Fibonacci numbers: a mysterious sequence in mathematics and nature 🌀

0, 1, 1, 2, 3, 5, 8, 13, 21... These numbers continue to fascinate. Even in 2025. Each one is the sum of the two preceding ones. An infinite mathematical melody. It was named after the Italian Fibonacci. In 1202, he introduced this beauty to Europe through the book "Liber Abaci".

Golden Ratio: something like a natural code ✨

This is where the real magic happens. The connection with the golden ratio (~1.618033). You divide a number by the previous one — you get approximately this value. It seems almost mystical. Binet's formula gives the n-th number through the golden ratio: F(n) = (φ^n - (1-φ)^n)/√5.

This strange pattern is everywhere around. Galactic spirals 🌌. Hurricanes. Seeds in sunflowers 🌻. Leaves on stems. Nature seems to know math better than we do.

From ancient times to new technologies 🚀

It all started in ancient India. Now, in 2025, the influence is only growing. Modern computation algorithms have become smarter. Dynamic programming. Fast doubling. Matrix exponentiation. Complexity — Θ(logn). Fast even for huge numbers.

Architects still love the golden ratio. From Greek temples to the skyscrapers of our time. In music too. Bach seemed to know. Our contemporaries also feel this harmony 🎵.

Traders and Their Love for Fibonacci 📊

Traders in 2025 are looking for Fibonacci support and resistance levels. Entry points. Exit points. It doesn't always work, to be honest. It needs to be combined with other tools.

These strange correction levels: 38.2%, 50%, 61.8%. In the 2025 cryptocurrency market, it seems to help. Sometimes. In such instability, any hint is valuable 🔥.

Science looks further 🔮

Scientists do not stop. They find Fibonacci even in quantum systems. It's not entirely clear how this works, but it looks promising for quantum computing.

Biotech is also interesting. Cells grow and divide according to these rules. They create biomaterials by copying nature 🧬. They imitate, but have not yet achieved its perfection.

Not just numbers. Some universal language of the cosmos. From atoms to galaxies. From cells to symphonies. Mathematics and nature intertwine in a dance that we are just beginning to understand 🌕.