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The One
2nd June 2016, 20:25
“Without mathematics there is no art,” said Luca Pacioli, a contemporary of Da Vinci.

What makes a single number so interesting that ancient Greeks, Renaissance artists, a 17th century astronomer and a 21st century novelist all would write about it? It's a number that goes by many names. This “golden” number, 1.61803399, represented by the Greek letter Phi, is known as the Golden Ratio, Golden Number, Golden Proportion, Golden Mean, Golden Section, Divine Proportion and Divine Section. It was written about by Euclid in “Elements” around 300 B.C., by Luca Pacioli, a contemporary of Leonardo Da Vinci, in "De Divina Proportione" in 1509, by Johannes Kepler around 1600 and by Dan Brown in 2003 in his best selling novel, “The Da Vinci Code.” With the movie release of the “The Da Vinci Code”, the quest to know Phi was brought even more into the mainstream of pop culture. The allure of “The Da Vinci Code” was that it creatively integrated fiction with both fact and myth from art, history, theology and mathematics, leaving the reader never really knowing what was truth

Just as the Golden Section is found in the design and beauty of nature, it can also be used to achieve beauty, balance and harmony in art and design. It’s a tool, not a rule, for composition, but learning how to use it can be a great Art 101 lesson on laying out a painting on a canvas.

For those with a deeper understanding yet, the golden ratio can be used in more elegant ways to create aesthetics and visual harmony in any branch of the design arts. As you’ll find in the examples below, it has been used by some of the greatest artists the world has known.

Oddly enough, you may also find critics who say that the golden ratio cannot be found in art at all. Such statements often come from Ph.D.s in mathematics who hold a very theoretical viewpoint that nothing in the real world can be a golden ratio. Why? Simply because it has an infinite number of digits. Pi does too, so this way of thinking says there are no circles in the real world either. For the rest of us, practical applications of mathematical concepts are a simple and necessary everyday occurrence in the arts, engineering and applied sciences.

Leonardo da Vinci

The Golden Section was used extensively by Leonardo Da Vinci. Note how all the key dimensions of the room, the table and ornamental shields in Da Vinci’s “The Last Supper” were based on the Golden Ratio, which was known in the Renaissance period as The Divine Proportion. The lines showing Da Vinci’s intricate use of the Divine proportion were creating using PhiMatrix golden ratio design and analysis software: (http://www.phimatrix.com/)

Note in Da Vinci’s “The Annuciation” that the brick wall of the courtyard is in golden ratio proportion to the top and bottom of the painting:

Even the fine details of the emblems on the table appear to have been positioned based on golden proportions of the width of the table:

Other golden proportions can be found in “The Annunciation” that illustrate the point and give evidence of Da Vinci’s intent. See other examples of Da Vinci’s use of the Divine proportion here (http://www.goldennumber.net/leonardo-da-vinci-golden-ratio-art/) .The golden ratios that Leonardo da Vinci used in the composition of this painting are explored in the video below:

Michelangelo

In Michelangelo’s painting of “The Creation of Adam” on the ceiling of the Sistine Chapel, look at the section of the painting bounded by God and Adam. The finger of God touches the finger of Adam precisely at the golden ratio point of the width and height of the area that contains them both. Alternatively, you can use the horizontal borders of the width of the painting and get the same result

Raphael

Raphael’s “The School of Athens” provides another wonderful example of the application of the golden ratio in composition. A small golden rectangle at the front and center of the painting signals the artist’s express intent in the use of this proportion. We find that Raphael used golden ratios throughout the painting, giving it a wonderful visual harmony.

Botticelli

Some say that Bottocelli composed “The Birth of Venus” such that her navel is at the golden ratio of her height, as well as the height of the painting itself. Some argue this isn’t the case. Close examination shows that you can take the golden ratio point using several different logical variations, and they all come to her navel, as well as the bottom tip of her right elbow:

Red line – From the very top of her hair to the bottom of her lower foot.

Green line – From her hairline at the top of her forehead to the bottom of her upper foot.

Blue line – Her height, as measured from the middle of the feet to the top of her head at the back of the part in her hair.

Perhaps a coincidence in composition, but then again perhaps not. See a more extensive analysis yet of golden ratios in The Birth of Venus. The best evidence is that the canvas itself is a golden rectangle, with the ratio of its height to its width in golden ratio proportion. The dimensions of the canvas is 172.5 cm × 278.5 cm (67.9 in × 109.6 in). The width to height ratio is 1.6168, a variance of 0.08%, only 1/20th of an inch, from the Golden Ratio of 1.618.

