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MATHÉMATICS & ARTS |
Exhibit & Lecture |
Initialy
presented at the Institut Henri Poincaré,
Paris. France. |
January
22 - June 30, 2005 |
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- FRIEDMAN Nathaniel
- Mathematician
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Nat Friedman is a mathematician, sculptor and graphic artist. He was a member of the Department of Mathematics at the University at Albany, State University of New York, from 1968 until retirement in 2000. He organized the first Art and Mathematics Conference in Albany in 1992 (AM92). This was followed by AM 93-AM 97 at Albanay and AM 98 at the University of California-Berkeley. In 1998 he founded the International Society of the Arts, Mathematics, and Architecture (ISAMA). The conference ISAMA 99 was held at the University of the Basque Country, San Sebastian, Spain, co-organized with Javier Barrallo. Annual ISAMA conferences have followed in Albany, 2000; Freiburg, Germany, 2002; Granada, Spain, 2003; and Chicago, 2004.
Nat Friedman is currently developing educational material for visualization in the arts and mathematics. He has recently completed a three DVD set for knot theory in grades 5-12 with a workbook. He has also recently developed a range of mathematical sculptures in high-fired stoneware, including knots, Möbius bands, and minimal surfaces.
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| I joined the Department of Mathematics at the University at Albany in 1968. On a whim, I took an adult evening sculpture course there in the fall of 1971. I soon discovered that I was hopelessly addicted to carving and I have been carving wood and stone ever since. My main influences were Arp, Brancusi, Hepworth, and Moore. Carving was a release from research mathematics and it is only in the last ten years that mathematical ideas have influenced my work, which can be seen at www.isama.org under Sculpture.
For me, the major development in sculpture was the opening up of the solid form to create space, as in the work of Hepworth and Moore. I generally begin a sculpture by carving out a space. A shortcut to forming space is to break a stone into several pieces and then separate the pieces to form space between the pieces. One then has the so-called fractal geometry of the broken stone. Benoit Mandelbrot told me that “ the word fractal came from fracture, as in the edge of broken granite, rather then fraction as some people think.” This statement definitely influenced me since I had been working with broken granite and led me to the technique for making fractal stone prints. |
Click thumbnail to enlarge picture |
Rectangle Inside Out
I begin with a planar shape of one-inch thick polished granite, which is then broken into several pieces. I separate the pieces to form space and may also remove some pieces. Black ink is rolled on the polished surface of the stone pieces and a sheet of thin Japanese paper is placed on the inked stones. When pressure is applied on the paper with a barren, the ink permeates the paper. The lower surface of the paper on the stones has a solid black image, which was the original intent.
In the print Rectangle Inside Out, a rectangle was broken into four pieces and the pieces were then rearranged so that the fractal edges are on the outside and the straight Euclidean edges are on the inside. It came as a surprise that the ink permeating the paper resulted in an interesting “ gray-black” image on the upper surface of the paper that is visible as the print is made. By applying pressure with a burnishing tool along the broken edges, these edges show up as black on the upper surface due to the ink permeating the upper surface of the paper. |
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River and Streams
Here the spaces were chosen so that the wide spaces correspond to the horizontal river and the narrow spaces correspond to the vertical streams. The fractal stone print conveys the idea of a river and streams since the fractal geometry of the broken granite and the fractal geometry of a river and streams is the same geometry |
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Adagio
In the print Adagio, one actually obtains two prints, where the lower side is a black print and the upper side is a gray-black monoprint controlled by the pressure of the barren and the burnishing tool. One can combine the two sides by folding one side over onto the other side. The black side can be folded over onto the gray-black side or the gray-black side can be folded over onto the black side. The result is a two-sided print where the black side is folded over on the right and left sides. Note that the folds are made so that the fractal spaces match up. |
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Flamenco
Introducing colored inks has introduced many possible color variations. The print Flamenco is an example of a two-sided print in black and red. Here the black side was folded over on the left and the red side was folded over on the right. |
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