Are There Rules in Art?  Geometrical Perspective 
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Geometrical Perspective.
Geometrical perspective creates a realistic threedimensional view on a twodimensional plane. It is said to have been invented at the time of renaissance. However, perspective was discovered rather than invented, since perspective is due to the fact that the apparent size of objects diminishes with their distance from the observer.
Horizontal parallel lines such as borders of a road or the top and bottom of a wall converge at a point at the horizon. All objects situated above the level of our eyes are seen above the horizon, and those below it are below the horizon. (fig. 17)
Fig. 17
The green and yellow lines connect at the horizon, (red) which marks the eye level of the observer.
Fig. 18 illustrates the effects of perspective on a set of shelves, and one of horizontal circles, at various heights. The uppermost shelve and circle are seen from below. The black circle indicates the height of the Horizon.
Ever since Cézanne, painters have ignored or stretched the rules of perspective, stressing the flatness of the canvas, and so can we (Fig. 19). Still, when we paint a landscape, we include or imply a horizon. Where should we put it? Of the three seascapes (after Canaletto) on fig. 20, the middle one is the least interesting. It is not usually best not to divide a picture by the middle into sets of equal size. (See, however, Fig, 7!)
. Fig, 18
Fig 19. (K.H.)
The golden rule is often cited as a prescription for harmonious size relations in a picture. If a length is to be divided into two segments, or a rectangle is defined by the length of its height and width, the ratio of the larger segment or side to the smaller one should be equal to the ratio of the sum of both to the larger fragment or side. This ratio turns out to be about equal to 1.6. Measurements of the height and width of common commercial canvases show that they have ratios close to this number. In fig. 20, the ratios of the total height to the mayor field are 1.4 for the upper and lower picture, and 2.0 for the middle, which is less satisfactory. In fig. 21, the ratio of height to width is also 1.4. While we should not worry too much about these numbers, it is advisable that lines and areas should not be divided into two equal parts.
Fig 20 (fragments from a painting of Canaletto).
Fig. 21 (Leonardo da Vinci)
This beautiful portrait by Leonardo da Vinci of Emilia Gallerani, mistress of Lodovico Sforza, is painted with a limited set of colors. The contours are simplified to elegant arcs, and a drop shape is used repeatedly in the construction of the painting. (Fig. 22). The black hair band on the forehead is seen as a straight line; it is at the eye level of the painter. The ermine has symbolic connotations, which, however, seem to be controversial.
Fig. 22
