Fibonacci Spiral And The Golden Ratio
This animation builds the Fibonacci sequence term by term, then draws matching squares that tile together into a spiral. Alongside, a column of consecutive-term ratios is computed live, visibly converging toward 1.618..., ending with the closed-form golden ratio formula. It helps students connect a simple recursive number pattern to a geometric spiral and an irrational constant, making the idea useful for algebra and geometry classes introducing sequences and limits.
16:9 · Preview before teaching · automatic layout checks do not establish subject accuracy
The prompt that made it
The Fibonacci sequence and the golden ratio: title, the sequence 1,1,2,3,5,8,13 below it, a spiral of squares, and a column of ratio calculations converging to phi with the final formula.
Make the next one in this series
- Derive Binet's formula for the nth Fibonacci number step by step
- Show how the golden ratio appears in the pentagon and pentagram
- Compare Fibonacci spirals to real nautilus shell and sunflower seed patterns
