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Why is the golden ratio significant to history?
Its too long to explain with the space alotted, but reading The Da Vinci Code explains it in detail.
What is the golden ratio of a snail shell?
The golden ratio or the Fibonacci number is apparent in many natural objects. This mathematical equation proves that by dividing a line in two parts, the longer part divided by the smaller part is also equal to the whole length divided by the long part.
How long have prime numbers been around for?
They have always been around
How did the golden ratio help find the height of a pyramid?
The golden ratio is also known as 'phi' (a Greek letter written like an 'o' with a vertical line through it. It is an irrational number, but not a transcendental number like e and pi. You can find its value on a calculator by entering (sqrt5 + 1)/2 = 1.6180339887499..... If you break a stick into two unequal parts so that the ratio of the large part to the small part is the same as the ratio of the original stick to the large piece, then that ratio is the golden ratio. The golden ratio was known to Greek mathematicians as long as 2400 years ago. Luca Pacioli wrote about in 1509, sparking modern fascination . The golden ratio is said to be used in the proportions of Greek temples, and to be found in the ratio of various parts of an ideal human body. It is found in many places in nature, such as the pattern of the seeds in a sunflower, and the shape of a snail shell. As far as the pyramids go, many things have been said about the dimensions, proportions and orientation of the Egyptian pyramids, but my view is that this may be our imagination as much as it was actually the method of the builders of the pyramids. This is not to deny that the pyramids are an amazing feat of engineering. By the way, the first pyramids were built about 4600 years ago, 2200 years before the writings of the Greek mathematicians.
How does the Fibonacci Sequence relate to the Golden Ratio and what is the Golden Ratio. Why is it so important?
I will explain a method of constructing an illustration:Construct a square with the length of a side = 1 (one unit).Add another square of the same size to the first so they have one common edge (1 * 2).Add a square to the long edge of the exisiting squares (2 * 2 units).Add another square to the long edge ( that square should be 3 * 3)Contionue adding squres to the ling edge of the construction.The lengths of the sides form a Fibonacci series. The lengths of the sides of the constructed rectangle approch a golden Ratio (the longer you continue the closer to the ratio you get.This is considered a plesing shape by many and many artists and architects use these proportions in their compositions.
