Surprise with the golden ratio in nature

We can observe the expression of the Fibonacci number sequence and the ratio of natural gold, from galaxies to animals and plants.

The ratio of gold in nature

The universe is chaotic and unstable, but it is also a material world with a high level of organization, and is bound by mathematical rules. One of the manifestations of these basic rules is through the golden ratio.
The golden ratio is usually represented by the letter ϕ (phi) in Greek.It is directly associated with the Fibonacci number sequence (the sequence begins with 0 and 1, the number behind is the sum of 2 preceding numbers: 0 + 1 = 1, 1 + 1 = 2, 1 + 2 = 3 , 2 + 3 = 5, 3 + 5 = 8, .) If the previous number is divided by the following number in the Fibonacci sequence (1: 1 = 1; 2: 1 = 2; 3: 2 = 1.5; 5: 3 = 1,666; 8/5 = 1,6; 13/8 = 1,625 .), the result will be closer to the irrational number 1.6180339887 . This number is the golden ratio.

When the logarithmic spiral is in contact with the edges of a series of consecutive golden rectangles, it is called the Golden Spiral.
Vi Hart, the mathematician, said that similar shapes The yellow spiral in nature is very rich, the most prominent are shells, ocean waves, spider webs and even chameleon tails.

Galaxy Messier 83, 15 million light-years from Earth, has the same shape as the Golden Spiral.(Photo: ESA)

The golden spiral is expressed through the chameleon's tail.(Photo: Ryan M. Bolton / Shutterstock)

Many types of snail shells, such as snail shells and shells, are perfect examples of the Golden Spiral.(Photo: Shutterstock)

The curled young leaf of Fiddleheads Fern fern has a special spiral shape.(Photo: Zamada / Shutterstock)

The top part of the ocean wave is in spiral form.(Photo: Shutterstock)

The golden spiral shape appears when looking at flower buds from the top down.(Photo: Shutterstock)

The whirlpool image also shows a connection to the golden ratio.(Photo: Shutterstock)

Like shells, tropical storms often have a golden spiral.(Photo: Mike Trenchard / NASA)

The shape of a spider web.(Photo: Shutterstock)

Pine nuts have spiral lines that follow the golden ratio.(Photo: Shutterstock)