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Year 12s: what will be the first way you research your future options? >>

Reply 1

dvs

x = W(1) (http://mathworld.wolfram.com/LambertW-Function.html)

Or were you looking for a numerical solution?

yes.

ok, i found this, which kind of answers my question - http://en.wikipedia.org/wiki/Omega_constant

however now i have another. that page says "It has properties that are akin to those of the golden ratio, in that

e^− Ω = Ω"

what is the golden ratio's corresponding property?

Reply 4

Dekota

chewwy

e^-x = x

find x.

Let x = 1, after some iterations, x = 0.567 (3.s.f)

Reply 5

dvs

I think the golden ratio thing is because we have 1 + (phi)^(-1) = phi, and [e^(omega)]^(-1) = omega.

Reply 6

Esquire

What does it mean to say that e is trancendental (heavenly?). I thought it was just irrational...

Reply 7

Handy

It occurs all over the place in nature. A bit like pi.

Reply 8

AlphaNumeric

Esquire

What does it mean to say that e is trancendental (heavenly?). I thought it was just irrational...

Transcendental => Irrational

Irration just means it cannot be expressed as a/b for finite a,b. Trancendental means it is not the solution to a polynomial (ie a finite power series) with integer coefficents.

Pi is trancendental, and while it satisfies sin(pi) = 0, sin is not a finite power polynomial. Same goes for practially all numbers.

Reply 9

Christophicus

chewwy

e^-x = x

find x.

Use Newton-Raphson process

f(x) = e^-x - x
f'(x) = -e^-x -1

let a = 1 and denote the approximation to the root of f(x) = 0 be a
=> a - f(a)/f'(a) is a better approximation.

Continue this process and the root is 0.567 (3 s.f)