Seurat

The French impressionist painter Georges Pierre Seurat is said to have “attacked every canvas by the golden section.” In the examples, below the horizons falls exactly at the golden section of the height of the paintings, as are other key compositional elements of the paintings.

Edward Burne Jones

Below, Edward Burne Jones, who created “The Golden Stairs” , also meticulously planned the smallest of details using the golden section. Golden sections appear in the stairs and the ring of the trumpet carried by the fourth woman from the top. The lengths of the gowns from the sash below the breast to the bottom hem hits the phi point at their knees. The width of the interior door at the back of the top of the stairs is a golden section of the width of the top of the opening of the skylight. How many more can you find?

In “The Sacrament of the Last Supper,” Salvador Dali framed his painting in a golden rectangle. Following Da Vinci’s lead, Dali positioned the table exactly at the golden section of the height of this painting. He positioned the two disciples at Christ‘s side at the golden sections of the width of the composition. In addition, the windows in the background are formed by a large dodecahedron. Dodecahedrons consist of 12 pentagons, which exhibit phi relationships in their proportions

Source (http://www.goldennumber.net/art-composition-design/)

enjoy being
2nd June 2016, 21:56
Cool, this is always of interest, being an artist. The maths and the conscious knowledge of these proportions are proven to be known about for centuries. I personally am a little undecided on how this all might have come about.
When you look at branching ratios within the body, or of spirals in shells or the center of flowers, this language is present in every organic form on the planet.
What I have noticed is that being a language of sorts, a geometric mathematical one, the ratio is sort of like the dialect peculiar to Earth. Well Earth at least, it may very likely be universal. Anyhow the point of interest I have noticed and then extrapolated in 'perhapsness', is that we as humans tend to work with and understand these ratios without needing to think about it. Our perception of harmony and balance is tuned to this ratio. We see beauty in symmetry of faces. The times you might arrange objects on a mantle piece or place furniture in your house... the conversation you are having with yourself about "Does that look good there? A little to the left?" seems very often to be that you are placing things in relation to the golden proportions. An alien may walk into that room you have arranged and (should the ratio be only an earth ratio) find it not as pleasing as a human... or if it is indeed a universal ratio, they may appreciate and understand it and it could be a commonality.
I have done a few tests in which I have made paintings by considering the composition and taking my time to place things that look good by eye. I have done the same making paintings fast and focusing on compositional balance while tuning out of being aware of the ratio perse. Every time, when I have made a painting which has balance in the composition, one can overlay the golden ratios and even the flower of life and find the that key armature of the composition is sitting on these points. One time when the flower of life was over laid, the tree of life could be plotted from elements I had placed in the composition.
The artists of the past have probably known this, maybe they discovered it the same way I don't know, but by the time we reach the periods in which the given examples were made it was very much understood, and understood that you can save a lot of time working backwards. If you push lines around the canvas until it looks right, or if you draw the structure you want to end up with and place the elements within it. It is far better, a short cut.

As an extra that is not totally related, colour. Just that I already have a diagram image uploaded so will put that in. It is colour wheel that intends to show opaque colours on the outside and transparent in the center with semi transparent in the middle ring. Included are the 3 primary colours with the secondaries in between each, showing the proportions relative to position similar to a compass where you have, as example North, East, NE, NNE, NEE... Between the primaries of North and East. The opposite colour to a colour is called a complimentary colour, the opposite colour of equal contrast (or tone) is called a discordant. There are language similarities with music.
These can be found by looking at the colour directly opposite in the wheel, I am sorry my diagram drawing is not super accurate. And just like a compass, or rather as if using it like some sort of compass, if you stand in any particular point at any shade or transparency level, the colour which you plot directly opposite and the same distance from the center, will be the discord. In the diagram I have filled in these colours around the circles in the negative space. A discord will vibrate with its partner. Black and white are colourless equivalents in some ways. If you were to use the two colours interlaced in a pattern, they start to buzz optically. They will seem to shimmer or appear as a void. Especially if you say, use blue and orange (can use red too) and place an orange filter over one eye like a pair of 3d specs. Bridget Riley is famous for making black and white optical art that does similar things, except with black and white, one can start to see colour along the seams between the black and white.
Lastly, if you were to turn the colour wheel diagram 180 degrees leaving the background where it is, the circles would disappear into the background. I find that intriguing by the fact our eye sees things upside down and flips it up the right way. I would presume it is this part of the biological physics (or whatever the word is) that creates the buzzing of discords to us.

