x - 1 = 1/x
x² - x -1 = 0
this equation can be solved in
x = 1/2 ± √5/4
but when x is +ive
then
x = 1/2 + √5/4
x = 1.618033988749
x ≈1.62
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NOTE
we solve the equation ax² + bx +c = 0
with formula
x = (-b ±√(b² -4ac) )/2
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this number is called the golden ratio φ
Two quantities are in golden ratio if their sum is to the larger quantity as the larger is to the smaller. Stated mathematically:
(a+b)/a = a/b
where a is the larger and b is the smaller quantity.
This ratio, denoted (φ), is an irrational number with value
φ ≈1.618033989
The first calculation of the golden ratio, was described by Euclid in his Elements (greek: Στοιχεῖα).
The most common other names used for the golden ratio are golden section (Latin: sectio aurea), golden mean (which has another unrelated meaning, see Golden mean (philosophy)), golden number, and phi (referring to the Greek letter φ).[1][2][3] Other names include medial section, divine proportion (Italian: divine proportione), divine section (Latin: sectio divina), golden proportion, golden cut,[4] extreme and mean ratio, and mean of Phidias.[5][6][7]
Since the sixteenth century, shapes proportioned according to the golden ratio have been considered aesthetically pleasing in Western cultures; the golden ratio is still frequently used in art and design. The golden ratio has attracted a large following for its supposed aesthetic, psychological, historical, mystical, natural, and metaphysical properties, in addition to its mathematical properties.
2006-08-28 20:02:55
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answer #1
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answered by M. Abuhelwa 5
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