The golden ratio ( \( \varphi \approx 1.618 \) ) is a special mathematical constant that appears in art, architecture, and nature. One way to approximate the golden ratio is through the Fibonacci sequence.
The Fibonacci sequence is defined recursively as: $$ F_n = F_{n-1} + F_{n-2}, $$ with initial terms \( F_0 = 1 \) and \( F_1 = 1 \).
As \( n \) increases, the ratio of consecutive terms converges to the golden ratio: $$ \frac{F_n}{F_{n-1}} \to \varphi. $$
In this visualizer, you can specify the number of Fibonacci terms to compute and see the sequence along with the approximations to the golden ratio.