse at the architectural support systems. Computer models provide 360 degree topological maps of the twists, spirals, and folds incorporated into the fashion. Unfortunately it was very dark in the gallery and impossible to take photos but the Metropolitan Museum has a great website with videos and images at metmuseum.org. I have included two of my favorite dresses.

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Charles James – Four leaf clover dress

The evening dress “Four Leaf Clover”  features a hyperbolic curve for a sweeping skirt.

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Charles James – Spiral Dress

The green satin Spiral dress incorporates a spiral of fabric that seems to flow directly back into itself creating an Moebius strip that encircles the wearer.

There are many other examples in the exhibition of the complex geometry utilized to design these creations. Throughout his career James was also involved with teaching other designers to use his mathematical techniques. He invented his own schematic dress forms and mannequins that are also on display at the museum.

The engineering nature of Charles James’ approach to fashion combined with the technologically curated presentation of the Metropolitan Museum creates an exhibition that reveals connections between Mathematics and fashion design.

– Susan Happersett

Water Weavers at The Bard Graduate Center

“Water Weavers, The River In Contemporary Colombian Visual and Material Culture” is currently on view at the gallery of the Bard Graduate Center in Manhattan. This exhibition explores the connections between the river and culture exploring the art, craft, and design that has manifested from these connections. A number of the displays reflect the cultural importance of the symmetry in the objects created.

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Abel Rodriquez – Fish Trap
Picture courtesy of the artist and the gallery

The large scale woven form “Fish Trap” (2013)  by Abel Rodriquez was created using Yare’ fiber. This form features 3-D symmetry with a central horizontal axis of rotational symmetry as well as a vertical axis of reflection symmetry. In these weavings Rodriguez has expressed the grace and elegance of form of a traditional and functional object.

David Consuegra was one Columbia’s most influential graphic artists. In the 1960’s he developed a series of abstracted patterns based on the esthetics of pre-Hispanic designs. A group of his prints of the individual geometric images are on display in the gallery. Each of these elements of his visual dictionary is based on either reflectional or glide-reflectional symmetry.

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The art collective Tangrama has used technology  called “Applique” (2014) to create  wall paper designs incorporating the work of David Consuegra.

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Tangrama has also provided the viewer an opportunity to explore these patterning opportunities with a tablet-optimized web application based on David Consuegra’s designs installed in the gallery.31-4

This interactive software allows the participant to layer up to five different patterns with ten color choices, ten gradient variations, as well adjusting size. There is also the ability to allow the patterns to move by scrolling across or up and down the screen. I had a great time exploring a few of the multitude of visual possibilities available with this amazing design generator.

Susan Happersett

Transmutations – Benigna Chilla at Tibet House NYC

Benigna Chilla has incorporated mathematics into her art practice throughout her career. Her recent, large scale canvasses on display at Tibet House are inspired by her stay in Bhutan in 2011.

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Overview of the exhibition
Picture courtesy of the artist and the gallery

Chilla has included small segments of cultural pattern and textiles into the texture of these paintings. This enhances the connections between the bold symmetries and traditional Tibetan Art. In the painting “Two black Triangles” there is the obvious reflection symmetry of the black triangles, but there are also subtle almost-reflective symmetries. Near the bottom of the canvas there two added sculptural elements, but the right one is higher than the left. On the right hand side of the bottom border there are two red triangles with grey circles on top. On the left hand side, the triangles re grey, but the circles  are red.

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Two Black Triangles – Mixed Media – 8′ x 6′ – 2012
Picture courtesy of the artist

The painting “Full Moonstone” features a large central Mandala with 8-fold rotational symmetry.

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Full Moonstone – Mixed Media on Canvas – 8′ x 6′ – 2013
Picture courtesy of the artist

In the press release for this exhibition, Chilla discusses the importance of both the meditative and physical processes involved in the creation of these works. There are not many artists who can discuss creating mathematical symmetries and meditation, and I personally find that combination very inspiring.

Susan Happersett

 

Summer Show at McKenzie Fine Art

One of my favorite things about NYC in the Summertime is the Summer Group shows at the galleries. During the next month or so there are many opportunities to attend exihbitions that feature the perspectives of numerous artists, whose work is related by a consistent theme. The McKenzie Fine Art Gallery‘s current show is titled “Color as Structure” and exhibits the work of 16 artists, whose use of color defines the geometries within their paintings, drawings, and sculptures.

