Fibonacci Spiral And The Golden Ratio
This animation builds the Fibonacci spiral by drawing squares whose side lengths follow the Fibonacci sequence, arranging them so each new square attaches to the growing rectangle. A smooth arc traced through each square reveals the spiral, while the ratio of consecutive Fibonacci numbers is shown converging to the golden ratio, phi. Useful for students exploring number sequences, geometric growth, and the connection between algebra and natural patterns.
16:9 · every frame verified for overlaps, spacing and edges before rendering
The prompt that made it
Visualize the Fibonacci spiral with golden ratio
Make the next one in this series
- Show how the golden ratio appears in a regular pentagon's diagonals
- Animate the golden rectangle construction using a compass and straightedge method
- Compare the Fibonacci spiral to logarithmic spirals found in nature like shells
