In geometry, a golden spiral is a logarithmic spiral whose growth factor is φ, the golden ratio. That is, a golden spiral gets wider (or further from its origin) by a factor of φ for every quarter turn it makes. Look at the picture.
I made some music and a video about it. More spirals and some Techno over here :
The Golden Ratio Spiral is a beautiful shape found in nature, art, and mathematics. It is based on a special number called the Golden Ratio, which is approximately 1.618. This number shows up when things grow or expand in a way that feels balanced and natural.
How the Golden Ratio Works
- The Golden Ratio in Numbers:
Imagine two numbers, where the larger number divided by the smaller one equals 1.618. For example:- If one part is 1 and the other is 1.618, they fit the Golden Ratio.
- Building the Spiral:
To create the Golden Ratio Spiral:- Start with a rectangle where the sides are in the ratio of 1:1.618.
- Divide it into a square and a smaller rectangle.
- Repeat this process with the smaller rectangle, dividing it again and again.
When you connect the corners of the squares with a curve, it forms the spiral.
Where You Can Find It
The Golden Ratio Spiral appears in many natural and human-made things:
- Nature:
- Seashells: The curve of a nautilus shell often follows the spiral.
- Sunflowers: The way seeds are packed in the center forms a spiral pattern.
- Galaxies: Some spiral galaxies have arms that follow the Golden Ratio.
- Art and Architecture:
- Famous artworks like the Mona Lisa and buildings like the Parthenon are thought to use the Golden Ratio in their design.
- It makes designs look harmonious and pleasing to the eye.
Why Is It So Special?
- Balance and Beauty: The Golden Ratio is pleasing because it feels balanced and natural. Our brains seem to like this proportion instinctively.
- Endless Growth: The spiral shows how things grow in a way that stays proportional, like plants growing new leaves or animals growing shells.
Conclusion
The Golden Ratio Spiral is a fascinating pattern that connects math, nature, and art. It’s all around us—if you look closely, you might just find it in the most unexpected places! 🌿✨
Message From One 