Golden Ratio, Phi Ratio

Golden Mean, Golden Section, Divine Proportion

The Human Skull Obeys the 'Golden Ratio,' Study Suggests. Anatomists Say That's Ridiculous Live Science - October 10, 2019

In a world where a mathematical temptress known as the golden ratio is supposedly hidden in every beautiful site, from a snail's shell to Greece's Parthenon and Egypt's pyramids, it's perhaps not surprising that humans have long tried to link it to É well, humans. But the golden ratio is more urban legend than secret key to the universe; it doesn't describe a snail's shell, the Parthenon, the pyramids or beautiful faces, as popular belief would have it. The same goes for a new study that suggests the golden ratio exists within the human skull: Anatomists say it's nonsense. The golden ratio, also known as the divine proportion, is an infinite number that is approximately equal to 1.618 and is calculated by dividing a line into two unequal parts, such that the longer part divided by the smaller part is equal to the entire line divided by the longer part. (a/b = (a+b)/a = 1.6180339887498948420 É)

The golden ratio is also called the golden section or golden mean. Other names include extreme and mean ratio, medial section, divine proportion, divine section golden proportion, golden cut, and golden number. Many artists and architects have proportioned their works to approximate the golden ratio - especially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio - believing this proportion to be aesthetically pleasing.

Mathematicians since Euclid have studied the properties of the golden ratio, including its appearance in the dimensions of a regular pentagon and in a golden rectangle, which can be cut into a square and a smaller rectangle with the same aspect ratio. The golden ratio has also been used to analyze the proportions of natural objects as well as man-made systems such as financial markets, in some cases based on dubious fits to data. Read more ...

Long-Standing Problem of 'Golden Ratio' and

Other Irrational Numbers Solved with 'Magical Simplicity'

Live Science - September 17, 2019

The Golden Ratio in Space

Ancient Pueblo Used Golden Ratio to Build the Sun Temple

Live Science - February 13, 2017

The Great Pyramids in Giza, the Parthenon in Athens and Chichen Itza in Mexico have something in common. Besides attracting hordes of tourists, all of these architectural wonders appear to use the golden ratio. This mathematical number is often written as 1.618, the first few digits of its infinite decimal form. Expressed another way, two quantities - let's call the larger one "a" and the smaller "b" - are in the golden ratio if "a is to b" as "a + b is to a." The result is a composition with aesthetically pleasing proportions. Now, shapes with the golden ratio, as well as other geometric shapes, have been found in another, unexpected site: the Sun Temple at Mesa Verde National Park in Colorado, built by the ancient Pueblo people who lived in what is now the modern-day Southwest; they had no known written language or written number system.

The Vitruvian Man is a drawing created by Leonardo da Vinci circa 1490. It is accompanied by notes based on the work of the architect Vitruvius. The drawing, which is in pen and ink on paper, depicts a male figure in two superimposed positions with his arms and legs apart and simultaneously inscribed in a circle and square. The drawing and text are sometimes called the Canon of Proportions or, less often, Proportions of Man.

Fibonacci Numbers or Sequence in Creation - 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811 ...

Seed of Life

When things come fun circle