Elise Ferguson

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Elise Ferguson – NW, bold
2014 – Pigmented plaster on mdf – 24 x 124 inches
Picture courtesy of the artist and the gallery

Elise Ferguson uses pigmented plaster on board in her work “NW,bold”. This square work is structured using reflection or mirror symmetry. The diagonal on the square running from the upper left corner to the lower right corner is the line of symmetry. Ferguson creates a dynamic rhythm in this work through her use of parallel lines of modulating widths. The bolder set of lines parallel to the top and left edge of the board contrast with the thinner lines that are parallel to either the edges or the diagonals. There are only a few lines that are not parallel to either the edges or the diagonals. These lines divide the board into geometric regions, creating defined sections of parallel lines going in different directions. There is a hand drawn qualtity to this work that I really appreciate. I feel that the varying widths of the lines enhances the nature of the material and gives the work great energy.

Alain Biltereyst

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Alain Biltereyst – 2/0/12
2012 – Acrylic on wood panel – 10 1/2 x 7 1/2 inches
Picture courtesy of the artist and the gallery

Alain Biltereyst’s intimate painting on wood panel “2/0/12″ has historical references to earlier geometric abstractions from the 1960’s. With a background in graphic design Biltereyst is interested in signage in the public environment. This work brings the cultural phenomenon of text and images we see in advertising and street art and distills the geometric content to abstract paintings. He introduces the imperfections of the shapes inherent in the street and some handmade signs into the realm of the clean edge geometries of his historical influences. In “2/0/12″ Biltereyst has created a rectangular grid system: three columns of five rectangular sections. The pattern in the left column has has been shifted down one rectangle and is repeated in the right column. The middle column features two parallelograms that have the same width as the rectangles in the other columns but are stretched to reach the corners at twice the height.

Paul Corio

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Paul Corio – Megalicious
2011 – Acrylic on canvas – 60 x 48 inches
Picture courtesy of the artist and the gallery

Near the front of the gallery Paul Corio’s painting “Megalicious” drew me into the gallery like a sirens song. All of the pulsing squares and triangles painted like color wheels are the perfect marriage of math and art. Corio has divided the squares into ten triangles by trisecting the sides of each square and then drawing lines from each of those six points and each of the four corner points to the the center of the square. The resulting triangles have been filled in with the colors from a color wheel in sequence. To decide which color goes into the top triangle to begin the progression, Corio has created his own random number generator, using the numbers of the winning thoroughbred horses from race tracks in NY. The number one results in yellow being the top center triangle. Not only does “Megalicious” use geometric forms, there is also an interesting algorithm to determine color placement.

Lygia Clark at MOMA

The Museum of Modern Art in NYC is currently hosting a huge retrospective of the work of Lygia Clark (1920-1988). Clark was a member of the Brazilian Constructivist movement. The walls of the first few rooms of the exhibition display the artist’s geometric abstract paintings.  On platforms in the center of the gallery, an assortment of  her hinged metal sculptures are on display. It is these sculptures I would like to discuss. There are a number of excellent reviews of the show online – the Brooklyn Rail is an example – but I would like to focus on the sculptures. Clark created these sculptures so that viewers could manipulate the shapes, creating different
forms, becoming part of the artistic process. At the MOMA show work tables are set up throughout the galleries with reproductions of the sculptures available for the public to participate. Photography is forbidden in these galleries so I decided to reproduce one of Clarks’s more simplistic forms using paperboard and tape and taking photos of my model.

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Here is the construction process, in case you want to make one. You will need seven congruent isosceles right triangles.
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Lay out four triangle to form a square and make three hinges leaving two triangles attached on only one side.

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Take a fifth triangle and attache it to one those single attachment triangles so it is on top of the other triangle with one attachment .

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Add the sixth triangle to the fifth so they form a parallelogram.

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Turn the structure over and attach the seventh triangle to the fourth triangle from the original square so you have like a trapezoid. Now you can stand up the structure in many positions.
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– Susan Happersett

Off the Wall in Chelsea

I discovered a very interesting trend at the Chelsea galleries this week. I found three different exhibitions where an artist presented drawings, paintings, or sculptures, but also built an installation work that protrudes off of a gallery wall.

