When are two quantities 'a' and 'b' said to have a "golden ratio"?

Golden ratio is a mathematical ratio. Two quantities "a" and "b" are said to have golden ratio if their ratio is equal to the ratio of their sum to the larger of the two. It is an irrational number which means that its value cannot be determined exactly. It is approximately equal to 1.6180339887....It may look absurd but the fact is that this ratio appeals to the architects and the artists a lot. It is believed that this ratio is very pleasant to the eyes.

Golden ratio has been observed in the works of Leonardo da Vinci.

Golden ratio is found in nature also, for example, in arrangements of parts of plants such as the leaves and the branches along the stems in the plants, arrangement of veins in the leaves, branching of the nerves and the veins in animals etc.

Golden ratio is used in the fields as diverse as music, financial markets, arts, architecture, design and optimization.