Golden Ratio

Can you tell the similarities between the given pictures?

The similarity between them is that they follow the Golden Ratio. So then what exactly is this Golden Ratio ??

In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities a and b with a > b > 0,

where the Greek letter ({\displaystyle \varphi } or {\displaystyle \phi }) represents the golden ratio.

The golden ratio is also called the golden mean or golden section. Other names include extreme and mean ratio, medial section, divine proportion, divine section, golden proportion, golden cut, and golden number.

Mathematicians since Euclid have studied the properties of the golden ratio, including its appearance in the dimensions of a regular pentagon and in a golden rectangle, which may be cut into a square and a smaller rectangle with the same aspect ratio. The golden ratio has also been used to analyze the proportions of natural objects as well as man-made systems such as financial markets. The golden ratio appears in some patterns in nature, including the spiral arrangement of leaves and other plant parts.

This golden ratio can be seen in architect, art, music, designs, painting, and mathematics, in ancient pyramids, and at many places in nature.

Some disrupted observations of the golden ratio are:-

• Some specific proportions in the bodies of many animals (including humans)and parts of the shells of mollusks are often claimed to be in the golden ratio.

• Historian John Man states that both the pages and text area of the Gutenberg Bible were "based on the golden section shape".

• Studies by psychologists, starting with Gustav Fechner c. 1876, have been devised to test the idea that the golden ratio plays a role in the human perception of beauty.

• In investing, some practitioners of technical analysis use the golden ratio to indicate support of a price level, or resistance to price increases, of a stock or commodity; after significant price changes up or down, new support and resistance levels are supposedly found at or near prices related to the starting price via the golden ratio. However, other market analysts have published analyses suggesting that these percentages and patterns are not supported by the data.

So have you seen the Golden ratio in any other objects in your daily lives?