The difference between Algebraic number and Phi
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 phi means φ, the 21st letter of the euclidean and modern greek alphabet, usually romanized as "ph".
check bellow for the other definitions of Algebraic number and Phi
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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 (φ) 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."
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Phi as a noun:
Φ, the 21st letter of the Euclidean and modern Greek alphabet, usually romanized as "ph".
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Phi as a noun (mathematics):
The golden ratio.
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Phi as a noun:
A visual illusion whereby a sequential pattern of lights produces a false sense of motion.