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Geometry in Art
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Ed
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May 12, 2011 08:37PM
I thought this would be a great topic.
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Geometric Sculpture of George W. Hart, mathematical sculptor. These are incredibly intricate designs....www.georgehart.com
"As a sculptor of constructive geometric forms, my work deals with patterns and relationships derived from classical ideals of balance and symmetry. Mathematical yet organic, these abstract forms invite the viewer to partake of the geometric aesthetic. "
"I have jumped from the faculty of Stony Brook University to be full time Chief of Content at The Museum of Mathematics...."
He is also involved in 3-D printing and some other high tech techniques such as laser cutting and computer rapid prototyping. He is also involved in collective "barn raising" sculpture assembly projects.
He is also an expert on how to cut a bagel into two interlocking pieces as he demonstrated at the Whitney Bienniel. :)
I love math along with art. This is very interesting to me. It's like a bunch of Mobius strips. Thanks, Ed.
Sol LeWitt used lines, geometric solids, ratio, patterns, formulas, and permutations to create his modern structures and wall paintings.[image error]
Sol LeWitt, Wall Drawing No. 681 C, 1993
[image error]
Sol LeWitt, Four-Sided Pyramid, first installation 1997, fabricated 1999
http://www.nga.gov/education/classroo...
Tony Smith mixed art and math; for him, it was the most natural thing in the world.Smith suffered from tuberculosis as a child. To avoid spreading the disease, he spent hours by himself, making buildings and miniature cities from small medicine boxes. He put the boxes—cubes and other polyhedra—together in different ways for his creations.
Smith became an architect and painter. When a serious car accident laid him up, he returned to his childhood pastime of making sculpture from boxes. From there, he went on to produce some of the most striking works of monumental outdoor sculpture of the 20th century.
[image error]
Tony Smith, Moondog, model 1964, fabricated 1998-1999
Moondog doesn't stand perfectly upright, as you might expect when looking at it head-on. It actually leans, tilts, and twists. Scholars say this gives it both a human aspect and a spiritual side. In fact, Tony Smith's goal was to express the spiritual in his work.
Smith said the sculpture reminded him of a Japanese lantern and of the human pelvis, the bones that hold our spine and legs together. But he named it Moondog for two reasons: after a blind poet and musician called "Moondog" who hung out on the streets of New York where Smith lived, and after a painting by Spanish artist Joan Miró of a dog barking at the moon.
http://www.nga.gov/education/classroo...
Oh, I just found out that M.C. Escher's brother was a crystallographer....Makes sense.....
Interesting! (I had to look it up)Before the development of X-ray diffraction crystallography, the study of crystals was based on their geometry. This involves measuring the angles of crystal faces relative to theoretical reference axes (crystallographic axes), and establishing the symmetry of the crystal in question. The former is carried out using a goniometer. The position in 3D space of each crystal face is plotted on a stereographic net, e.g. Wulff net or Lambert net. In fact, the pole to each face is plotted on the net. Each point is labelled with its Miller index. The final plot allows the symmetry of the crystal to be established.
http://en.wikipedia.org/wiki/Crystall...
OK this is almost more of a science gee whiz. But it was forwarded on to me by an artist friend. Fifteen uncoupled simple pendulums of monotonically increasing lengths dance together to produce visual traveling waves, standing waves, beating, and (seemingly) random motion.
Antoine Pevsnerb. 1884, Orel, Russia; d. 1962, Paris
Antoine Pevsner was born on January 18, 1884, in Orel, Russia. After leaving the Academy of Fine Arts in St. Petersburg in 1911, he traveled to Paris, where he saw the work of Robert Delaunay, Albert Gleizes, Fernand Léger, and Jean Metzinger. On a second visit to Paris in 1913 he met Amedeo Modigliani and Alexander Archipenko, who encouraged his interest in Cubism. Pevsner spent the war years 1915–17 in Oslo with his brother Naum Gabo. On his return to Russia in 1917 Pevsner began teaching at the Moscow Academy of Fine Arts with Vasily Kandinsky and Kazimir Malevich.
