PaintsightBoth split the canvas with two lines across and two lines down. The rule of thirds puts them a third of the way in from each edge; the golden section puts them 38.2% of the way in, a little nearer the center. Neither has the evidence its fans claim, but both are a quick way to get the horizon and the main shapes off the middle.
Where the lines fall
For the rule of thirds, divide each side into three equal parts. For the golden section, divide each side so the longer part is 1.618 times the shorter, the golden ratio. That puts the lines at 38.2% and 61.8% of the way across and down.
Measured from the left or top edge of the canvas:
| Side | Rule of thirds | Golden section |
|---|---|---|
| 16 in | 5.33 and 10.67 in | 6.11 and 9.89 in |
| 20 in | 6.67 and 13.33 in | 7.64 and 12.36 in |
| 30 cm | 10 and 20 cm | 11.46 and 18.54 cm |
| 40 cm | 13.33 and 26.67 cm | 15.28 and 24.72 cm |
On a 16 × 20 in canvas the two systems are less than an inch apart. The drawing grid maker draws either one on your reference photo, fitted to your canvas size: choose Rule of thirds or Golden section under Composition guide.
Where the rule of thirds comes from
The name comes from the engraver John Thomas Smith, in Remarks on Rural Scenery (1797). He had noticed that in Rembrandt's pictures the main light usually sits near the middle, with more than two thirds of the picture in shadow. He proposed dividing other things the same way: the sky at about two thirds of a landscape or about one third, two thirds water to one third land, a long wall broken by something in front of it. He found two to one "a much better and more harmonizing proportion, than the precise formal half".
Smith's rule is about proportion: how much sky, how much shadow, where to break a long line. He says nothing about a grid or about putting the subject where lines cross. That reading came later.
Where the golden section comes from
Euclid described cutting a line so that the whole is to the longer part as the longer part is to the shorter, and called it division in extreme and mean ratio. Luca Pacioli called it the divine proportion in De Divina Proportione (1498), which Leonardo da Vinci illustrated. The name "golden section" is far younger than the idea: it seems to have first appeared in print in 1835, in a German mathematics book by Martin Ohm.
What the evidence says
The golden ratio in old paintings. The mathematician George Markowsky checked the common claims in "Misconceptions about the Golden Ratio" (1992). The idea that Leonardo built his paintings on it rests on his drawings for Pacioli's book; the biographies Markowsky consulted show no sign of it anywhere else. The golden rectangle some books draw around Leonardo's Saint Jerome leaves the saint's right arm sticking out, and Leonardo met Pacioli 13 years after painting it. Markowsky shows other diagrams that find the ratio by leaving out whatever doesn't fit.
Golden rectangles as the most pleasing shape. The claim rests largely on Gustav Fechner's experiments in the 1860s. His most chosen rectangle was the golden one, but 76% of choices were spread over three shapes, with height to width of 0.57, 0.62 and 0.67. In Markowsky's informal tests, audiences shown 48 rectangles most often picked one of 1.83 to 1, and most people couldn't tell apart rectangles between 1.6 and 1.7.
The rule of thirds in paintings. In 2014, researchers at the University of Jena used a computer model of visual salience to find the most eye-catching parts of 727 paintings by well-known artists. The paintings scored about as low on the rule of thirds as photographs that don't follow it, and the eye-catching areas leaned toward the center. Portraits scored slightly higher, probably because painters tend to put the face high in the picture, near the upper third line.
How to use them
- Place the big divisions: the horizon, the edge of a large shadow, a tree trunk, the main mass. That was Smith's point: unequal areas instead of halves.
- Try both on the reference. Put the guides on your photo and crop until the main lines sit near one set. If the subject looks pushed toward the edge on thirds, the golden section gives it a little more room.
- Don't put the focal point on an intersection by habit. Put it where the design needs it; see the focal point in painting.
- Check the result in values. The lines place shapes, but they can't tell you whether the lights and darks hold together. Make a notan or a value study of the cropped photo before you paint.
Sources
- John Thomas Smith, Remarks on Rural Scenery, London, 1797, "Of Light and Shade", pages 15 to 17. Internet Archive, from the Getty Research Institute's copy.
- George Markowsky, "Misconceptions about the Golden Ratio", The College Mathematics Journal 23, no. 1 (1992), pages 2 to 19. For Euclid's definition, the history of the name, the Leonardo claims, Fechner's experiments and Markowsky's own tests.
- Seyed Ali Amirshahi, Gregor Uwe Hayn-Leichsenring, Joachim Denzler and Christoph Redies, "Evaluating the Rule of Thirds in Photographs and Paintings", Art & Perception 2 (2014), pages 163 to 182. Open access.
