Brian+Kim+Golden+Ratio

The Golden Ratio: ** (other names for it**- Extreme and mean ratio**,**medial section**, **divine proportion**, **golden proportion**, **golden** **number, and Phi)**

"In mathematics and the arts, two quantities are in the golden ratio if the ratio between the sum of those quantities and the larger one is the same as the ratio between the larger one and the smaller." (wikipedia.org) The golden ratio is an irrational mathematical constant, which is approximately 1.6180339887." Golden Ratio exists in almost everywhere; houses, paintings, in the woods, buildings, etc. The golden ratio is an extraordinary discovery by people, stunning the majority. When research was beginning based on this ratio, people had no idea that this topic they found, the Golden Ratio, was all around us! (Never new it was this imporant, too). But, despite it is a very important concept to the world today, it is simply an equation that people could memorize, too., represented by (√5+1)/2 So, the golden ratio practically is, "The total length //**a + b**// is to the longer segment //**a**// as //**a**// is to the shorter segment //**b**// ." The Golden Ratio, is just as it is said, "A golden ratio." This means that, it is practically where certain measurements of objects/materials have a perfect/unnoticable/mysterious ratio.
 * What is the Golden Ratio?**

How is this possible? When did we start using this thing? These questions fumbled many professional workers while doing their work, and is still quite amazing today. Since 2000~2400 years ago, amazing mathematicians, mainly from Greece, have studied about ratios. There were many people around the world, too, that were stunned, worried/confused about this beautiful but ugly ratio. Well, there were cases of people other than the mathematicians, like the Biologists, musicians, artists, etc. Main/Famous places the Golden Ratio is found to be in is, in Architecture, Paintings, the Human Body, and Nature.
 * The History of Golden Ratio:**

Timeline (facts given by [] and timeline by WIkipedia.org)
 * [|Phidias] (490–430 BC) made the [|Parthenon] statues that seem to embody the golden ratio.
 * [|Plato] (427–347 BC), in his //[|Timaeus]//, describes five possible regular solids (the [|Platonic solids]: the [|tetrahedron], [|cube], [|octahedron], [|dodecahedron] and [|icosahedron]), some of which are related to the golden ratio.[|[14]]
 * [|Euclid] (c. 325–c. 265 BC), in his //[|Elements]//, gave the first recorded definition of the golden ratio, which he called, as translated into English, "extreme and mean ratio" (Greek: ἄκρος καὶ μέσος λόγος).[|[5]]
 * [|Fibonacci] (1170–1250) mentioned the [|numerical series] now named after him in his //[|Liber Abaci]//; the ratio of sequential elements of the [|Fibonacci sequence] approach the golden ratio asymptotically.
 * [|Luca Pacioli] (1445–1517) defines the golden ratio as the "divine proportion" in his //Divina Proportione//.
 * [|Johannes Kepler] (1571–1630) proves that the golden ratio is the limit of the ratio of consecutive Fibonacci numbers,[|[15]] and describes the golden ratio as a "precious jewel": "Geometry has two great treasures: one is the [|Theorem of Pythagoras], and the other the division of a line into extreme and mean ratio; the first we may compare to a measure of gold, the second we may name a precious jewel." These two treasures are combined in the [|Kepler triangle].
 * [|Charles Bonnet] (1720–1793) points out that in the spiral [|phyllotaxis] of plants going [|clockwise] and counter-clockwise were frequently two successive Fibonacci series.
 * [|Martin Ohm] (1792–1872) is believed to be the first to use the term //goldener Schnitt// (golden section) to describe this ratio, in 1835.[|[16]]
 * [|Edouard Lucas] (1842–1891) gives the numerical sequence now known as the Fibonacci sequence its present name.
 * Mark Barr (20th century) suggests the Greek letter phi (**φ**), the initial letter of Greek sculptor Phidias's name, as a [|symbol] for the golden ratio.[|[17]]
 * [|Roger Penrose] (b.1931) discovered a symmetrical pattern that uses the golden ratio in the field of [|aperiodic tilings], which led to new discoveries about [|quasicrystals].

What is the Golden Ratio? media type="youtube" key="BHXN3LVwlK0" height="278" width="352" []
 * Sources in order to help gain more knowledge about the Golden Ratio:**

Golden Ratio in the Human Body & the world: media type="youtube" key="085KSyQVb-U" height="344" width="425" []

A helpful website to learn more about Golden Ratio: []

Web Sources: 1. Huntley, H.E. The Divine Proportion: A Study in Mathematical Beauty. London: Dover Publications, 1970. 2. "Golden Ratio." __Golden Ratio__. 18 Oct. 2009 http://mathgoldenratio.blogspot.html 3. "Golden ratio - Wikipedia, the free encyclopedia." __Wikipedia, the free encyclopedia__. 18 Oct. 2009 . 4. [|Weisstein, Eric W.] "Golden Ratio." From [|//MathWorld//]--A Wolfram Web Resource. []