The Golden Ratio in Art

    Santa Trinita Madonna
    Madonna Rucellai
    Ognissanti Madonna
    Cimabue, c1260/80
    Duccio, 1285
    Giotto, c 1310
    height-to-width ratio=1.726
    height-to-width ratio=1.552
    height-to-width ratio=1.593
    6.67% more than &phi
    4.08% less than &phi
    1.55% less than &phi
    I don't believe it!
    I don't believe it!
    Definitely possible!
    Giotto's Madonna, with rectangle defined by
    central figures
    Same Madonna, with rectangle defined by
    throne
    height-to-width ratio=1.83
    height-to-width ratio=1.78
    13% more than &phi
    10% more than &phi
    I don't believe it!
    More likely but I still don't believe it
    Jill Britton's Mona Lisa and Golden Rectangles applet
    The Last Supper
    Leonardo da Vinci, 1495-1498
    The tops of the windows defines a horizontal line.
    Does that line divide the height of the mural into Extreme and Mean Ratio?
    The rear wall (down to the bottoms of the windows) forms a rectangle. Is it Golden? Looking at vertical lines drawn around the central window, does it look as if the width of this window may have been chosen for a reason?
    I then also drew vertical lines along the other windows.
    Adoration of the Magi, 1619
    Diego Velázquez
    80.25" x 49.25"
    h/w=1.62944
    Thus h/w is only .7% off of φ
    Diagram from Bülent Atalay's
    Math and the Mona Lisa.

    In it, the painting appears to be subdivided into a smaller
    golden rectangle and a square gnomon. The smaller
    golden rectangle is then subdivided again into a third
    golden rectangle and its square gnomon; that dividing line
    is extended down through the larger square. The intersection
    point of the two red lines is sometimes referred to as the
    Golden Spot.

    My version of this same diagram, using a photo from a book on Velázquez. That photo did not have the same proportions as the painting is supposed to, which makes it impossible to draw the internal golden rectangle and square gnomon. Instead, I drew the horizontal and vertical lines through the eyes, and then measured to see how close the various rectangles were to being Golden, and the supposed squares were to being in fact square.

    • Photo of painting: h/w=1.551, 95.8% of φ, so 4.2% away from φ
    • Big square: h/w=1.019, 101.9% of 1, so 1.9% away from 1
    • Upper rectangle: w/h=1.592, 98.4% of φ, so 1.6% away from φ
    • Small square: h/w=1.066, 106.6% of 1, so 6.6% away from 1
    • Small rectangle: h/w=1.529, 94.5% of φ, so 5.5% away from φ

    Golden Ratio in Nature, again

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