Developable Surface (Surface développable), 1938–August 1939
Bronze and copper, 52.1 x 31 cm, including base
Peggy Guggenheim Collection, Venice
[image error]
Developable Column 1942
Pevsner was especially interested in curved forms that are the locus of a moving rotating line: developable surfaces, where a line can lay flat on the curved surface.
Terrific! I love this section of the forum. Science and math are so beautiful! I always believed in consilience. Ed wrote: "OK this is almost more of a science gee whiz. But it was forwarded on to me by an artist friend.
Fifteen uncoupled simple pendulums of monotonically increasing lengths dance together to produce..."
Reminds me of my math books in college! LOLEd wrote: "Antoine Pevsner
b. 1884, Orel, Russia; d. 1962, Paris
Antoine Pevsner was born on January 18, 1884, in Orel, Russia. After leaving the Academy of Fine Arts in St. Petersburg in 1911, he traveled ..."
Aloha wrote: "I love math along with art. This is very interesting to me. It's like a bunch of Mobius strips. Thanks, Ed."maths and architecture,Pi is fascinating
http://en.wikipedia.org/wiki/Pi
The Great Pyramid at Giza, constructed c.2589–2566 BC, was built with a perimeter of 1760 cubits and a height of 280 cubits; the ratio 1760/280 ≈ 2π. The same apotropaic proportions were used earlier at the Pyramid of Meidum c.2613-2589 BC and later at the pyramid of Abysir c.2453-2422. Some Egyptologists consider this to have been the result of deliberate design proportion. Verner wrote, "We can conclude that although the ancient Egyptians could not precisely define the value of π, in practice they used it".[39] Petrie, author of Pyramids and Temples of Gizeh concluded: "but these relations of areas and of circular ratio are so systematic that we should grant that they were in the builders design".[40]
http://en.wikipedia.org/wiki/FullereneA fullerene is any molecule composed entirely of carbon, in the form of a hollow sphere, ellipsoid, or tube. The name was an homage to Buckminster Fuller, whose geodesic domes it resembles.Spherical fullerenes are also called buckyballs, and they resemble the balls used in Association Football. Cylindrical ones are called carbon nanotubes or buckytubes. Fullerenes are similar in structure to graphite, which is composed of stacked graphene sheets of linked hexagonal rings; but they may also contain pentagonal (or sometimes heptagonal) rings.[1]
http://en.wikipedia.org/wiki/Buckmins...
Richard Buckminster “Bucky” Fuller
nternational recognition began with the success of his huge geodesic domes during the 1950s. Fuller taught at Washington University in St. Louis in 1955, where he met James Fitzgibbon, who would become a close friend and colleague. From 1959 to 1970, Fuller taught at Southern Illinois University Carbondale. Beginning as an assistant professor, he gained full professorship during 1968, in the School of Art and Design. Working as a designer, scientist, developer, and writer, he lectured for many years around the world. He collaborated at SIU with the designer John McHale. During 1965, Fuller inaugurated the World Design Science Decade (1965 to 1975) at the meeting of the International Union of Architects in Paris, which was, in his own words, devoted to "applying the principles of science to solving the problems of humanity."
Thank you, Fran, for the great information! You might be interested in a great book I'm reading The Information: A History, A Theory, A Flood, which covers all the elements that lead to our computer age today, starting with the invention of writing. This is a very thorough book that pulls from all sources, but put in an entertaining layman's way. I can read this book again. I am loving it.
Has anyone seen "Italian Pavements: Patterns in Space" by Kim Williams? A very beautiful and scholarly book. She reproduces with meticulous colored pencil drawings the huge variety of geometric designs in the tile floors of Italian cathedrals from the Middle Ages to the Baroque.
I tried to go on Amazon to see if there was a sample. Unfortunately, they let you see the title page, table of contents, but no pictures! The only picture is on the cover. It looks good, though.
That sounds really interesting! Thank you for the recommendation, Tony!
I read this some time ago. Einstein, Picasso: Space, Time, and the Beauty That Causes Havoc
I just saw this article in Physics World. http://physicsworld.com/cws/article/p...
