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What Is The Golden Ratio?
What Is The Golden Ratio?

The Golden Ratio is the equivalent to the number 1.618. It is found by dividing a line into two parts, so that the longer part divided by the smaller part is equal to the whole length divided by the longer part. It is largely associated with beauty, as the rectangle it creates is very aesthetically pleasing to the eye. Fun fact: credit cards follow the Golden Ratio, which might explain why it's so fun to swipe away your money.

The Golden Ratio Is The Most Irrational Number
The Golden Ratio Is The Most Irrational Number

The Golden Ratio comes out to be 1.6180339887498948420... and it just goes on and on, with no pattern. For simplicity, it's just represented with the Greek letter "phi."

How Was The Golden Ratio Discovered?
How Was The Golden Ratio Discovered?

Phi (rounded to 1.618) has been discovered over and over again throughout history, which is why it was given the names the Golden Ratio, the Golden Mean, the Golden Section, etc. Ancient Greek mathematicians were among the first to study the Golden Ratio, with the ancient mathematician Euclid being the one to eventually define it. Euclid was also the one who linked the Golden Ratio to the pentagram.

The Golden Ratio In Art:
The Golden Ratio In Art:

The Golden Ratio appears not just in geometry and mathematics, but throughout the creative and natural world as well.

Many artists use this in their work and even frame their canvases with the Golden Ratio rectangle. The Golden Ratio was used in many Renaissance-era paintings and sculptures in order to achieve balance and beauty. Leonardo da Vinci even used the Golden Ratio to paint his masterpieces The Last Supper, the Mona Lisa and Vitruvian Man, which suggests man's relationship to the Golden Ratio.

Salvador Dali's 1955 painting The Sacrament of the Last Supper explicitly and purposefully incorporates the Golden Ratio, in which Dali placed Jesus in the center.

The Golden Ratio In Architecture:
The Golden Ratio In Architecture:

Throughout the world, architects have built structures that adhere to The Golden Ratio. The Great Pyramid of Giza, constructed between 2580 and 2560 B.C., adheres to this ratio -- the ratio of each side of the base to the height is approximately 1.57, which is close to The Golden Ratio.

Similarly, the Parthenon in Athens, Greece, is known to be one of the most pleasing and mathematically perfect structures created. It is theorized that the architect, renowned mathematician Phidias, knowingly incorporated "phi" into the temple. This temple to Athena, the Greek goddess of wisdom and war, was constructed between 447 and 432 B.C. and is commonly regarded as the finest example of Greek architecture. The external walls of the Parthenon form a perfect golden rectangle.

The Golden Ratio In Nature:
The Golden Ratio In Nature:

The Golden Ratio is a natural recurring shape in nature -- from the makeup of our DNA to the pattern of stars in our galaxy. If you connect the dots in the Golden Ratio's rectangles, you create a spiral that is found all throughout nature -- in the curve of a snail shell, the pattern of rose petals, and the twist of a ram's horn.

In the mid-19th century, German mathematician Adolf Zeising discovered the prevalence of the Golden Ratio in leaves, branches and plant veins. Upon further research, he discovered that the Golden Ratio was a universal law when it came to patterns of nature.

The Golden Ratio is even present in human faces -- people who are deemed more attractive often have facial features which align with the Golden Ratio.

The Golden Ratio In The Pentagram:
The Golden Ratio In The Pentagram:

The pentagram is a symbol used in many different ways, such as mysticism, religion and magic. Its construction is also tied to the Golden Ratio. The idea is there is a pentagram within every pentagon, and the diagonals of the pentagon (a pentagram) cut it into a Golden Ratio.

What Is The Fibonnacci Sequence?
What Is The Fibonnacci Sequence?

Around 1200, Italian mathematician Leonardo Fibonacci discovered a sequence of numbers: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, etc.

The following number is calculated by adding the two numbers before it. This became known as the Fibonnacci Sequence, and it has a direct relationship with the Golden Ratio. When you take any two numbers next to each other in this sequence, their ratio is very close to the Golden Ratio. The higher the number, the closer to the Golden Ratio. For example, the ratio 13 to 21 is 1.625 -- very close to the Golden Ratio's 1.618. No matter how high you go through the Fibonnacci Sequence, this will stay true.

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