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The golden ratio
“Numbers are the essence and principal of all things,” stated Greek mathematician and philosopher Pythagoras of Samos over 2,500 years ago. From this belief followed theories of mathematical proportion – and the model of the golden ratio.
The golden ratio is formed when a length is divided such that the proportion between the two segments is equal to the proportion between the longer segment and the total length (see animation, right).
a:b = (a+b):a
The ratio of a to b is approximately 1.618 to 1 – usually denoted by the Greek letter φ(phi)
Expressing the golden ratio
The icosahedron is the most complex of the five Platonic solids, occurring frequently in nature – a structure formed by many atoms combined to form a molecule.
From the icosahedron, a series of rectangles can be derived whose sides are in the golden ratio – the inner structure thus ideally represents the golden ratio.
The icosahedron symbolizes the objectives of the Holcim Awards competition because sustainability always strives for harmony – between today and tomorrow, between resources and consumption, between needs and opportunities.
 | The Holcim Awards trophy symbolizes the quest for harmony. Read more about the golden ratio, the prizes and their connection.
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| |  | | The rectangle on the right with the sides (a) and (b) is in the golden ratio if the proportions of the larger rectangle are in the golden ration (a+b):a = a:b. The "golden rectangle” is therefore always divisible into a smaller rectangle also possessing the golden ratio. |
 | | The animation shows a rectangle being divided using the golden ratio. The two objects which result are a square and a smaller rectangle that has sides that are themselves in the golden ratio. |
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