The difference between Algebraic integer and Golden ratio

When used as nouns, algebraic integer means a real or complex number (more generally, an element of a number field) which is a root of a monic 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 integer and Golden ratio

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

    A real or complex number (more generally, an element of a number field) which is a root of a monic polynomial whose coefficients are integers; equivalently, an algebraic number whose minimal polynomial (lowest-degree polynomial of which it is a root and whose leading coefficient is 1) has integer coefficients.

    Examples:

    "A Gaussian integer <math> z = a + i b </math> is an [[algebraic integer]] since it is a solution of either the equation <math> z^2 + (-2 a) z + (a^2 + b^2) = 0 </math> or the equation <math> z - a = 0 </math>."

  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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