36,349
edits
Golden Ratio: Difference between revisions
no edit summary
No edit summary |
|||
| Line 1: | Line 1: | ||
[[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 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]]. | 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. | |||
[[Phi]] is also used as a symbol for the [[Golden Ratio]] and on other occasions in math and science. This use is separately encoded as the Unicode glyph ϕ. The [[Fibonacci]] sequence, provides yet another way to derive [[Phi]] mathematically. | [[Phi]] is also used as a symbol for the [[Golden Ratio]] and on other occasions in math and science. This use is separately encoded as the Unicode glyph ϕ. The [[Fibonacci]] sequence, provides yet another way to derive [[Phi]] mathematically. | ||