The golden mean
Creating good compositions should not be guesswork
“Without mathematics there is no art,”
~ Luca Pacioli, a contemporary of Da Vinci.
“Without mathematics there is no art,”
~ Luca Pacioli, a contemporary of Da Vinci.
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What is the Golden Mean?
The Golden Mean is the Ratio most pleasing to the eye and therefore by using it in your artworks you can create good compositions. The Golden Mean is the divine proportion or golden section is a special number approximately equal to 1.618. It appears regularly in living things but also is used in art and architecture. |
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EXAMPLES OF THE GOLDEN MEAN
How to determine the Golden Mean
The Golden Number is 1.6182… The actual number is very long, but we will refer to it as 1.6182. It is actually a ratio and is also referred to as the golden ration.
To explain how the ration works, consider a line 3cm long:
If this line was broken into two segments like this:
Then the ration between the lengths of the two segments would be:
1.5/1.5 = 1, also written as 1:1 (The first segment is the same length as a the second segment
If the line was broken like this:
Then the ratio between the lengths of the two segments would be
2/1 = 2, also written as 2:1 (the first segment is twice as long as the second segment)
If the line was broken into segments according to the golden ration, the ration would be 1.6182:1 (the first segment is 1.6182 times longer than the second segment).
To calculate how long each segment is, we divide the total length by the number:
3 divided by 1.6182 = 1.85cm
So the first segment will be 1.85cm and the second segment will be what’s left of the 3cm
(3-1.85 =1.15)
WATCH
http://www.youtube.com/watch?v=gKzcDZswj5A&feature=related
http://www.youtube.com/watch?v=fmaVqkR0ZXg
http://thevirtualinstructor.com/composition3.html
The Golden Number is 1.6182… The actual number is very long, but we will refer to it as 1.6182. It is actually a ratio and is also referred to as the golden ration.
To explain how the ration works, consider a line 3cm long:
If this line was broken into two segments like this:
Then the ration between the lengths of the two segments would be:
1.5/1.5 = 1, also written as 1:1 (The first segment is the same length as a the second segment
If the line was broken like this:
Then the ratio between the lengths of the two segments would be
2/1 = 2, also written as 2:1 (the first segment is twice as long as the second segment)
If the line was broken into segments according to the golden ration, the ration would be 1.6182:1 (the first segment is 1.6182 times longer than the second segment).
To calculate how long each segment is, we divide the total length by the number:
3 divided by 1.6182 = 1.85cm
So the first segment will be 1.85cm and the second segment will be what’s left of the 3cm
(3-1.85 =1.15)
WATCH
http://www.youtube.com/watch?v=gKzcDZswj5A&feature=related
http://www.youtube.com/watch?v=fmaVqkR0ZXg
http://thevirtualinstructor.com/composition3.html
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PRACTICE ACTIVITY 1
1. Draw a line 8cm long 2. 2. Calculate how to separate this line using the golden ration and mark on the line. GOLDEN RECTANGLES Rectangles are shapes where the width is longer than the height or vice versa. A golden rectangle has a shape where one side is 1.6182 times longer than the other side. PRACTICE ACTIVITY 2: Drawing a Golden Rectangle 1. Draw a horizontal line 10cm long. 2. In this case, we will make the vertical lines shorter than the horizontal lines. To calculate the length of the vertical line, divide the length of the line (10cm) by the golden number. 3. Use the vertical length calculated to complete the rectangle. Shapes associated with the golden number are found in nature |
Golden rectangles and golden ratios are used in art for their aesthetic (pleasing to the eye) appeal. A golden rectangular canvas may be used.
The Painting area may be broken up into three golden segments, with feature of interest along the golden lines. Figure 1: A golden rectangle with golden lines showing interesting features could be framed within these segments, or distinguishing components placed along the lines.
The Painting area may be broken up into three golden segments, with feature of interest along the golden lines. Figure 1: A golden rectangle with golden lines showing interesting features could be framed within these segments, or distinguishing components placed along the lines.
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PRACTICE ACTIVITY 3: Finding the golden lines in a golden rectangle
1. Draw a horizontal line of 12cm.
2. Calculate the length of the vertical line and complete the rectangle.
3. You are now going to break both the horizontal and the vertical line into golden segments.
(a) To break the horizontal line, divide 12cm by the golden number. Measuring from left to right, mark a spot on your horizontal line equal to the number calculated.
(b) The line could also be split in the other direction. To do this, measure from right to left and mark on your horizontal line equal to the number calculated.
(c) Now repeat the same process with the vertical line. Divide the length of the vertical line by 1.6182, and mark this distance measuring first from top to bottom and secondly from bottom to top.
1. Draw a horizontal line of 12cm.
2. Calculate the length of the vertical line and complete the rectangle.
3. You are now going to break both the horizontal and the vertical line into golden segments.
(a) To break the horizontal line, divide 12cm by the golden number. Measuring from left to right, mark a spot on your horizontal line equal to the number calculated.
(b) The line could also be split in the other direction. To do this, measure from right to left and mark on your horizontal line equal to the number calculated.
(c) Now repeat the same process with the vertical line. Divide the length of the vertical line by 1.6182, and mark this distance measuring first from top to bottom and secondly from bottom to top.
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Golden Ratio
Components within a painting or photograph may be broken up using the golden ratio. The Golden Stairs (1880), by Edward Burne Jones. PRACTICE ACTIVITY 4: Measure & Sketch - Measure the lengths of the gowns from the sash below the breast, to the bottom hem The golden number point should be at the women’s knees. Measure to find out. - Sketch the object in front of you. Show a feature broken up using the golden ratio. PRACTICE ACTIVITY 5: Find the Golden Ratio
- Find two painting examples that are based on the Golden Mean. - Find two advertising/man made object examples that uses the Golden Mean - Find two examples in nature of the Golden Mean Save the images, print and stick in your sketchbook. Draw over each image to demonstrate where the golden mean has been used. (BE CAREFUL NOT to change the proportions of your images as this may interfere with the divine proportions) |
ACTIVITY 6: Dorrit Black and the Golden Mean
- Identify how The Golden Mean has been used in the following paintings. The first one is completed for you.
Save the images, print and stick in your sketchbook. Draw over each image to demonstrate where the golden mean has been used. (BE CAREFUL NOT to change the proportions of your images as this may interfere with the divine proportions)
