The Golden Section and the Divine Proportion
For thousands of years, mathematicians, artists and philosophers have been inspired by the number 1.618033988….. The Golden Ratio (also known as the Divine Proportion) is a number that describes the ratio of two lengths that have been divided in such a way, so that when an object is split into two parts and the longer part divided by the smaller resulted in perfect symmetry, this number arises because it’s also equal to 1+5 / 2. The mathematical constant has an uncanny tendency to appear where it’s least expected—from seashells’ cochlear structure spirals, ancient temples structures throughout history or even more visibly trees and our own bodies. The fact that it recurs in so many different disciplines, and that we find it woven into the structure of the natural world at a fundamental level, raises a deep puzzle: why does this number even appear in nature — and why is the appearance of this number so deeply harmonious to all who encounter it?
What Is the Golden Ratio?
If a line be cut into two unequal parts, and the whole be to the greater part as the greater is to the less, then that line is broken in accordance withthe `golden section'. This ratio, mathematically the value about 1.618 and expressed as the Greek letter φ (Golden Ratio: phi), is considered aesthetically pleasing by many people based on various researches.
It can also be found using the Fibonacci sequence of numbers (1, 1, 2, 3, 5, 8, 13 …), in which each number is the sum of the two before it. As the sequence is as follows, the ratio of adjacent to is approaching φ.
The Golden Ratio in Nature
Nature appears to have a preference for efficiency and harmony, which are both embedded in the Golden Ratio.
Plants and flowers: A frequent explanation of their numbers Petals often in Fibonacci sequence (3 lilies, 34 (and daisies), or 55, or even 89) This arrangement maximizes sunlight capture.
Shells and galaxies: Logarithmic spirals in nautilus shells and spiral galaxies similarly approach φ as they grow, helping to explain the efficiency of growth and energy use.
Human body proportions: Some people believe that the proportions of the human body are in some ways influenced by φ, and prefer it to other ratios (e.g., rectangles with a rational aspect ratio) because it is closer to the golden ratio. Art and design Several early culture of humans, going back at least 2±3 thousand years, built structures using a value for φ; including certain articles that are considered especially beautiful by present-day persons. 30 Many designers believe the Golden Ratio represents beauty as being characterized by symmetry and proportion. 31 There is also the notion that when a rectangle has lengthto-width ratio close to φ, it can provide elements with global alignment: namely — alignment that commands respect which hearkens instinctively acknowledged value. helpful source?
These are not magic bullets but effective responses to biological and physical phenomena.
The Golden Ratio in Art & Architecture
The Golden Ratio has been actively applied in art, architecture and design for a few thousand years.
Classical Greece: The dimensions of the Parthenon are minutely related to φ, leading to aesthetic balance and harmony.
Renaissance Art: Vitruvian Man by Leonardo da Vinci — Famous visual representation of the Golden Ratio as it relates to human proportion, also used in da Vinci’s art including The Last Supper.
Modern design: When designing logos, another product or digital user interface, you may use the φ as a way to bring balance and organic elegance.
Not all masterpieces are based on φ but when they aren’t, the omnipresence of this number seems to speak directly to beauty and value.
Why Is It Known as the "Divine Proportion"?
AFTERWORD The term “Divine Proportion” entered popular usage in the 15th century, when mathematician Luca Pacioli and Leonardo da Vinci published their illustrated book De Divina Proportione. The latter was so termed, with the design of naming it divine, inasmuch as they imagined it to be seen things by φ,—which seemed oxide and:
unity in diversity One — a ratio that shows up within plants, animals, galaxies and human creations.
Infinity: Like pi (π) itself, φ is irrational—the numerical string it creates redoes infinitely.
Order and balance: The human psyche naturally finds its beauty in proportions around φ. This has been evidenced in cognitive science and design articles.
To many thinkers, the repetition of φ pointed to a grander ordering principle within reality.
The Golden Ratio: Wonder's Lens
Though it's not exactly a perfect universal “law of beauty” (not all that is beautiful complies by φ), the Golden Ratio has without a doubt been one of the most recurrent patterns in both nature and art. Acknowledging it can change the way we perceive reality:
A sunflower’s spiral is transformed into a mathematical marvel.
The proportions of a cathedral arch are the same as those found in seashells.
Even the expansion of populations and financial markets can be tracked through Fibonacci proportionality.
"In noticing, we are reminded that order and harmony is not imposed, it simply emerges."
Conclusion
The Golden Ratio is simultaneously a mathematical fact and a literary conceit. Scientifically, it refers to economy of growth and balance among components. Spiritually and aesthetically, it echoes the order behind what is seemingly chaotic. To see φ within a flower, in the contour of a face or the whirl of a galaxy is to view not simply this single number but also the deep harmony that ties mathematics, nature and human design into an all-encompassing unity.
Maybe that is why it appears divine – not because it is something outside of us, but rather that he reveals the beauty intrinsic in the world we inhabit together.