Fibonacci Sequence Generator

Efficient Iteration, Not Slow Recursion

The Fibonacci sequence's textbook definition is recursive, but calculating it that way directly recalculates the same values repeatedly, becoming impractically slow as term count grows. This generator iterates forward, storing each value once, producing the identical mathematically correct sequence far more efficiently.

The Golden Ratio Connection Is Real, Not Approximate

As you move further into the sequence, the ratio between consecutive terms converges ever closer to the golden ratio (φ ≈ 1.618033...) -- a genuine, well-established mathematical relationship that becomes more precise with more terms, not a rough approximation that only works for small numbers.