• 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 unpeeled banana will usually be a Fibonacci number—and the number of ridges on a peeled banana will usually be a larger Fibonacci number.

    1. The Fibonacci sequence starts with 0 and 1, and proceeds by adding the previous two numbers. What are the first 10 Fibonacci numbers?

      0
      1
      1 (0+1)
      2 (1+1)
      3 (2+1)
      5 (3+2)
      8 (5+3)
      13 (8+5)
      21 (13+8)
      34 (21+13)

    2. The so-called "golden rectangle" has appeared in architecture for centuries. Perhaps the most famous golden rectangles are the proportions of the Parthenon in Athens, Greece. What do you think the proportions of a golden rectangle are?

      A golden rectangle uses the golden ratio: 1 (short side) by 1.618 (long side).

    3. You ARE a golden ratio! Where do Fibonacci numbers appear on the human body?

      Fibonacci sequences are everywhere in your body. Look at yourself in the mirror: two eyes, two ears, two nostrils in one nose, five fingers on an arm with three segments (hand, forearm, upper arm) . . . Fibonacci numbers are even encoded in your DNA. Each DNA molecule is 34 angstroms long and 21 angstroms wide: a golden ratio.

      Don't look too closely, though! Just like the four-leaf clover, there are plenty of natural sequences that do not correspond to the golden ratio. (A full set of permanent teeth, for instance, is 32—not a Fibonacci number. Your heart has four chambers—not a 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.