Leonardo DaVinci
"...no human inquiry can be called science unless it pursues its path through mathematical exposition and demonstration."� -Leonardo DaVinci
� Sketch of an Old Man
One can see the symmetry in a face Leonardo da Vinci's drawing of an old man.� The
artist has overlaid the picture with a square subdivided into rectangles, some of which
approximate golden rectangles.
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The Annunciation
Divide this picture into a square on the left and another on the right.� These lines mark out two golden section rectangles as the parts remaining after a square has been removed. Also mark in the lines across the picture which are 0.618 of the way up and 0.618 of the way down it as well as the vertical lines which are 0.618 of the way along from both ends.� One can see that these lines mark out significant parts of the picture, such as the angel and the woman, or go through important objects.
Madonna with Child and Saints
This pictures is in a square frame.� The golden section lines in it are 0.618 of the way down and up the frame and 0.618 of the way across from the left and from the right.� These lines mark out significant parts of the picture, such as the two saints, the Madonna, and the baby Jesus in the center.
The Mona Lisa
Draw a rectangle around the Mona Lisa's face and the resulting quadrilateral is the golden rectangle. Subdividing this rectangle using the line formed by using her eyes as a horizontal divider and one further divides the golden rectangle.� Also, the dimensions of the painting itself form a golden rectangle. In addition, the three main areas of the Mona Lisa, the neck to just above the hands, and the neckline on the dress to just below the hands form golden rectangles. Click here to see a picture of the Mona Lisa with golden rectangles drawn in.
DaVinci extensively studied the proportions of the human body.� The
drawing to the left is shown to illustrate the use of the golden section.
The height of a person was divided into two line segments, the dividing point being the person's navel. Leonardo da Vinci drew his portraits so that the distance from the soles of their feet to their navel, then divided by the distance from their navel to the top of their head was equal to 0.618, the golden mean.
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St. Jerome
The golden section is present in this unfinished work.� St. Jerome fits into a golden rectangle.� It is thought that this wasn't an accident, but that DaVinci purposely made the figure to conform to the golden section because of his interest and use of mathematics in many of his works and ideas.
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