• The "golden ratio" is a unique mathematical relationship. Two numbers are in the golden ratio if the ratio of the sum of the numbers (a+b) divided by the larger number (a) is equal to the ratio of the larger number divided by the smaller number (a/b).

    The golden ratio is about 1.618, and represented by the Greek letter phi, Φ.

    The golden ratio is best approximated by the famous "Fibonacci numbers." Fibonacci numbers are a never-ending sequence starting with 0 and 1, and continuing by adding the previous two numbers. The next numbers in the Fibonacci sequence, for instance, are 1,2,3, and 5.

                        0
                        1
                        1 (0 1)
                        2 (1 1)
                        3 (2 1)
                        5 (3 2)

    The ratios of sequential Fibonacci numbers (2/1, 3/2, 5/3, etc.) approach the golden ratio. In fact, the higher the Fibonacci numbers, the closer their relationship is to 1.618.

                        2/1 = 2
                        3/2 = 1.5
                        5/3 = 1.66666666 . . .

    The golden ratio is sometimes called the "divine proportion," because of its frequency in the natural world. The number of petals on a flower, for instance, will often be a Fibonacci number. The seeds of sunflowers and pine cones twist in opposing spirals of Fibonacci numbers. Even the sides of an unreeled banana will usually be a Fibonacci number—and the number of ridges on a peeled banana will usually be a larger Fibonacci number.

  • Term Part of Speech Definition Encyclopedic Entry
    approximately Adjective

    generally or near an exact figure.

    Fibonacci numbers Plural Noun endless sequence of numbers starting with 1, 1, 2, 3, where each term is the sum of the previous two.
    golden ratio Noun

    mathematical relationship where the ratio of the sum of the numbers (a, b) divided by the larger number (a) is equal to the ratio of the larger number divided by the smaller number (a/b). The golden ratio is about 1.618, and represented by the Greek letter phi, .

    mathematics Noun

    study of the relationships between numbers, quantities, shapes, and spaces.

    ratio Noun

    relationship between numbers or numerical values.

    sequence Verb

    to put in order.

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