The golden ratio, often referred to as the "golden number," is approximately 1.618033988749895.
The golden ratio, symbolized by the Greek letter phi (Φ), is an irrational number defined as the ratio between two numbers where the ratio of the sum of the numbers to the larger number is the same as the ratio of the larger number to the smaller number. It's deeply rooted in mathematics, art, architecture, and nature.
Think of a line divided into two parts. The golden ratio exists when the ratio of the whole line to the longer segment is the same as the ratio of the longer segment to the shorter segment.
Here are some key aspects of the golden ratio:
- Irrational Number: Its decimal representation never ends and doesn't repeat.
- Mathematical Definition: It can be expressed algebraically as the positive solution to the equation x² - x - 1 = 0, which yields (1 + √5) / 2.
- Appearance in Nature: The golden ratio appears in patterns such as the spiral arrangement of leaves on a stem, the seed heads of sunflowers, and the shell of a nautilus.
- Application in Art and Architecture: Many artists and architects have used the golden ratio to create aesthetically pleasing designs, believing it contributes to balance and harmony. The Parthenon and works by Leonardo da Vinci are often cited as examples.
The number continues infinitely, but the digits provided offer a high degree of accuracy for practical purposes.
