There is a generally-held consensus among classicists, and historians of mathematics, that the Golden Ratio was first understood and used by ancient Greek mathematicians during the periods known as the Classical and Hellenistic Periods of Greek Mathematics (from around 600 BCE to 600 CE).
a. The uses date to the ancient Egyptians and Greeks
Greeks also showed the advanced understanding of the Golden Ratio. Phidias (500 BC – 432 BC), Plato (circa 428 BC – 347 BC), Euclid (365 BC – 300 BC), had put the ratio in their works.
Significance and Use of the Golden Ratio in Art
The concept of the golden ratio can be traced back to ancient times, with evidence of its use found in various cultures and civilizations, including ancient Egypt, ancient Greece, and medieval Europe.
18th-century mathematicians Abraham de Moivre, Nicolaus I Bernoulli, and Leonhard Euler used a golden ratio-based formula which finds the value of a Fibonacci number based on its placement in the sequence; in 1843, this was rediscovered by Jacques Philippe Marie Binet, for whom it was named "Binet's formula".
The golden ratio, also known as the golden number, golden proportion, or the divine proportion, is a ratio between two numbers that equals approximately 1.618. Usually written as the Greek letter phi, it is strongly associated with the Fibonacci sequence, a series of numbers wherein each number is added to the last.
The ancient Egyptians, Greeks, and Romans all did take an arcane interest in Φ, although they referred to it as the “extreme and mean ratio.” Part of its appeal has been attributed to how easy it is to construct geometrically. But no one wrote down that the Parthenon was designed using the golden ratio.
So, What is this Golden Ratio? The Greek scholar Pythagoras is credited with discovering the golden ratio. The golden ratio, also known as the golden mean, golden section, or divine proportion, is rounded to 1.618.
Evidence of the Golden Ratio in the Great Pyramid complex.
Some say, however, that this single piece of evidence is just a simple coincidence. The primary rationale given to deny this claim is that there is no written historical evidence that the ancient Egyptians had any knowledge of the golden ratio.
The beauty standard for females prioritizes a slim, hourglass figure, small face, a v-shaped jaw, straight eyebrow, flawless skin, and 165cm (5'4") or taller in height. They also adhere to a golden ratio of 1:8, meaning your total height should measure to eight of your head.
In order to calculate this golden number of beauty, De Silva based his list on a calculated measurement of the size and position of the eyes, eyebrows, nose, lips, chin, and jaw. Among all the data collected, Bella Hadid ranked highest with a result of 94.35% of symmetry.
Golden Spiral:
After each bend, the bending points on the spiral are 1.618 times the center and after completing a full round from the center, the ending point dimension equals 1.618 x 8 = 6,854 times the distance between the last bend and center .
Hence, the value of golden ratio ϕ is approximately equal 1.618. Interesting Facts: Golden ratio is a special number and is approximately equal to 1.618.
Another ratio that appeared frequently in Maya architecture is the golden ratio 1+√52. To form a golden rectangle using a cord, again start with a square. Measure the length of a side of the square with a cord and fold in half to mark the midpoint of a side of the square.
The golden ratio is a number, present in architecture. It's value is 1.61803398875. The Eiffel Tower is good example. The golden ratio equation is height of tower biggest part= 1.6180...
The most famous monuments of ancient Egypt are the Great Pyramids of Giza. Believed to have been constructed around 4,600 years ago, these pyramids were built around the golden ratio, long before the Greeks and the Parthenon. The largest of the pyramids in Giza contains the use of phi and the golden ratio.
Phidias widely used the golden ratio in his works of sculpture. The exterior dimensions of the Parthenon in Athens, built in about 440BC, form a perfect golden rectangle.
Popular pop singer Ariana Grande, a popular singer, is ranked fifth with a golden ratio score of 91.81%.
Some of the proportions they may discuss, as outlined by the Golden Ratio, include: A visually balanced face is approximately 1.618 times longer than it is wide. The distance from the top of the nose to the center of the lips should be around 1.618 times the distance from the center of the lips to the chin.
The ideal Indian woman is fair or medium-complexioned, has a narrow waist but wider hips and breasts, and has large eyes, full red lips, and long black hair that is either straight or wavy.
Because 43200 has special significance, achieving this particular scaling factor would have required exact knowledge of the equatorial circumference and polar radius of the Earth, and as will be shown later, 43200 is also used to encode the speed of light in the Great Pyramid.
Some theorize that the phi ratio (phi = 1.61803…) is evidence that nature is inherently perfect, and that when mankind strays away from the natural law, sickness and imbalance occur. While the Golden Ratio doesn't account for every structure or pattern in this world and others, it most certainly is a key player.
The golden ratio is an irrational number with an approximate value of 1.618. It is often found in nature and is believed to be aesthetically pleasing to the human eye. The Taj Mahal is a mausoleum located in Agra, India, that was built by the Mughal emperor Shah Jahan in memory of his beloved wife Mumtaz Mahal.
The Pythagoreans and the Golden Ratio
The Pythagoreans first discovered the Golden Ratio, also called the “Divine Proportion”, about 2,400 years ago.
Zeus, king of the gods, His statue a wonder stood, Olympia's grand feat. A golden rectangle is a rectangle whose side lengths are in the golden ratio, one-to-phi, that is, approximately 1:1.618.
Some artists and architects believe that the golden ratio makes the most beautiful shapes. As a result the ratio can be found in many famous buildings and artworks, such as those by Leonardo da Vinci.