2phi2

2phi2 is a mathematical expression that can denote the quantity two times the square of the golden ratio, written as 2φ^2. The symbol φ refers to the golden ratio, φ = (1+√5)/2, an irrational number that arises in geometry and number theory.

Since φ^2 = φ + 1, it follows that 2φ^2 = 2φ + 2. Using φ = (1+√5)/2, this evaluates to 3 + √5, which is approximately 5.2360679.

Algebraically, the quantity y = 2φ^2 satisfies the quadratic equation y^2 − 6y + 4 = 0. Its roots are 3 ± √5, and 2φ^2 corresponds to 3 + √5. Thus 2φ^2 is a quadratic irrational with degree two over the rationals.

In mathematical contexts, 2φ^2 can appear in formulae involving the golden ratio and its powers, and it relates to linear recurrences and closed forms for Fibonacci numbers.

Because the string "2phi2" can have other interpretations in other domains, the meaning is context dependent. Without additional specification, it is common to interpret it as twice the square of the golden ratio, 2φ^2.