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Golden Ratio: Difference between revisions
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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]]. | ||
[[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. | [[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. | ||
The [[Golden Ratio]] 1.618033988749894848204586834... in mathematics, art, and architecture. | The [[Golden Ratio]] 1.618033988749894848204586834... in mathematics, art, and architecture. | ||