kuldlõiget

Kuldlõige, also known as the golden ratio, divine proportion, or phi (φ), is a special irrational number approximately equal to 1.6180339887. It is often found in nature, art, and architecture, and is believed to possess aesthetically pleasing qualities. Mathematically, it is defined by the equation (a+b)/a = a/b = φ, where a is the longer segment and b is the shorter segment of a line.

The golden ratio can be visualized using the golden rectangle, where the ratio of the longer side to the shorter side is equal to φ. If a square is removed from a golden rectangle, the remaining rectangle is also a golden rectangle. This process can be repeated infinitely, creating a spiral known as the golden spiral, which closely approximates the logarithmic spiral found in many natural formations, such as seashells and galaxies.

Throughout history, the golden ratio has been incorporated into various artistic and architectural designs. Ancient Greek architects are thought to have used it in the construction of the Parthenon, and Renaissance artists like Leonardo da Vinci are believed to have employed it in their compositions, such as in the Mona Lisa. While the extent of its intentional use is debated, the prevalence of the golden ratio in both natural and man-made forms continues to fascinate mathematicians, artists, and scientists.