The difference between Golden ratio and Irrational number

When used as nouns, golden ratio means the irrational number (approximately 1.618), usually denoted by the greek letter φ (phi), which is equal the sum of its own reciprocal and 1, or, equivalently, is such that the ratio of 1 to the number is equal to the ratio of its reciprocal to 1, whereas irrational number means any real number that cannot be expressed as a ratio of two integers.

check bellow for the other definitions of Golden ratio and Irrational number

  1. Golden ratio as a noun (geometry):

    The irrational number (approximately 1.618), usually denoted by the Greek letter φ (phi), which is equal the sum of its own reciprocal and 1, or, equivalently, is such that the ratio of 1 to the number is equal to the ratio of its reciprocal to 1.

    Examples:

    "synonyms: golden number"

  1. Irrational number as a noun (mathematics):

    Any real number that cannot be expressed as a ratio of two integers.

    Examples:

    "The square root of a positive integer is an [[irrational number]] unless the positive integer is a perfect square, in which case the square root will also be a positive integer."

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