What is the exact value of PHI?

Answer 1

Phi (φ) = (1 + √5) / 2 = (a + b) / a = a / b = 1.6180339887 4989484820 4586834365 6381177203 0917980576...

Answer 2

So I am no matematitian, but i can tell you this and a web page where to look for more about Phi and there is plenty...

http://goldennumber.net/math.htm

Phi can be derived by solving the equation:

n2 - n1 - n0 = 0

which is the same as

n2 - n - 1 = 0

This equation can be rewritten as:

n2 = n + 1 and 1 / n = n - 1

The solution to the equation is the square root of 5 plus 1 divided by 2:

( 5½ + 1 ) / 2 = 1.6180339... = Phi

This, of course, results in two properties unique to phi:

If you square phi, you get a number exactly 1 greater than phi: 2.61804...

Phi2 = Phi + 1

If you divide phi into 1, you get a number exactly 1 less than phi: 0.61804...:

1 / Phi = Phi - 1

Phi, curiously, can also be expressed all in fives as:

5 ^ .5 * .5 + .5 = Phi

This provides a great, simple way to compute phi on a calculator or spreadsheet!

Phi = 1.6180339...

Answer 3

Value Of Phi

Answer 4

Do you mean PI ?

It has an exact value, which is the ratio of the circumference of a circle to its diameter, but it hasn't an exact decimal representation.

There is a whole class of numbers such as pi which cannot be represented exactly as a terminating or recurring decimal. They are called irrational, and there are more of them than there are rational numbers (i.e. whole numbers and fractions). Numbers such as the square roots of 2, 3, 5 are also irrational, but they are the roots of algebraic equations, e.g. the square root of 5 is a solution of the equation

x^2 - 5 = 0.

PI is a member of the class of numbers which are not solutions of any such equation, and are called transcendental numbers.

PS. Perhaps you meant to ask for a value of PI correct to lots of decimal places, i.e. a highly accurate value (not the same as exact). I remember only as far as

3.1415926538 .....

but if you google pi you might find it to hundreds of places.

Answer 5

1.61803398874989484820...(Look at Jim's answer instead.)

Edit:Hy,Phi and Pi are two different things. Pi is the ratio of a circle's circumference to its diameter,according to wiki,whereas Phi is the golden ratio.

Jim:Darn,good point. >_<

Answer 6

Here's a site illustrating the value: (couldn't copy it)

http://jwilson.coe.uga.edu/EMT669/Student.Folders/Frietag.Mark/Homepage/Goldenratio/goldenratio.html

Answer 7

φ = (1 + √5)/2

The decimal expansion is neat, but you used the word EXACT, and the decimal is not exact, no matter how far you take it.

Answer 8

1.618,,,,