Jay Hambidge 1867-1924, a Canadian born artist and mathematician wrote Elements of Dynamic Symmetry. In the book Hambridge lays out the mathematical formulas that underline classical architecture and the structures of various parts. of nature. I expect that most of you have seen a nautilus shell with a drawing overlaid upon it to show the geometric and mathematical ratios of which it is composed. Hambidge laid out his idea of natural symmetry which some artists and many more designers have found useful. The book is still in print and can be had from Amazon.
Hambidge made careful measurements of the Greek temples including the Parthenon and reached a design theory he called dynamic symmetry. Much of it is based on root rectangles.The drawing below shows how they are created.
If you draw a square and pull an ascending line from one corner to it's opposite, then measure along the base with that line you get a root v2 rectangle. If you draw a new line through the corners of that and drop it down to the baseline again you have a root 3 rectangle.Forms designed with this system have pleasing proportions. Tomorrow I will take this out another step and we will see how it can be used to plot the arrangement of as painting in further posts. I do not use this system in my own painting except perhaps instinctively, but some classical realists are very fond of this stuff and I think It is useful to know a little about it.
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27 comments:
"Euclid Alone Has Looked on Beauty Bare" - E.S.V.M
Just a quick report from Open Studios - from our stand point here in Newton,MA the art "market" for paintings is picking up. Good News for everyone out there. Keep heart.
The root 2 does not look like twice the volume of the original square.
This exercise reminds me of the method of laying out frets on a stringed instrument using a straight edge and a compass. The difference is that the top horizontal line is not parallel with the bottom line but intersects it at the string length. I forget how the hight of the first perpendicular is arrived at, as it has been some years since I build guitars. (It is the length of the nut.) The interesting thing is that by dropping those arcs with a compass and establishing the fret with a perpendicular, after twelve of those perpendiculars, you arrive at the mid-length of the string length!!
Sorry for the digression.
Everyone's mind works a little differently of course.
Sometimes knowledge leads us to see more, other times it can stand in our way like cobwebs and obscure our view.
Honestly I think the artist who benefits from such geometrical musings would be in a distinct minority.
Leonardo had a saying about the tragedy of one's theory outstripping one's practice. In a lot of cases, I fear that's just what would happen.
You need a ruler and a compass to do this. You measure from point "A" to the diagonal of point "B". You then draw and arc from point "B" down to the base line which will give you "C"
Pull a line up from C to give you D.
Measure again using the compass from A to D.
You can't eye ball this and expect good results.
Also look up the golden ratio.
Albrecht Dürer apparently thought all drawing was geometry.
I'm inclined to agree.
A lot of artist used this.
George Bellows knew and I think studied with Hambidge and he used this idea in a lot of his work.
You can find this kind of geometry in a lot of Renaissance and Baroque art.
I personally think to ignore this and the study of composition in general is not a good idea and it is detrimental to producing decent work.
I like that you have brought up the study of composition, Stape. Some artists seem to have a natural sense for composing while others do not. We tend to find some artwork pleasing and not realize why. Composition is an important element in any artform. You can't dress a body without bones.
Stapleton,
A recently published book entitled Classical Drawing Atelier, by Juliette Aristides, in the chapter on design discusses at length use of the Fibronacci sequence in both art and architecture. The author, using the sequence, relates drawing and painting to music through rhythm, melody, and harmony. She goes on to demonstrate in "The Annunciation" by Leonardo da Vinci how he used Fibronacci's sequence. She also quotes Durer as saying that one must learn geometry to become " an absolute artist"
I do not think, at this stage of my life, I am going to go through all the jigs and reels involved in learning to apply Fibronacci"s sequence. However, in the end the mathematics is reduced to the ratio of 1.618 to 1 {the golden ratio) which apparently has all sorts of applications in design beginning with, for example, the ratio of the sides of a canvas to that which is painted upon it.
Thank you for all your thought provoking writings.
Here's a video illustration...amazing!
Nature by Numbers
http://www.youtube.com/watch?v=kkGeOWYOFoA
I've heard numbers play a roll in music, so maybe in art as well.
I don't paint by numbers, that's for beginners : )
My brain hurts.
In my opinion, the definitive work on this topic is the contemporary book "The Golden Ratio" by astrophysicist Mario Livio published in 2002. I won't go into detail here as I wrote a post about it on my blog; however, Livio mentions Hambridges work and states that "few today take his ideas seriously." It is a fascinating topic, but I am inclined to agree with Livio's detailed and thorough analysis of the subject.
Michael:
The last time I saw beauty bare I was not alone.
..................Stape
Marian:
Seems that way to me too.
......Stape
Willek:
You are quite right. I went in and corrected that. I apologies for the mistake. I am straining my math skills to do this.
.................Stape
Holy cow! My seventh grade math teacher was right after all!
quote: "You're going to need to know this one day..."
Jefff:
Yes we are getting to the golden ratio.I believe I will use your description out on the blog, I will credit you, I hope you don't mind.
...........Stape
Jeff:
I believe I heard that about Bellows also.
....................Stape
Durinda:
Thank you. The best dressed woman I ever knew was had no bones. She was like a big dolphin.Swedish,blond and very funny.
..................Stape
Jim,
I will mention her book on the blog. It contains a good section on all of this.
.............Stape
Linda:
Thanks.
............Stape
bill:
Numbers are everywhere. I am not inordinately fond of them either.
..................Stape
Mary:
Mine too. This is not my thing.
..............Stape
Michael;
I think that some of the new Classical Realist guys are enamored with these ideas.
..............Stape
Deb;
There are other things mathematical that are more useful.
...............Stape
Philip:
I agree, but I thought I should show the rudest idea of this stuff. It would be an incomplete series on design with out a mention of this. Arthur Dow is lurking out there in the distance, in plaid.
.......Stape
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