Since the invention of numbers, mathematics has been an important tool for us to understand and describe nature, from the pattern of stars to the spiral of shells, mathematics has helped us better understand the complexity and beauty of nature. And there is a very mysterious mathematical concept in nature that has attracted countless scientists and artists for centuries, and that is the golden ratio. This mysterious and elusive ratio seems to have become intertwined in the various structures of nature, appearing in everything from the proportions of the human body to the arrangement of leaves on the stem.

So what is the golden ratio? The golden ratio is a mathematical concept often referred to as "phi" or "golden section". It is an irrational number, approximately equal to 1.61803398875, which is the ratio of two quantities proportional to each other. Specifically, if we have two quantities A and B, and the ratio of A to B is the sum of the proportions of A and B to A, then the ratio of A and B is equal to phi. To understand it simply, you have a line and divide it into two parts of unequal length, the long part is a + b and the short part is a. The golden ratio is a fascinating concept because it appears in many different aspects of mathematics and nature, from the shape of galaxies and the curves of ocean waves, to the growth patterns of plants and the proportions of the human body.

Perhaps the most famous example of the application of the golden ratio in our human art and architecture is the Parthenon in Athens, Greece. This ancient temple was built in the 5th century BC and its architects incorporated the golden ratio into its design. The size of the temple's foundations and the height of the columns are based on the golden ratio, giving the Parthenon a harmonious beauty that has attracted countless sightseeing for centuries.

The golden ratio also appears in many works of art, both ancient and modern, with Renaissance painters such as Leonardo da Vinci and Michelangelo very good at using the golden ratio to create pleasing compositions, and modern artists such as Salvador Dalí and Jackson Pollock often incorporating the golden ratio into their works. In fact, many art historians believe that the golden ratio is one of the main reasons why certain works of art are considered "great" because they naturally feel balanced and harmonious.

Our music is also another area where the golden ratio seems to be working, and many believe that the golden ratio is the key to creating music with aesthetics, some composers often use the golden ratio to determine the length of individual notes or the spacing between chords, good composers are good at using this ratio to create more appealing rhythmic melodic patterns, the most famous example of the golden ratio in music is the work of Johann Sebastian Bach. Bach is known for his use of complex mathematical patterns in his works, the golden ratio appears in many of his works, and in his famous Goldberg Variations, the overall structure of the work is based on the Fibonacci sequence, a related mathematical concept that also often appears in nature.

Although the golden ratio is universally applied in our art and music, it first appeared in nature, and the most famous example of the golden ratio in nature is the spiral pattern found in shells, such as the nautilus shell. The curve of the shell follows the law of the logarithmic helix, a spiral based on the golden ratio, and as the nautilus grows, new chambers are added to its shell, each of which is one phi coefficient larger than the previous one.

In the branching pattern of various plants, especially trees, the stems of many plants follow a pattern known as the "plant axis", in which the leaves are arranged in a spiral around the stem, and the angle between successive leaves is often a multiple of the golden horn, which is about 137.5 degrees, this arrangement of plants allows the leaves to receive maximum sunlight exposure to minimize competition for resources.

In addition to shells and plants, the golden ratio appears in many other things in nature. For example, the proportions of the human body are also based on the golden ratio, the length of the arm is about 1.618 times the length of the forearm, and the spiral pattern found in galaxies, hurricanes, and even the cochlea of the human is also based on the golden ratio.

Although the golden ratio is common in nature, it remains a mystery to us, and for centuries our scientists and mathematicians have wanted to unravel the mysteries about it, but they still can't fully understand why it appears in so many different areas of nature. Some scientists believe that the golden ratio is simply the result of natural selection, and that organisms that exhibit this ratio may have a survival advantage over those that do not, while others suggest that this ratio may have a deeper meaning, and may reflect some of the underlying mathematical structure of the universe.