This means that if you want to square the Golden Ratio, just add one to it. Where 1.618 is represented in upper case as Phi or Φ, its near twin or reciprocal, 0.618, is often represented in lower case as phi or φ. Phi is an irrational number, a number which cannot be expressed as a ratio of two integer numbers. Where Pi or p (3.14…) is the ratio of the circumference of a circle to its diameter, Phi or Φ (1.618 …) is the Golden Ratio that results when a line is divided in one very special and unique way. There’s any number of places that you could cut it, and each place would result in different ratios for the length of the small piece to the large piece, and of the large piece to the entire string. The Taj Mahal is another example where the Golden Ratio is believed to have been used in its design.
Uncanny Examples of the Golden Ratio in Nature
As evidenced by the other names for the number, such as the divine proportion and golden section, many wondrous properties have been attributed to phi. Novelist Dan Brown included a long passage in his bestselling book „The Da Vinci Code“ (Doubleday, 2000), in which the main character discusses how phi represents the ideal of beauty and can be found throughout history. As we know, ϕ can be obtained from the ratio of two successive Fibonacci numbers; the golden ratio forms a spiral pattern. This spiral follows a constant angle close to ϕ and is thus known as the Golden Spiral. The golden ratio is thus a proportional concept that describes the relative lengths of two line segments.
Method-2: The quadratic formula
That’s the first amazing thing about one of the most famous number sequences in the world — its simplicity. The second fascinating thing about Fibonacci numbers is, like the golden ratio in nature, that we see them everywhere. The golden ratio is derived from a famous — and very simple — mathematical sequence called the Fibonacci sequence. The sequence begins with the numbers 0 and 1 and we just add them together.
- In case of bivalve type clams, which exhibit grooves on their shells, the ratio of the grooves to the ridges equals the golden mean.
- In these fruits and vegetables, it is easy to visualize the spiral patterns along their surface.
- While phi is certainly an interesting mathematical idea, it is we humans who assign importance to things we find in the universe.
- 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.
The concept of the golden ratio is evident because it is a sign of the most effective method of growth and organization. It aids animals and humans in developing sizes and dimensions that are practical and artistic. Spiral galaxies such as the Milky Way have spiral arms spiraled proportionately to the golden ratio. The arms of these galaxies are usually logarithmic spirals, like the shell of the nautilus, and specified by the golden section.
The Fibonacci Sequence
When the main trunk of a tree branches out, it gives rise to a side-branch, which will further go on to divide and produce two more branches. One of these branches will split and form two new growth points, while the other branch remains dormant. This occurs at each branching event along the length of the tree over the course of its lifetime. This gives rise to branches, whose number follow the Fibonacci progression.
Each cone consists of pairs of alternating whorls, each oriented in the opposite direction to the other whorl. The ratio of the turn of each pod and the ratio between the number of pods in successive whorls is the golden ratio, i.e., 1.618. The golden ratio is derived from the Fibonacci sequence, and is seen universally in varied natural elements.
Dr Verguts was thrilled to discover that when women are at their most fertile, between the ages of 16 and 20, the ratio of length to width of a uterus is 1.6 – a very good approximation to the golden ratio. The data shows that this ratio is about 2 at birth and then it steadily decreases through a woman’s life to 1.46 when she is in old age. Looking at the length of our fingers, each section — from the tip of the base to the wrist — is larger than the preceding one by roughly the ratio of phi. The “Vitruvian Man” perfectly and beautifully illustrates the proportionality and balance of the Golden Ratio. Notice that the coefficients of and the numbers added to the term are Fibonacci numbers. Another interesting fact arises when looking at the ratios of consecutive Fibonacci numbers.
The Golden Ratio is a unique mathematical principle that appears throughout the natural world as well as in human-made structures, such as art and architecture. And because of its existence in the natural world, it has special meanings in the field of sacred geometry. golden ratio in nature The golden ratio is visible in the sunflower, as it is in many other plants.
The Parthenon, perhaps the most famous and recognizable example of ancient Greek architecture, is often identified as a masterpiece of the Golden Ratio. From the dimensions of the columns to the placement of the friezes, and even the overall layout of the temple all abide by the Golden Ratio. Speaking of architecture, some of the most famous and prominent buildings throughout history have incorporated the Golden Ratio into their structural designs, through perfect architectural proportions. Fibonacci numbers also appear in spiral growth patterns such as the number of spirals on a cactus or in sunflowers seed beds. In matters of reason, seeing is believing but in matters of faith, it is believing that first opens the door to seeing. Just as we need two eyes to add depth to our perception in vision, both faith and reason serve us in adding depth to our understanding of life and the universe in which we live.