 Many paintings as well as some of the world's most beautiful buildings,
including the Parthenon in Athens, derive much of their artistic appeal from mathematics. In particular, they make use of rectangular shapes based on a proportion of height to
width known as the golden ratio, or the golden mean. Each rectangle has its sides in the proportion of 1 to 1.618033989. Like the number pi  , which expresses the mathematical relationship between the diameter of a circle and the circle's circumference, this golden ratio number - often denoted by the Greek letter phi  - is a never-ending decimal. It also has some remarkable properties.If a golden ratio rectangle is divided into a square and a rectangle, the smaller rectangle repeats the same proportion. If the smaller rectangle is divided again, the same is true of the yet smaller rectangle, and so on. If corresponding points on the rectangles are joined in the way pictured above, the result is what mathematicians call a logarithmic spiral - exactly the same spiral as the shell of a snail. Uniquely, too, the golden ratio is the only number that can be squared by adding 1 to it ( 2 = + 1) and the only number that can be turned into its own reciprocal (1/) just by subtracting 1 (that is 1/ = - 1).Source Unknown |