Robert Curry at Bryce Wolkowitz Gallery

Bryce Wolkowitz Gallery  had a collection of Robert Currie’s perspex cases with monofilament line 3-D drawings.

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9,772 inches of Black and Red Monofilament (2013)
Picture courtesy of the artist and the gallery

In the sculpture “9,772 Inches of Black and Red Monofilament”,  Currie uses a series of threads hand-strung in grids to form angled wedges of red and black that intersect at the center, forming an area of at what – at first – looks like disorder. Upon closer inspection the consistency of the patterns becomes clear. This work has a number of mathematical connections: The careful measurement of the monofilament is a defining factor in the title for this work. Currie uses a series of grid patterns to thread the work. There are intricate geometric shapes created within the cases. The finally mathematical connection is his allusion to Chaos Theory, where there is underlying order in what at first appears to be disorder.

At the entrance and in the hall of the gallery, Currie has installed a site-specific thread drawing based on the architecture of the room “12 miles 1647 yards of Black Filament”. This work explores the gallery space using repetitive straight lines.

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12 miles 1647 yards of Black Filament
Picture courtesy of the artist and the gallery

Mark Hagen at Marlborough Chelsey Gallery

At the Marlborough Chelsea Gallery, Mark Hagen has created an aluminum and stainless steel space frame installation named “To Be Titled Ramada Chelsea #3″,  that climbs in front of his “To Be Titled Gradient Painting #35″. This geometric construction features cube formations meeting at star formations formed by 12 line segments radiating out from a central point.

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“To Be Titled Ramada Chelsea #3″in front of “To Be Titled Gradient Painting #35″
Picture courtesy of the artist and the gallery

Ryan Roa at Robert Miller Gallery

The Robert Miller Gallery is presenting a group show titled “Six Features”.  One of the artists, Ryan Roa, is exhibiting drawings that relate to fractions and geometry. In the same room he has created site-responsive installation that create a sense of movement within the space.

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Site-specific installation
Picture courtesy of the artist and the gallery

In his drawing “12X12 series #01″,  Roa has drawn a multitude of equal line segments radiating out from two opposite corners of the square, creating two equal quarter circles that overlap along the diagonal.

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12X12 series #01
Picture courtesy of the artist and the gallery

In “12X12 series #02″, the artist uses the same technique of drawing equal line segments, but in this case they radiate out from the two left corners of the squares. The circles overlap to form a pointed dome shape.  The right square is not completely filled in with lines: it  retains the curves of the circle segments.

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12X12 series #02
Picture courtesy of the artist and the gallery

It is fascinating to me how Roa has been able to create two drawings with such different proportion shapes and energy using basically the same technique by only changing one parameter.

It is amazing that within the course of an afternoon walking only a few blocks I was able visit three installations of Mathematical constructions by artists with very different practices and techniques. By expanding their formats off the gallery walls, each artist has created an exciting space to engage with the measures, proportions, and geometries that make up their work.

Susan Happersett

Math Trends at the Whitney Biennial

The Whitney Biennial exhibition closed last week, but for those of you unable to visit the museum I wanted to briefly discuss a few examples of work with Mathematical implications.

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Terry Adkins’ large wall installation “Aviarium” from 2014 was assembled using repurposed stacked cymbals. Adkins was a musician and the sizes of the cymbals were determined by the mathematics of bird songs. The horizontal columns of circles protruding from the gallery wall become a physical manifestation of sound.

Suzanne McClelland

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In her diptych “Ideal Proportions” 2013, Suzanne McClelland explores the psychological and social implications of our relationship to numbers. McClelland’s expressive renderings of groups of Arabic numerals reveal the anxiety and judgement associated with numbers that refer to the weights and measures of the human body.

Shio Kusaba

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Ceramicist Shio Kusaba has created a series of vessels featuring striking pattern work. I am particularly interested in her pieces that have grid patterns. The use of linear rectangular grids on the organ forms create a subtle juxtaposition between the curved surfaces and the lines. I find the spaces  where the gridded sections meet in triangles fascinating. The concept of lines on curves is an area of geometry ripe for artistic exploration.

The Whitney Biennial always received a lot of attention and press. Now that the excitement and fan fare have concluded I wanted to offer some personal observations.