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 May 30th, 2013, 03:46 AM #1 Newbie   Joined: May 2013 Posts: 2 Thanks: 0 Proportions in painting Hi all, my first time here, I am a painter and I work very intuitively but find much of my spatial issues in my painting reflect classical proportions or other ratios. Sometimes its a bit surprising! In the last few years I have settled on a 240 cm x 290 cm format for my paintings, I wondered if there is anything mathematically significant about the proportions of this? And, I suspect that those here might have interesting things to say about this? Curious, A
 July 8th, 2013, 12:51 PM #2 Senior Member   Joined: Sep 2012 From: British Columbia, Canada Posts: 764 Thanks: 53 Re: Proportions in painting The only number that seems to be significant in art, in my opinion, is the golden ratio, which equals approximately 1.618034. In fact, if you take a look at some historical buildings and monuments, you would find that most of them incidentally have the golden ratio included in them! As for your proportions, it is purely a matter of opinion if it looks good to you, or not.
July 8th, 2013, 02:48 PM   #3
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Re: Proportions in painting

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 Originally Posted by anthonyhark In the last few years I have settled on a 240 cm x 290 cm format for my paintings, I wondered if there is anything mathematically significant about the proportions of this?
Well, the continued fraction for 240/290 is [0; 1, 4, 1, 4], which says that
1:1
4:5
5:6
24:29
are the 'best' approximations to your chosen ratio, in terms of having small numerator and denominator. You'll notice that until the last these alternate between overestimates and underestimates, so you can see the process as improving on itself until it hits on your ideal ratio.

In a less aesthetic sense you might see the ratios 1:1, 4:5, and 5:6 as substitutes for your size if you were forced to use pre-sized canvasses, papers, etc..

Mathematically, your number is close to sqrt(e)/2 which is nice. If you take the sum of the two ratios (24/29 + 29/24) you get (roughly) the golden ratio times the third root of 2.

 July 9th, 2013, 12:40 AM #4 Newbie   Joined: May 2013 Posts: 2 Thanks: 0 Re: Proportions in painting Wonderful feedback! Thank you! That's very interesting and will help me think about perhaps scale both up and down in size. I am so glad this forum exists! A
 July 9th, 2013, 05:40 AM #5 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 931 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Proportions in painting One more thing. If the continued fraction was [0, 1, 4, 1, 4, 1, 4, 1, 4, ... ] instead, you would have $2\sqrt{2}-2$ which as a quadratic irrational is again similar to phi. The best approximations to this are 1 2:3 3:4 4:5 5:6 24:29 29:35 140:169 169:204 816:985 which might provide scaling opportunities in the other direction.
July 20th, 2013, 02:16 PM   #6
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Re: Proportions in painting

Quote:
 Originally Posted by CRGreathouse One more thing. If the continued fraction was [0, 1, 4, 1, 4, 1, 4, 1, 4, ... ] instead, you would have $2\sqrt{2}-2$ which as a quadratic irrational is again similar to phi. The best approximations to this are 1 2:3 3:4 4:5 5:6 24:29 29:35 140:169 169:204 816:985 which might provide scaling opportunities in the other direction.
Seriously cool.

 February 2nd, 2014, 11:03 AM #7 Newbie   Joined: Jan 2014 Posts: 11 Thanks: 0 Re: Proportions in painting Awesome info!! Didn't Da Vinci also use some kind of ratios in his paintings?
February 2nd, 2014, 05:58 PM   #8
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Re: Proportions in painting

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 Originally Posted by Noritaka Awesome info!! Didn't Da Vinci also use some kind of ratios in his paintings?
As I understand it, his Vitruvian Man was a study in "how many ways can we use the ratio phi?", where phi = (1 + sqrt(5))/2 is a quadratic irrational similar to the one mentioned above.

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