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The answer is "The positive real number that is one greater than its multiplicative inverse." What is the question?

2006-08-28 19:36:49 · 4 answers · asked by Deep Thought 5 in Science & Mathematics Mathematics

4 answers

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
***************
NOTE
we solve the equation ax² + bx +c = 0
with formula
x = (-b ±√(b² -4ac) )/2
**************
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 · answer #1 · answered by M. Abuhelwa 5 · 0 0

any comment on the number 2?

2006-08-28 20:05:00 · answer #2 · answered by ettezzil 5 · 0 0

What is the definition of φ (divine ratio/golden ratio)?

^_^

2006-08-28 22:10:50 · answer #3 · answered by kevin! 5 · 0 0

What is phi? (1.618034..)

2006-08-28 19:40:10 · answer #4 · answered by Anonymous · 2 0

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