the golden ratio. ahh help me! ?

Question

okay well i have a report on the golden ration but i cant find any information that i need. i need to find out who invented it and where. can anyone give me any links or infoo please&&thank youu =]

Answer 1

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: ακρος και μεσος λογος).[9]



Source:

Wikipedia--



http://en.wikipedia.org/wiki/Golden_ratio#History



φ is WAY cooler than pi since it can be found in ratios throughout nature.







Timeline



Timeline according to Priya Hemenway[13].



* 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: ακρος και μεσος λογος).[9]

* Fibonacci (1170–1250) mentioned the numerical series now named after him in his Liber Abaci; the Fibonacci sequence is closely related to the golden ratio.

* Luca Pacioli (1445–1517) defines the golden ratio as the "divine proportion" in his Divina Proportione.

* Johannes Kepler (1571–1630) 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.[15]



* 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.[16]

* 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.





If you google these names with Phi you should get some good results.

Answer 2

The golden ratio is many times called the divine ratio, because it is likewise the ratio of stability. while you're making a cellular, you will use the golden ratio to make certain the place to place the subsequent point, etc. So, if this is the ratio of stability, the two bodily and artistically, i could see the place superstitious minds could see it as something religious or maybe godlike. purely like casting out 9s.

Answer 3

The golden ration is commonly known as "phi" which is a Greek letter (φ).



Phi=(1+sqrt(5))/2



Phi is a number: nobody invented it, but many people did study it. Some facts about it are...



If you take the Fibonacci sequence, and you divide one term by the term after it, then the numbers get closer and closer to phi as you increase the numbers.



Phi squared=Phi+1

Phi^(-1)=Phi-1



There are actually quite a lot of applications of phi. It is used in nature and geometry very often, such as in a nautilus, pine cone, and sunflowers. See the source page for more details (listing everything about phi would be incredibly long)