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+The golden ratio, often denoted by the Greek letter phi, is a special number approximately equal to 1.618. It appears throughout mathematics, art, and nature. Two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. The golden ratio is an irrational number that is a solution to the quadratic equation x squared equals x plus one. The golden ratio is closely related to the Fibonacci sequence. As Fibonacci numbers increase, the ratio of consecutive Fibonacci numbers approaches the golden ratio. For example, 8 divided by 5 equals 1.6, and 13 divided by 8 equals 1.625, which are close approximations. The golden ratio appears in the geometry of pentagons and in the arrangement of leaves and petals in many plants.