(requires a free subscription to read)
It discusses the book Insights of Genius: Imagery and Creativity in Science and Art
and Einstein, Picasso: Space, Time, and the Beauty That Causes Havoc
Here's some excerpts from the article:
Was it a coincidence that Picasso developed Cubism at about the same time that Einstein published his theory of relativity? Arthur I Miller thinks not, as he explains to Ciara Muldoon...
Particle theory and beyond
A physics graduate of the City College of New York, Miller gained his PhD from the Massachusetts Institute of Technology and started his career in particle theory. After further research at the University of Massachusetts, he moved to Harvard, where he switched disciplines to study the history and philosophy of science. "It was unknown territory for me at the time," he recalls. "I wasn't even aware that the field existed."....
Miller has since moved away from conventional history of science, having become interested in visual imagery through reading the German-language papers of Einstein, Heisenberg and Schrödinger - "people who were concerned with visualization and visualizability". Philosophy was an integral part of the German school system in the early 1900s, Miller explains, and German school pupils were thoroughly trained in the philosophy of Immanuel Kant.
According to Kant, visualizations are abstractions of phenomena that we have actually witnessed, while visualizability refers to the properties of an object that exist whether or not we look at it or take measurements of it. In Newtonian physics, visualization and visualizability are synonymous, but in quantum mechanics they are not....
In his most recent book, Einstein, Picasso: Space, Time and the Beauty That Causes Havoc (2001 Basic Books), Miller argues that Poincaré is the link between relativity and Cubism. Both Einstein and Picasso, he claims, were influenced by Poincaré's non-Euclidean approach to geometry and his speculations on simultaneity - Einstein directly through reading a German translation of Poincaré's La Science et l'hypothèse,. and Picasso indirectly through a circle of friends and acquaintances known as "la bande à Picasso". Miller's argument is that Einstein and Picasso were both working on the same problem, the nature of simultaneity - temporal simultaneity for Einstein and spatial simultaneity for Picasso - and that for both of them there were no preferred reference frames in which to view phenomena....
Many historians of art have felt that relativity somehow influenced the development of Cubism, but they have never believed that there was a direct link between the two. What prompted Miller to delve into the topic in such detail? "I always had an interest in art, and Picasso particularly, and Cubism even more particularly," he says. "It seemed to me that there was more science in there than met the eye and had been investigated before....
Miller regards Cubism as a "research programme" in which Picasso, like Einstein, discovered a new aesthetic - the reduction of forms to geometrical representations. This involved simultaneously representing, on a single canvas, many different viewpoints. "That had to have something to do with science," says Miller, "so I looked into it in great detail. I reviewed all the newspapers Picasso had read and looked back into what was going on at that time in literature as well." Although Einstein and Picasso were unaware of each other, the avant-garde movement in the first decade of the 20th century encouraged them both to question the traditional understanding of space and time....
Miller discovered someone in Picasso's circle - an insurance actuary called Maurice Princet - who studied advanced mathematics as a hobby. Princet had read and lectured on Poincaré to Picasso and his friends. "Princet was in Picasso's atelier at the time that Picasso was having a great deal of trouble with Demoiselles," he explains. "My hypothesis is that just at that point, Picasso realized the importance of what Princet was discussing concerning geometry." However, Miller is careful to point out that we will never know for sure how much Picasso was influenced by the work of Poincaré.
"Brilliant Noise" is based on raw black and white solar astronomical footage, and this gives it an especially eerie quality.http://www.youtube.com/watch?v=hmrX0w...
"Brilliant Noise takes us into the data vaults of solar astronomy. After sifting through hundreds of thousands of computer files, made accessible via open access archives, Semiconductor have brought together some of the sun's finest unseen moments. These images have been kept in their most raw form, revealing the energetic particles and solar wind as a rain of white noise. This grainy black and white quality is routinely cleaned up by NASA, hiding the processes and mechanics in action behind the capturing procedure. Most of the imagery has been collected as single snapshots containing additional information, by satellites orbiting the Earth. They are then reorganised into their spectral groups to create time-lapse sequences. The soundtrack highlights the hidden forces at play upon the solar surface, by directly translating areas of intensity within the image brightness into layers of audio manipulation and radio frequencies."