http://jandeane81.com/attachment.php?attachmentid=1375&d=1440482293

Oh and one other point about complimentaries and discords is that if you mix them, you get a grey. Well you get a black if it was to be deep red an
d deep green etc. But by mixing the two colours you get a grey. This is how you work out what colour a shadow is. You dont add black to make a shadow, you use the complimentaries mixed together. The complimentary of the colour of the object that you wish to draw a shadow on.
Sorry I could go on for hours about this. The next would be Magenta and green, and how those two seem to be in nature a LOT. For some strange reason, when mixed, they make blue. What? two secondaries mixed make a primary? yes, there is a reason on it with complimentaries cancelling each other out. But look in double shadows when light is bouncing around and you might be able to make out that often one shadow is slightly green, and the other slightly magenta. The main occurrence is in pearlescence. Abalone colouring, there is no blue in there as far as I am concerned as it is made by these two other colours.
It makes sense to a point as opaque colours are RYB Red Yellow Blue. Yet light and printing uses CMYK cyan, magenta, yellow, black. Cyan and yellow make green, so there is those colours again not to far away.

Amanda
1st July 2016, 03:10
Wonderful thread that I shall re-visit and re-read. Knowing a little about the topic of this thread - my lateral thinking leads me to think about Fractals as well as the Fibonacci sequence - and - how they are woven into the Golden Ratio/Golden Mean.

Admitting that my fine art skills are lacking and need practice I will admit to being a design artist. Love shape and colour and can spend hours perfecting circles. Lovvvvveeeeee circles - not sure why but they creep into my artwork often. Am aware that circles, in an engineering sense are the strongest shape to work with as, from a physics sense, they can withstand pressure evenly all the way around.

Will return. Much Peace - Amanda

Dreamtimer
1st July 2016, 16:48
Nothing, thanks for sharing about art and colors. I'm an undeveloped and frustrated artist. Mostly because I never had time or space. Now that I'm not Mom every day, I plan on pursuing both art and music. You help to inspire me.:group hug:

On this trip I've been reading Memory and Dream by Charles de Lint. I highly recommend it. The main character is a painter and she has a rare talent for bringing her creations to life. Literally.

Elen
1st July 2016, 16:54
Nothing, thanks for sharing about art and colors. I'm an undeveloped and frustrated artist. Mostly because I never had time or space. Now that I'm not Mom every day, I plan on pursuing both art and music. You help to inspire me.:group hug:

On this trip I've been reading Memory and Dream by Charles de Lint. I highly recommend it. The main character is a painter and she has a rare talent for bringing her creations to life. Literally.

I have been painting for years now, but not to famous yet, and not seeking it either.... there is so much more to be achieved than that. :smiley-dance013:

modwiz
1st July 2016, 20:37
I have been painting for years now, but not to famous yet, and not seeking it either.... there is so much more to be achieved than that. :smiley-dance013:

I see a lot of art from "nobody" painters among my friends and much of it I would be happy to have in my home. Paintings have an energy and aesthetic and that is what I seek from them. Bragging rights from a known or uo and coming artist that has been recognized by the "right" people is vanity and it comes with a price. I have no plans to include art in my "net worth". My worth derives form the Creator, my performance and friends. Anyone can apply the proportions of sacred geometry into their work and the effects will be there. I would gladly offer my massage work or musical service for a painting I liked. Money too if the "contract" was to mutual agreement.

bsbray
1st July 2016, 21:51
I see a lot of art from "nobody" painters among my friends and much of it I would be happy to have in my home. Paintings have an energy and aesthetic and that is what I seek from them. Bragging rights from a known or uo and coming artist that has been recognized by the "right" people is vanity and it comes with a price.

Agreed. Almost all of my favorite artwork is by people who aren't well known, and sometimes I don't even know who created it at all. My girlfriend does a lot of very delicate watercolors of trees and landscapes and I don't know much about "art theory" (if it's anything like music theory then it's not too important anyway really) but I like her work better than a lot of other things I see hanging on walls.

It all really just comes down to a matter of taste. Same as with any form of art. And if it makes you happy and you can channel things through it that you can't express to people in other ways, that's what's supposed to matter.

modwiz
1st July 2016, 22:04
Agreed. Almost all of my favorite artwork is by people who aren't well known, and sometimes I don't even know who created it at all. My girlfriend does a lot of very delicate watercolors of trees and landscapes and I don't know much about "art theory" (if it's anything like music theory then it's not too important anyway really) but I like her work better than a lot of other things I see hanging on walls.

It all really just comes down to a matter of taste. Same as with any form of art. And if it makes you happy and you can channel things through it that you can't express to people in other ways, that's what's supposed to matter.

When we see much of the commissioned artwork on public display we see chaos and ugliness. We are then told we do not have an eye for art and are ignorant. That's how the parasites work because many people just follow the lead of others "better informed".

Gurumata62
23rd December 2016, 07:16
17th century astronomer and a 21st century novelist all would write about it