Nature, The Golden Ratio and Fibonacci Numbers
There, he learnt how the Hindu-Arabic numerals of 0-9 could be used to complete calculations more easily than the Roman numerals still in use across much of Europe. Fibonacci explained his findings in a book called Liber Abaci, published in 1202, which had a section devoted to the intriguing sequence which would be named after him hundreds of years later. If the degree of turn was a fraction, like 1/4, that doesn’t help matters much because after four turns the golden ratio in nature seed pattern would be right back at the start again. There would be four lines of seeds, but that’s not much better than one when trying to cover a circular area.
Unraveling the Enigma of the Golden Ratio in Nature: A Fascinating Journey
- Enjoy the “phi”nomemon, whether to enhance your own understanding and appreciation of beauty and harmony in life or to apply it to your own artistic creations, like Leonardo Da Vinci and other masters before you.
- Application examples you can see in the articles Pentagon with a given side length, Decagon with given circumcircle and Decagon with a given side length.
- It appeared again in the 1980’s in the three-dimensional molecular arrangement of quasi-crystals, a newly discovered form of matter.
- Luca Pacioli, in the year 1509, published a book on the golden ratio called divine proportion.
While this is undeniable, some people creatively overlay golden spirals to images where others do not believe they were intended by the artist. The dimensions of the treasured Stradivarius violins built around 1700 show Phi relationships. More modern applications of the Golden Ratio in architecture can be seen in Notre Dame in Paris, the United Nations Headquarters Secretariat building in New York and the CN Tower in Toronto. It’s commonly used in the design of products and logos and by many major corporations. It has even been used in high fashion clothing design, such as in the “Phi Collection” announced in 2004 and covered by Vogue, Elle and Vanity Fair. It’s also the basis for The Fashion Code, a style guide to women’s dress.
As well, in physics and cosmology, it’s seen in the structure of atoms and the distribution of galaxies. Spiraling patterns of seed heads, as seen in case of sunflowers, are a great example of the Fibonaccian process and the divine ratio. In a seed head, typically, new seeds are formed at the center, and they migrate outwards in a radial fashion as they grow older. Since each whorl of the seed heads follow the sequence, it logically follows that the ratio of any two adjacent whorls is the golden ratio. If he number of total seed heads oriented in the two directions are compared, they yield the divine proportion. Golden Ratio, often found in nature, is a fascinating example of how mathematics shapes the world around us.
It appeared again in the 1980’s in the three-dimensional molecular arrangement of quasi-crystals, a newly discovered form of matter. As we enter the 21st century, Phi seems to be having a rebirth in integrating knowledge across a wide variety of fields of study, including time and quantum physics. Golden Ratio, Phi, 1.618, and Fibonacci in Math, Nature, Art, Design, Beauty and the Face.
In addition, the shape of the ear resembles the shape of a Fibonaccian spiral. Numerous studies have concluded that faces with facial features that exhibit a precise golden ratio are deemed to be highly attractive and regarded as extremely beautiful. The same pattern is observed in the case of fractal-like fruits and vegetables.
If you divide a line into two parts where the whole length divided by the longer part equals the longer part divided by, the shorter part, you will get the golden ratio of about 1.618. With this comprehensive article, we hope to provide valuable insights into the enchanting world of the Golden Ratio in nature and beyond. As we unravel the mysteries behind this fascinating ratio, we discover the hidden symmetries and connections that underpin the aesthetics of our universe. As in the case of shells and spiral galaxies, the movement of air and wind in hurricanes also follows the Fibonaccian spiral, revealing the golden ratio. The spiral nature of a hurricane is largely due to the simultaneous movement of the air and atmospheric elements between a low pressure area (epicenter of the hurricane) and the surrounding high pressure area. Certain other entities within the galaxy also exhibit the golden ratio.
1. Spiral Galaxies
From the patterns of leaves and flowers to the spirals of seashells and galaxies, this unique ratio appears in many beautiful and unexpected places. The unique properties of the Golden Rectangle provides another example. This shape, a rectangle in which the ratio of the sides a/b is equal to the golden mean (phi), can result in a nesting process that can be repeated into infinity — and which takes on the form of a spiral. Curiously enough, we even find golden ratio relationships in the solar system and universe.
Golden Spiral vs Fibonacci Spiral
Various studies have tested to see if a golden rectangle is the most pleasing rectangle to the human eye. Results of the studies are mixed, but generally point to rectangles with shapes close to the golden rectangle as being most pleasing. Fibonacci numbers frequently appear in the numbers of petals in a flower and in the spirals of plants. The positions and proportions of the key dimensions of many animals are based on Phi. Examples include the body sections of ants and other insects, the wing dimensions and location of eye-like spots on moths, the spirals of sea shells and the position of the dorsal fins on porpoises.
The diameters of the Earth and Moon form a triangle whose dimensions are based on the mathematical characteristics of phi. The distances of the planets from the sun correlate surprisingly closely to exponential powers of Phi. The beautiful rings of Saturn are very close in dimension to the golden ratio of the planet’s diameter. NASA released findings in 2003 that the shape of the Universe is a dodecahedron based on Phi. More intriguing yet is the extensive appearance of Phi throughout the human form, in the face, body, fingers, teeth and even our DNA, and the impact that this has on our perceptions of human beauty.