Early on in our fellowship we came across one still image of what turned out to be the Sun. We were fascinated by this image and wondered why we hadn't seen anything like it before. After some rooting about we discovered there were archives full of these documents of the sun but they required specialised knowledge just to extract each individual still from the data package it was stored in. We set about learning from the scientists the methods of extracting them and over the course of three months we downloaded gigabytes of archives. From here we turned these files into time lapse sequences according to their spectral frequencies and the film Brilliant Noise began to emerge.
Awarded second prize by the Science Film Festival, a Coruna Spain. 2008.
Awarded second prize at Onion City Experimental Film and Video Festival 2006.
Awarded Best Video at Experimental Film and Video Festival, Seoul, Korea 2006.
Specifications
Single channel version 09.38 mins /single channel DVD version 05.55 mins 4:3
HD limited edition / 3 + 10 screen 5.1 audio versions.
A Semiconductor film by Ruth Jarman and Joe Gerhardt made at the NASA Space Sciences Laboratory, UC Berkeley, California, USA. 2006
OK here is another Math + Art Leo Villareal turns math and code into emotional art
By ALICE THORSON
The Kansas City Star
This summer, sculptor Leo Villareal lights up the galleries at the Nerman Museum of Contemporary Art with computer-driven LED artworks, including “Star” (2008) (left), and “Amanacer” (2010), as seen in this installation view of the show.
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A highlight of the Nerman Museum of Contemporary Art’s 2007 grand opening was a pulsing lightwork by sculptor Leo Villareal.
Permanently installed on the underside of the museum’s cantilevered entrance, the large grid of flashing, chasing, white LEDS continues to welcome visitors with an overhead array of myriad, ever-changing patterns driven by computer.
Nerman director Bruce Hartman says the piece, titled “Microcosm,” has become “one of the museum’s most iconic works.”
This summer, the Nerman looks at “Microcosm’s” antecedents and some of Villareal’s more recent projects in the New Mexico-born artist’s first museum survey....
[image error]
Read more:
http://www.kansascity.com/2011/07/16/...
The Great Pyramid at Giza, constructed c.2589–2566 BC, was built with a perimeter of 1760 cubits and a height of 280 cubits; the ratio 1760/280 ≈ 2π. The same apotropaic proportions were used earlier at the Pyramid of Meidum c.2613-2589 BC and later at the pyramid of Abysir c.2453-2422. Some Egyptologists consider this to have been the result of deliberate design proportion. Verner wrote, "We can conclude that although the ancient Egyptians could not precisely define the value of π, in practice they used it"...."I saw a program once on how they think they did it and got the value of pi so accurately. They used a wheel!
Think about it. If you have a wheel 1 cubit in diameter, and mark a point on it and record the distance covered after 10 rotations it will be about 31.14159 cubits. If you then mark off 10 cubits, the ratio will be pi, or 3.14159.... So it would be possible to get pretty accurate results without much math.
I liked the pendulum waves, I could watch that all day. Reminds me of an exhibit at the Academy of Arts many years ago, where they did the works of art in glass, but it pretty much looked like some of the sculptures in the art pieces that I have seen on this thread. Thanks, Ed.
I just ran across the old Arthur C. Clarke documentary on fractals. Quaint desktop computers but pretty good visuals, and they explain the math really well.Math, art and the sublime all seem to intersect here. You can almost taste infinity in some of these visuals, sort of a spiritual feeling of awe.
I'll post a link to the first one, you can find the rest on YouTube.
http://www.youtube.com/watch?v=qB8m85...
Arthur C. Clarke presents this unusual documentary on the mathematical discovery of the Mandelbrot Set (M-Set) in the visually spectacular world of fractal geometry. This show relates the science of the M-Set to nature in a way that seems to identify the hand of God in the design of the universe itself. Dr. Mandelbrot in 1980 discovered the infinitely complex geometrical shape called the Mandelbrot Set using a very simple equation with computers and graphics.
One of my Facebook friends is a digital artist, and she makes frequent use of fractals in her work:http://pamrenovato.com/online-art-gal...
I like your friends artwork. Very colorful. Thanks, Ed
Fractals are incredible! I could only dream of being so intelligent as to understand something so complicated, yet so beautiful.
@ Ed Thanks for introducing us to Pam Renovato.
