The Golden Ratio in Art The golden rectangle (a rectangle whose sides are in a golden ratio) has been recognized as aesthetically pleasing. 3x5 notecards are a golden ratio. So are playing cards, windows, postcards, and credit cards. In the early 1900s, German psychologist Gustav Fechner measured the dimensions of thousands of common rectangles and found that their ratios tended to be close to the golden ratio. He then tested hundreds of people on their favorite (or most pleasing) rectangle, and found that the average choice tended to be very close to the golden ratio. Ad agencies use it to promote all sorts of products. The Golden Ratio in Architecture The golden ratio has long been a tool for architects. One of the most famous building using the golden ratio is the United Nations building, designed by the French architect Le Corbusier. Le Corbusier was deeply dedicated to the use of the golden ratio in his buildings, and incorporated it into many of his Parisian Villas. Unfortunately, little is know (or can be found) about his reasons, only that he favored the golden ratio. The golden ratio is by no means limited to modern structures: The Great Pyramid at Gizeh, built 4600 years ago, uses the golden ratio in both its outer dimensions and its layout. The surface triangles on the exterior of the pyramid are believed to be shaped after a golden rectangle cut along the diagonal and connected along the long side. The floor plan of the burial chambger has three large rectangles inset: one is a double square, one is a golden rectangle, and one is a double golden rectangle. The Parthenon also uses the golden ration and was built about 150 years before Euclid was born. The floor plan of the tomb of King Ramses IV also used the golden ratio. The Golden Ratio in Paintings Leonardo da Vinci called the the golden ratio the "divine proportion", and used it in many of his paointings, as did many of the other great painters, both in exterior dimensions and in the underlying grid. An example of the later is Giotto's Ognissanti Madonna. The implied border around the Virgin Mary is a golden ratio. Click on the image on the right for a visual demonstration. Piet Mondrian is probably the most widely known of the artists who deliberately incorporated the golden ratio; he avoided any suggestion of reproducing the material world. Instead using he expressed ultimate harmony and equilibrium through a style he called neoplasticism. His Composition with Gray and Light Brown is on the left. Mondrian's Composition with Gray and Light Brown Giotto's Ognissanti Madonna