Phi


Phi - The Golden Ratio

The golden ratio is also called the golden mean, golden section,
divine proportion, golden proportion, golden number, and Phi.




Phi: Integrated Information Theory




Phi: The Golden Ratio -   Live Science - November 25, 2019

The golden ratio is one of the most famous irrational numbers; it goes on forever and canŐt be expressed accurately without infinite space. The number phi, often known as the golden ratio, is a mathematical concept that people have known about since the time of the ancient Greeks. It is an irrational number like pi and e, meaning that its terms go on forever after the decimal point without repeating.

Over the centuries, a great deal of lore has built up around phi, such as the idea that it represents perfect beauty or is uniquely found throughout nature. But much of that has no basis in reality.

Phi is closely associated with the Fibonacci sequence, in which every subsequent number in the sequence is found by adding together the two preceding numbers. This sequence goes 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 and so on. It is also associated with many misconceptions.

By taking the ratio of successive Fibonacci numbers, you can get closer and closer to phi. Interestingly, if you extend the Fibonacci sequence backward - that is, before the zero and into negative numbers - the ratio of those numbers will get you closer and closer to the negative solution, little phi -0.6180339887...




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