Sunday, September 25, 2011


Math and Art?  As I have stated before in previous posts, art and math are closely related. Math was often used in Renaissance paintings to achieve balance through the golden rule.

But, beyond that, the angle of 23.5 degrees can be found over and over in sculpture and painting.

"Vanitas" paintings , as they are known, were early 17th century still- life paintings containing symbols of death and vanity and made the viewer reflect on mortality and repentance.

These paintings are rich with 23.5 degree angles....(also known as one of the cosmic angles in Freemasonry)

The same angle can be found on  United States currency and the Great Pyramid of Giza.

Poussin used it in his self portrait.

His ring is also a pyramid. The angle from the ring to the diadem to the far left forms a 23.5 degree angle.

So why did artists, Egyptian architects and the federal reserve all use 23.5 degree angles? .....The earth's tilt of it's axis is also 23.5 degrees.

Here, the "John gesture"  -Hermetic motto "As above, So Below" also forms the angle. The hand reaches to the sky as a reference to the heavens. The math was deliberate to give reference to a supreme being.

Math and art have been used for centuries to relay messages. The next time you are in a museum, consider the angles you see . What once appeared random, you now know has a deeper meaning!


patrickgracewood said...

Theresa, I know about the golden means but was unaware of the 23.5 slant... and now must research it for myself.
It's interesting as I have a golden means proportional calipher, it usually confirms the spacing I've already chosen. Curious if it is true of 23.5

Lynne Rutter said...

neato! i love math and i love symbolism. although, the first thing I think of when I hear that particular number is Freemasons. you might like this article, Theresa:

Lynne Rutter said...

oh wait, duh, i didn't check your source. ha you beat me to it

Theresa Cheek said...

Lynne-thanks for the link....the Freemasons are definitely tied into this as well.

Patrick-glad I gave you something to think about!

Theresa Cheek said...

Lynne-that's ok. believe me, this is the dumbed down version of the whole "23.5" that is out there! So much more info to absorb.

Brillante said...

Great explanation of a complicated matter. Art appreciation is also made of layers and layers of understanding it, after the first impression.

Mark D. Ruffner said...

Like Patrick, I had never heard of the 23.5 slant. It's a fascinating posting and I'll look more into the subject, thanks to you.

kathi said...

Hi Theresa
I've never painted, not yet, but it's on the top 5 of my "new things to start" soon. I read all your new posts......I enjoy all.

Theresa Cheek said...

I enjoy your blog! Thanks for stopping by! :)

Alan said...

I can't help wondering though, if the 23.5 degree analysis is a kind of explanation-after-the-fact.

Like when Hockney 'de-mystified' Van Eyck by suggesting that he used Camera Obscura extensively. After Hockney's book came out and caused a furor, you could almost hear the collective "ahh, so *that's* the secret," as if painting is something that can be broken down into knowable chunks.

And since the Da Vinci Code it seems we all have a soft spot for the 'mystical secrets' hidden within paintings.

I mean, could it be that these artists (though no doubt familiar with the mathematical aspect of composition) simply composed intuitively, and that we are applying some sort of retrograde logic to their 'process'? I wonder if they really set about with rulers and protractors. It seems to me a very cold way of establishing a painting.

Then again, the whole step-by-step approach to Classical painting, with grisaille underpainting followed by methodical layering, seems to be an overly calculated process too in a way, yet that's exactly what they did and it produces staggering and time-tested results for sure. Maybe I'm being too pedestrian.

The composition process is something that's always been opaque to me. I tend to just throw things together in a way that I think looks nice. I know of other painters who talk about how the eye "flows" around a canvas, which is the most I've ever done in the way of structuring a painting. That's probably why it doesn't always work!

It's probably just laziness on my part, like "what, I have to go study a whole other thing now? I thought after Cézanne we could just make up our own rules." :)

A very interesting post.

Theresa Cheek said...

I totally considered the "after the fact" concept...but after reading volumes on this, I think there is something to it. In many allegorical paintings, a finger pointed upwards, rod or staff held by a figure, almost always is a 23.5 degree position. This is also one of the freemason's cosmic makes for a good read!

Alan said...

"Those who become enamored of the practice of art, without having previously applied to the diligent study of the scientific part, may be compared to mariners, who put out to sea in a ship without rudder or compass, and therefore cannot be certain of arriving at the wished-for port.
Practice must always be founded on good theory; to this Perspective is the guide and entrance, without which nothing can be well done."


Kaveri Singh said...

Really interesting thanks.

Alan said...

... I should have added that for 'Perspective' in the quote above, you could just as easily substitute any other fundamental theory, such as the mathematical theory of composition you are proposing in your article.

Theresa Cheek said...

That is a great quote! And so true, we must master the fundamentals before we can create any magic...follow the rules before we can break them.
I appreciate all of the input on this post!

Karena said...

Teresa, extremely fascinating! Regarding the after the fact thoughts; I believe there is just too much precision involved for that to be so.

I can see that you and now Lynne have both done research on this in Vanitas paintings.


Art by Karena

Anonymous said...

The tangent of 23,5 degree is ~
{ ( 1/sqrt 2 ) / golden ratio } which means that its the golden ratio of the only square inside the circle ;)

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