The difference between Algebraic number and Golden ratio

When used as nouns, algebraic number means a complex number (more generally, an element of a number field) that is a root of a polynomial whose coefficients are integers, whereas 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.

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

  1. Algebraic number as a noun (algebra, number theory):

    A complex number (more generally, an element of a number field) that is a root of a polynomial whose coefficients are integers; equivalently, a complex number (or element of a number field) that is a root of a monic polynomial whose coefficients are rational numbers.

    Examples:

    "The golden ratio (&phi;) is an [[algebraic number]] since it is a solution of the quadratic equation <math> x^2 + x - 1 = 0 </math>, whose coefficients are integers."

    "The square root of a rational number, <math>\textstyle\sqrt{\frac m n},</math> is an [[algebraic number]] since it is a solution of the quadratic equation <math>n x^2 - m = 0</math>, whose coefficients are integers."

  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"

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