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The Golden Ratio is 0=1.61803. Also known as the Golden Mean or Golden Section. It is a system of proportion first discovered by the ancient Greeks, and described as the most pleasing proportion to the human eye. Sections of a line or shape are related to one another according to an ideal which can be expressed with an algebraic formula. Visually it is a rectangle containing squares, a spiral forms by connecting intersecting lines. Examples of the concho-spiral seen in nature are shells, pine cones and ram's horns.
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History of the golden ratio?
See the link below
Who invented the the golden ratio?
There are several who discovered the significance of this ratio (see related link post). Euclid (around 300 BC) noted the ratio, but it looks like it was referred to as 'Golden' by Martin Ohm in 1835.
Why does the golden ratio exist?
Our appreciation of the golden ratio probably derives from some kind of subconscious mathematical process. Our brains do all sorts of things that we do not consciously know about. In an evolutionary sense, we are designed to recognize patterns, since that is central to our understanding of the world in which we live and our ability to function within it, and as a result, we often see patterns, even when they are illusionary. The golden ratio is a pattern of sorts.
What is Golden Mean and its uses?
Also called the golden ratio. See http://en.wikipedia.org/wiki/Golden_ratioA Greek philosopher and scientist, Aristole taught the golden mean philosophy.
Why is the golden ratio used in cubism?
Click link below. In the paintings shown you will see the geometrical details.
Where can a golden ratio be found?
in pentagons and triangles mostly.... Maybe you mean the golden section. See this http:/goldennumber.net/goldsect.htm I have known it as a naturally occurring fractal and an artistic composition guide.
Is Golden ratio a rational or irrational?
It is irrational. Any number that cannot be written as a fraction is irrational. So if the Golden Ratio were rational, instead of a never-ending decimal number, you'd see a fraction. The official measurement is (1+sqrt5)/2. sqrt5 is irrational.
What are some real life examples of the Golden Ratio?
You read about all the math related aspects of the golden ratio, and now you want to see it applied to real life, right? Well, you already know about various ways the golden ratio appears in real life, and you probably haven't even thought about it at all! ---- One of the first peoples to use the golden ratio in their art, architecture, and other aspects of daily life was the Egyptians. They called the golden ratio the "sacred ratio" and used it in their hieroglyphics and pyramids, as well as other monuments to the dead. ---- The sides of the Egyptian pyramids were golden triangles. Additionally, the three-four-five triangle is a golden ratio between the five unit side and the three unit side. The Egyptians considered this kind of right triangle extremely important and used it also in the pyramids. ---- ---- The Egyptian hieroglyphics also contained many proportions based on the golden ratio. The letter h, for example, is the golden spiral. Additionally, p and sh are created using golden rectangles ---- However, the use and occurance of the Golden Ratio in aesthetics doesn't end with the ancient Egyptians. It was used by the Pythagoreans, Greeks, Romans, and artists during the Renaissance. ---- The frequent appearance of the Golden Ratio in the arts over thousands of years presents us with an interesting question: Do we surround ourselves with the Golden Ratio because we find it aesthetically pleasing, or do we find it aesthetically pleasing because we are surrounded by it?In the 1930's, New York's Pratt Institute laid out rectangular frames of different proportions, and asked several hundred art students to choose which they found most pleasing. The winner? The one with Golden Ratio proportions.
What does Fibonacci and the golden ratio have in common?
The ratio of dividing the larger Fibonacci number into the smaller Fibonacci number gives you the golden ratio (1.618 to 1). -------- The Golden Ratio is the number (1+sqrt(5))/2~=1.618 The Fibonacci sequence is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ... . Skipping the first two terms, if you divide one term in this sequence by the previous term the resulting sequence converges to the Golden Ratio: 1.0000 2.0000 1.5000 1.6667 1.6000 1.6250 1.6154 1.6190 1.6176 1.6182 1.6180 Please see the link for more information.
How is chess associated with the golden ratio?
Gabries Bosia determined a way to construct the golden ratio (phi) while pondering the knight's move in chess. The method involves inscribing a right triangle of sides 3, 4 and 5 within a circle. For more information, please see the links below.
Can a golden eagle see in the dark?
the golden eagle can see in the dark
Why is the golden ratio important?
It's important because it is found (or appears to be) in so many areas of life, most notably in nature, and most importantly in mathematics. The Fibonacci sequence and the concept of fractals (like the infinitely divisible golden rectangle) are great examples of this. Ancient Egyptian and Greek architects built many of their structures with this ratio in mind. Philosophers see this ratio as having an important significance, since it occurs in nature so often. A lot of people believe that this formula, known as the golden ratio or phi (φ) pops up in everyday life. The truth is that it does not actually appear in the places it is said to. Many claims of its occurrence are false.
