kuldlõike

Kuldlõike, also known as the golden ratio, is a special mathematical constant often found in nature, art, and architecture. It is approximately equal to 1.618 and is represented by the Greek letter phi (Φ). The golden ratio can be defined by a simple equation: (a+b)/a = a/b = Φ, where a is the longer part and b is the shorter part of a line segment. This ratio has been observed in the proportions of the human body, the arrangement of leaves on a stem, the spiral patterns of seashells, and the branching of trees.

Throughout history, artists and architects have incorporated the golden ratio into their work, believing it creates aesthetically pleasing and harmonious compositions. Examples include the Parthenon in Athens and paintings by Leonardo da Vinci, such as the Mona Lisa. The idea is that proportions following the golden ratio are inherently beautiful to the human eye.

While the prevalence of the golden ratio in nature and art is sometimes debated, its mathematical properties are well-established. It is an irrational number, meaning its decimal representation goes on forever without repeating. The golden ratio is closely related to the Fibonacci sequence, where each number is the sum of the two preceding ones (e.g., 0, 1, 1, 2, 3, 5, 8...). As the Fibonacci sequence progresses, the ratio of consecutive numbers approaches the golden ratio. This connection further highlights its significance in mathematics and its observed appearances in various phenomena.