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Math in Art



Perfect Proportion
Roman, after a Greek original<br><i>Doryphoros (Spear Bearer)</i>, 120-50 B.C.<br>Pentelic marble<br>Minneapolis Institute of Arts<br>The John R. Van Derlip Fund and gift of funds from Bruce B. Dayton, an anonymous donor, Mr. and Mrs. Kenneth Dayton, Mr. and Mrs. W. John Driscoll, Mr. and Mrs. Alfred Harrison, Mr. and Mrs. John Andrus, Mr. and Mrs. Judson Dayton, Mr. and Mrs. Stephen Keating, Mr. and Mrs. Pierce McNally, Mr. and Mrs. Donald Dayton, Mr. and Mrs. Wayne MacFarlane, and many other generous friends of the Institute
  Roman, after a Greek original
Doryphoros (Spear Bearer), 120-50 B.C.
Pentelic marble
Minneapolis Institute of Arts
The John R. Van Derlip Fund and gift of funds from Bruce B. Dayton, an anonymous donor, Mr. and Mrs. Kenneth Dayton, Mr. and Mrs. W. John Driscoll, Mr. and Mrs. Alfred Harrison, Mr. and Mrs. John Andrus, Mr. and Mrs. Judson Dayton, Mr. and Mrs. Stephen Keating, Mr. and Mrs. Pierce McNally, Mr. and Mrs. Donald Dayton, Mr. and Mrs. Wayne MacFarlane, and many other generous friends of the Institute

 

This marble figure is a copy of a bronze sculpture made by the Greek artist Polykleitos about 440 B.C. To create this statue of an ideal human form, Polykleitos developed a mathematical system of proportions that brought sculpture to a new level. He called his system the Canon (meaning “rule”).

For Greek artists, the harmony, order, and balance they saw in nature was the standard of perfection they aimed for in art. In his Canon, Polykleitos set forth the mathematical relationships between different body parts that would result in a perfect human form. Historians think he based his system on the concept of symmetria, or harmony between the parts and the whole. They believe he may have used the proportions of a finger to determine the proportions of all the body's parts to each other and to the body as a whole.

Polykleitos sculpted his ideally proportioned Doryphoros (Spear Bearer) in a pose that looks natural but is not (try it out yourself). The figure stands in what is called the chiastic (ki-AZ-tic) pose. His tensed right leg bears his weight, while the left leg is relaxed. His left arm (now broken) is bent to hold a spear, while the right is relaxed. This balance of tension and relaxation on opposite sides makes the body look natural and gives a sense of movement though the figure is at rest.

The original bronze Doryphoros no longer exists. The version in the MIA’s collection was made by a talented Roman sculptor who copied the masterpiece, taking careful measurements to reproduce its proportions.


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1. Architects in ancient Greece used their knowledge of mathematical proportion to create balance and symmetry in this famous building, called the Parthenon. Photo: Simon music, Creative Commons License
2. This entrance to the MIA resembles the Parthenon but has different proportions.
3. The 20th-century cubist painter Juan Gris used geometric proportions and mathematical relationships to create visual harmonies strikingly different from the statues of Polykleitos.
Juan Gris, Spanish, Still Life, 1917, oil on panel, Minneapolis Institute of Arts, The John R. Van Derlip Fund

 

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March 2010