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Golden Ratio: Difference between revisions
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[[File:330px-Golden ratio line.svg.png|thumb|Golden Ratio]] | [[File:330px-Golden ratio line.svg.png|thumb|Golden Ratio]] | ||
In mathematics, two quantities are in the | In mathematics, two quantities are in the [[Golden Ratio]] if their ratio is the same as the ratio of their sum to the larger of the two quantities. The figure on the right illustrates the geometric relationship. [[Fibonacci]] spirals, [[Golden Spiral]]s and [[Golden Ratio]] based spirals often appear in living organisms. The Golden Ratio is also found in geometry, appearing in basic constructions of an equilateral triangle, square and pentagon placed inside a circle, as well as in more complex three-dimensional solids such as [[Platonic Solids|dodecahedrons]], [[Platonic Solids|icosahedrons]] and [[Buckyballs]]. | ||
There is a special relationship between the [[Golden Ratio]] and [[Fibonacci]] Numbers (0, 1, 1, 2, 3, 5, 8, 13, 21, ... etc, each number is the sum of the two numbers before it). When we take any two successive [[Fibonacci]] Numbers, one after the other, their ratio is very close to the [[Golden Ratio]]. This is called an approximation or limit value in calculus. | There is a special relationship between the [[Golden Ratio]] and [[Fibonacci]] Numbers (0, 1, 1, 2, 3, 5, 8, 13, 21, ... etc, each number is the sum of the two numbers before it). When we take any two successive [[Fibonacci]] Numbers, one after the other, their ratio is very close to the [[Golden Ratio]]. This is called an approximation or limit value in calculus. | ||