# Fibonacci

# Kelsey Brookes at the Jacob Lewis Gallery

Susan Happersett

# Mario Merz in Arte Povera at Hausser & Wirth

# Bridges Conference Art Exhibit – Waterloo 2017

# Natura Mathematica at Central Booking Gallery

# 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.

# Fibonacci on Mulberry Street

Walking down Mulberry street I spotted this great sign in front of The Picture Room McNally Jackson Store.

The sign is the work of Benjamin Critton. It features a series of squares whose sides increase based on the Fibonacci Sequence. The first two squares are the same size. The third square has sides twice the side of the first. The fourth has sides three times as long as the first. This continues until the 7th square has sides 13 times longer than the first. They all are spiraled into a neat Fibonacci rectangle with sides in an 8:13 ratio.

Susan Happersett

# Rotational Printing by Dikko Faust at Purgatory Pie Press

Dikko Faust has been making prints using rectangular sections of grids and other geometric line patterns. By shifting the grids across the plane he has created a series of overlapping prints. Recently he has added a new twist to his process. Faust has invented a new printing tool that allows him to rotate the rectangle around a central axis point.

(A quick note about printers’ measurements: In the print studio distances are measured in picas and points. One inch is equivalent to 6 picas and 1 pica is equivalent to 12 points.)

To measure the rotation of the rectangle, Faust uses a straight edge to form a line from the bottom corner of the rectangle that is perpendicular to the horizontal bottom edge of his press, and then measures how far from the center point to the horizontal line. The initial measurement for a straight up and down rectangle would be 12 picas from the center (the rectangle is 4″x 6″ or 24 by 36 pica).

Faust has been experimenting with what happens to different patterns throughout the rotation process

To better explore the relationship between the grids,Faust has made series of two-color prints. He has selected only the prints that are the most visually interesting. Making consecutive prints with the number of ratio of pica differences to correlate with the Fibonacci Sequence is one technique.

The day I was in the studio, Dikko was working with a pattern he had created using airline (1/2 point) rules. He used parallel lines: there is 1 point of space between the first two lines, 2 points between the 2nd and 3rd line, then 3 points between the 3rd and 4th….. up to 6 points of space between the 6th and 7th line. Then the whole pattern repeats 12 times.

While I was at the printing studio Faust was making a single print with multiple rotational images. I took pictures throughout the process.

This is an early stage of the process: it has the original line print plus a 5 pt and 10 pt rotation clockwise and a 5pt and a 10pt rotation counter clockwise.

This is the finished print. There are 5pt, 10 pt, 15 pt, 20 pt, and 25 pt rotations in both the clockwise and counter clockwise directions. The process that Faust has developed to create these new prints is very algorithmic. It requires a commitment to experimentation trying different patterns and rotations. The outcomes are then judged on their aesthetic merit determining which prints are to be completed works of art.

Susan Happersett

# Math at the Cooper Hewitt

The Cooper Hewitt, Smithsonian Design Museum in Manhattan was closed for renovation for three years before it reopened at the end of 2013. The current exhibition features an overview sample of their vast collection. I was very happy to discover that they have chosen to display quite a bit of work with direct Mathematical links. The debate over the critical delineations between Fine Art and Design is a hot button issue I am not going to address in this blog post. I have selected two pieces that have specific Mathematical themes.

“Prototype for an Environmental Screen, Fibonacci’s Mashrabiya”, 2009 is an architectural element designed by Neri Oxman at MIT Media Lab with Professor W. Craig Carter. It is was created using algorithms and digital processes but is based on traditional screens found in historic middle Eastern design.

The recursive Fibonacci Sequence was used to create the spiral pattern. Here is a detail of the center of the spiral.

Mathematician and artist Daina Taimina has been quite well known for her crocheted sculptures of Hyperbolic Geometry.

“Model of a Hyperbolic Space” 2011, is crocheted out of wool yarn. Working on these sculptures since 1997, Taimina has made major breakthrough on the modelling of figures in Hyperbolic space. Hyperbolic Geometry is a Non-Euclidean Geometry discovered by Janos Bolyai and Nicholay Lobatchevsky in the first half of the 19th century. In Hyperbolic Geometry each point has negative curvature and seems to curve away from itself.

At the Cooper Hewitt there were many more items that featured Mathematics as a design element. There was a very direct indication of the importance Mathematics plays in the field of both decorative and industrial design.

Susan

# 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.

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

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.

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.

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.

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