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Golden Ratio

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The golden ratio, also known as the divine proportion or the golden mean, is a mathematical concept that has fascinated scientists, mathematicians, artists, and philosophers for centuries. In its simplest form, the golden ratio is a mathematical ratio of approximately 1.618:1. It is found in various natural and human-made structures, such as the human body, plants, architecture, and art. The beauty and appeal of the golden ratio lie in its unique proportion and symmetry, which creates a sense of harmony and balance. The Golden Ratio is derived from a line segment that is divided into two parts in such a way that the ratio of the smaller part to the larger part is the same as the ratio of the larger part to the whole. This can be expressed mathematically as a/b = (a+b)/a = φ, where φ (phi) is the Golden Ratio. The origins of the golden ratio can be traced back to ancient civilizations, such as the Greeks, Egyptians, and Chinese. The Greeks were the first to formally define the concept, ...

The Golden Equation

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The Golden Equation, or Golden Identity, is an equation that contains 4 famous numbers, used frequently in maths and science.  1) phi (golden ratio) is related to Fibonacci sequence, and both are seen in many structures from galaxy shapes to fractal patterns in plants. 2) pi (Archimedes’ constant) is the ratio of a circle circumference to its diameter and used in trigonometry and physics whenever circles and oscillations are involved. 3) e (Euler’s number) is related to power laws and exponential growth/decay. 4) i (imaginary number) is the square root of -1 and is found to be essential in quantum physics, one of the two main pillars of physics.  5) The number 5 has interesting relations within the equation as well as other properties. a) The equation has 5 arithmetic operations: addition, subtraction, multiplication, division and exponentiation. It has 5 terms, which consist of 3 variables and 2 operators (= and +).  b) Humans have 5 fingers and 5 toes on each hand and f...