Heather wrote: "Fractals are incredible! I could only dream of being so intelligent as to understand something so complicated, yet so beautiful."The second and third parts are more mathematical, and do a really good job of explaining in really simple terms. I think the best explanation is the one given by Jonathan Swift, though:
...
"So nat'ralists observe, a flea
Hath smaller fleas that on him prey,
And these have smaller fleas that bite 'em,
And so proceed ad infinitum."
...
Here's two really cute animated images:
A Koch curve has an infinitely repeating self-similarity when it is magnified.
same for Mandelbrot set...
The Factor CongaThis is not quite geometry--it's geometric patterns made by arithmetic: "a promenade of primes, composites, and their constituents... what the dance clubs look like on Alpha Centauri."
Quite simple, really. As you probably remember from school, numbers can be factored into smaller numbers, and finally into their smallest divisors. So each number can be thought of groups of groups of groups.
So each number is broken into a diagram of these groups, and they are animated into a little dance. It's especially exciting when a prime happens (that's a number that can't be broken into smaller groups), and all the groups dissolve and from a circle.
Well worth watching. Warning: it's hypnotic, and there are an infinite number of integers...
http://www.datapointed.net/visualizat...
Hi this is the first time i'm posting a comment in this community mostly because i just don't really get art except for Van Gogh and that too at a very basic visual level but i like maths and these works are brilliant!!
Ed wrote: ""Brilliant Noise" is based on raw black and white solar astronomical footage, and this gives it an especially eerie quality.http://www.youtube.com/watch?v=hmrX0w...
"Brilliant Noise takes us i..."
Sorry, this link has now been blocked for copyright. It was really cool when it was available....
Shanawaz wrote: "Hi this is the first time i'm posting a comment in this community mostly because i just don't really get art except for Van Gogh and that too at a very basic visual level but i like maths and these..."All art is subjective; you know more about it than you think!:-)
Hi folks, first time for me to post, too. I joined a few weeks ago looking for interesting art-related groups. I'm a fiber artist who evolved out of traditional quilting. I still love the way good quilts use color, contrast and geometry to create a "work of art," I just don't make them big enough and sturdy enough to sleep with anymore. ;) Looks like a very interesting and intelligent group here!
Welcome, Sharon. Glad to have you! I was thinking, there is a thread where members can post pictures of their particular art if you would like to share...http://www.goodreads.com/topic/group_...
I would love to see your work!
That is really cool! Thanks for the link, Goose! Are you new? Welcome!
I just found a very interesting fractal animation.Watch how you keep getting into deeper and deeper levels but repeating.
https://www.youtube.com/watch?feature...#!
Sorry people, I find geometric art extremely boring and that said from a student who aced GEOMETRY with his eyes closed.
Geoffrey wrote: "Sorry people, I find geometric art extremely boring and that said from a student who aced GEOMETRY with his eyes closed."no wonder you find it boring!
Heather wrote: "Geoffrey wrote: "Sorry people, I find geometric art extremely boring and that said from a student who aced GEOMETRY with his eyes closed."no wonder you find it boring!"
Drawing in the dark was once de rigueur at Ohio State University. Wayne Gonzalez discusses that school's defunct "flash lab," which art professor Hoyt L. Sherman designed and where, during the 1940s, Sherman taught drawing and composition through the development of visual memory. In the darkened lab, images were momentarily flashed on a screen; students drew them from memory, in pitch blackness. Sherman's aim was broad-based visual acuity; his most famous success was the OSU football team's quarterback, whose passing game improved dramatically after flash lab training....
http://www.artinamericamagazine.com/b...
Ed wrote: "Heather wrote: "Geoffrey wrote: "Sorry people, I find geometric art extremely boring and that said from a student who aced GEOMETRY with his eyes closed."no wonder you find it boring!"
Drawing in..."
VERY interesting, Ed! Thank you for sharing!
That got a chuckle from me Heather. So if i kept my eyes open during class, would I appreciate geometric art more. Eye think not.
Art Lovers
Books mentioned in this topic
Insights of Genius: Imagery and Creativity in Science and Art (other topics)Einstein, Picasso (other topics)
The Information: A History, a Theory, a Flood (other topics)
