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What has the golden ratio in it?
A great many things have the golden ratio in them varying from things fabricated by humans such as architecture, the proportions of the sides of a book also fall into the golden ratio. The golden ratio also occurs naturally for example the spiral in the snail's shell falls into the golden ratio. Generally most man made things have the golden ratio in them as it has been found quite simply, to look good.
Why the golden ratio is ideal ratio?
The golden ratio is the ideal ratio because it is consistent throughout many aspects in nature - proportions of the human body, the crests and troughs of a heartbeat, the stripes on a tiger's head, et cetera. The value of the Golden Ratio is 0.5*[1 + sqrt(5)] = 1.61803 (to 5 dp)
Does golden ratio involve patterns?
No. The Golden ratio is an irrational number: [1 + sqrt(5)]/2 = 1.6180, approx. It is found in many patterns - in nature as well as man-made.
How or why did the golden ratio evolve in nature?
It didn't. It's an artefact of mathematics, found in the proportions of many geometric shapes. But although many people claim that this ratio organisms also show this ratio, this is simply not true, unless you apply such a wide margin of error as to make the entire notion of the golden ratio meaningless.
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.
