I thought pointillism was first used in the 19th Century, along with the Impressionists. IIRC, the idea was at least in part influenced by knowledge of the dual (particle/wave) nature of light, so the influence of physics is once again evident.
Regarding how computers draw, while it’s true that the display is a raster device (rows & columns of tiny dots), but images can be described vectorially in the processor - e.g., the PostScript page description language. But you can write a whole book on the subject. Actually, someone has.
During Salvador Dali’s religious period he incorporated weird mathematical symbols into his art. So in his Crucifiction he shows Christ crucified on a cross that, on closer examination, turns out to be a tesserac unfolded in 3-D space. (A tesseract is the four-dimensional analogue of a cube.) As a final touch, the “nails” are all cubes.
His Last Supper from the same period shows a beardless Christ presiding over the banquet , with a Sanish coastline in the background. Thre are also two modern priests in the foreground, as if serving a Mass. Hovering over the table is the torso of a naked figure presumably God. And, also superimposed over the scene is a dodecahedron. A dodecahedron* is a Platonic solid whose sides are all regular pentagons. It’s the only one with pentagonal sides. There are, as the name implies, Twelve sides – like the Twelve apostles.
Well I don’t know if you’re into folk art and math, but one thing you might want to look into is quilting patterns, many of which look very symmetrical and geometrical in design.
Another thing to look at might be crochet patterns too.
If you’re thinking about math and art in nature, you might want to consider spider web designs.
As far as more mainstream artists, I’d second Cubism, particularly the work of Georges Braque. I’d also recommend some of Cezanne’s work. In some of his later paintings, he tried to capture the geometry of nature. Some folks say that Cezanne’s efforts to capture the geometry of nature were the precursor to the Cubist movement. Or at least I think I read that somewhere. I don’t rightly recall at this point, though.
Good luck with your paper, and let us know what you finally decide to do.
Okay, celestina, resident math-idiot, will shut up now.
Yes, but other than education, roads, peace, plumbing, law, entertainment, and commerce, what have the Romans done for us?
Nothing!
Medicine?
Alright, other than education, roads, peace, plumbing, law, entertainment, commerce and medicine, what have the Romans done for us?
You can use math in art to the extent of your creativity.
Piet Hein was commissioned to build a pool or a fountain, I don’t recall which. Anyway, it was to be in a rectangular area. He wanted a rounded shape, but wanted to cover more area than an ellipse. He invented the super-ellipse. It is the formula for an ellipse, but instead of squaring the terms, you raise them the 2.5 power. It is a pleasing compromise between the rectangle and the ellipse.
Virtually yours,
DrMatrix
Problems worthy of attack
Prove their worth by hitting back. - Peit Hein
Here’s a poem by respected mathematician and author J. Bronowski that I think combines art and math (and science in general). I know strictly it isn’t “art” as it isn’t a painting, drawing or sculpture but I think it’s pretty artistic.
The Abacus And The Rose
*
I, having built a house, reject
The feud of eye and intellect,
And find in my experience proof,
One pleasure runs from root to roof,
One thrust along a streamline arches
The sudden star, the budding larches.
The force that makes the winter grow
Its feathered hexagons of snow,
And drives the bee to match at home,
Their calculated honeycomb,
Is abacus and rose combined.
An icy sweetness fills my mind,
A sense that under thing and wing,
Lies, taut yet living, coiled, the spring.
Jacob Bronowski
How about musical notes on any stringed instrument. There are mathematical equations relating string length to frequency(notes). I don’t remember them offhand but they are not terribly difficult and can be found in any basic physics book.
Or just relating musical notes to their frequencies, such as an A note = such and such a frequency. You could talk about harmonics and how they occur althought the mathematics is a bit more difficult with this.
Wow! All of these sites and suggetions are great! I’m going to spend the weekend investigating them, and make my final decision Monday.
You guys are all great, I really appreciate the help.
DrMatrix, I tried to get a wood Soma Cube through eBay without success. Did not want the color ones. I love Piet Hein’s “Grooks” and believe I have all volumes except VII.
Shun advice
at any price -
that’s what I call
good advice – Piet Hein
I was going to suggest fractals (that’s how that’s spelled, btw), but you already said that was out.
Then I thought of crafts such as knitting, crochet and cross stitch. In cross stitch, a lot of geometry can be involved in following the pattern, besides all that counting. Tatting (making lace) surely must involve some sort of math. All those crafty things, once created, can be considered art by some. Quiltmaking – definitely considered an art – must also involve some math, at least along the lines of geometry. (“Let’s see. I want to make a quilt that will cover the average queen size bed, which is [insert dimensions here] and I want to use 2” x 2" squares… [furiously does some math] Crap! That means I need 4,236 2" squares before I have enough fabric to create my warm and poofy work of art."
By me: Anything that can be done in more than one way, is art.
From the author’s preface to the 20th anniversary edition of GEB:
(A very good book, but doesn’t really address the relationship between math and art. GEB uses some art and music examples as analogies to the “Strange Loops and Tangled Heirarchies” the author believes are fundamental to consciousness. Besides, the OP said Escher couldn’t be used. )
Another place where math and art meet if it hasn’t already been mentioned, is a subset of sculpture. Not in physical ratios and such, but in the underlying physics of such things. While of course everyone thinks of the ratio math in architecture (Which is what I assume is prohibited for your paper) few consider things like the metalurgy used in constructing sculptures and modern buildings. Stress analysis and weight ratios can be very important in modern sculptures, where the form is more free flowing than classical works. Many kenetic sculptures need to incorporate feedback math to work (Think about things like the stairs that play music as people walk on them.)
Another place where one can consider the math is art argument, is in computer chip design, the math dictates the structure, and how you build it is very much an art form.
<<Quiltmaking – definitely considered an art – must also involve some math, at least along the lines of geometry. (“Let’s see. I want to make a quilt that will cover the average queen size bed, which is [insert dimensions here] and I want to use 2” x 2" squares… [furiously does some math] Crap! That means I need 4,236 2" squares before I have enough fabric to create my warm and poofy work of art." >>
Heh…and then you think “Oh, I can put BORDERS around the squares…”
I’ve used more math doing quilting than I have doing physics, I promise. One of the most interesting problems I’ve seen is this: Given that curved seams are a real pain in the behind, if I want to create something with a circle, how close of an approximation can I make using only whole-number unit sides and a moderate number of blocks? The quilt pattern “Shoemaker’s Puzzle” is a pretty decent fit for that…and how much math did someone have to do to figure out that a four-triangle piece that fits in a 7x7 square works so well?
