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Re: What do you know about the golden ratio?
Paul Houser Account Info
(Web Page)

Isn't the mathematical constant e the golden ratio?

Reply to this comment    9 May 2005, 18:40 GMT

Re: Re: What do you know about the golden ratio?
Paul Houser Account Info
(Web Page)

Nope.

Reply to this comment    9 May 2005, 18:41 GMT


Re: Re: Re: What do you know about the golden ratio?
Brian Gordon  Account Info

what? that's weird... you answered your own question

Reply to this comment    9 May 2005, 20:02 GMT


Re: Re: Re: Re: What do you know about the golden ratio?
Chris Williams  Account Info

And within a minute after the question!

Reply to this comment    9 May 2005, 21:47 GMT


Re: Re: Re: Re: Re: What do you know about the golden ratio?
Paul Houser Account Info
(Web Page)

Yeah, after reading the other comments.

Reply to this comment    10 May 2005, 21:09 GMT


Re: Re: What do you know about the golden ratio?
Zeroko  Account Info
(Web Page)

I think it is related to e. If I remember correctly, a radius (theta=constant) drawn over an exponential spiral (r=e^theta) will always make angle phi radians on the side of the spiral away from the pole every time it crosses the sprial.

Reply to this comment    10 May 2005, 00:44 GMT


Re: Re: Re: What do you know about the golden ratio?
Ben Cherry  Account Info
(Web Page)

of course they must be related somehow. e is the perfect number in calculus, phi is the perfect number in geometry (flat things with sharp angles) and pi is the perfect number in trigonometry (circles not triangles), and i is the perfect number in complex math... that doesn't really work, but oh well, thats what you get for making stuff up on the spot.

Reply to this comment    10 May 2005, 05:19 GMT


Re: Re: Re: Re: What do you know about the golden ratio?
Rob van Wijk  Account Info

Do you think you can expand
e^(pi i) + 1 = 0
to include phi?

Reply to this comment    11 May 2005, 06:31 GMT


Re: Re: Re: Re: Re: What do you know about the golden ratio?
Ben Cherry  Account Info
(Web Page)

of course!

e^(pi*i)+phi=1/phi

: )

Reply to this comment    12 May 2005, 00:56 GMT

Re: Re: Re: Re: Re: Re: What do you know about the golden ratio?
Jake Griffin  Account Info
(Web Page)

But then you get rid of the zero and make it seem like phi is more important...how bout this:
e^(pi*i)+phi=1*Phi+0

Reply to this comment    12 May 2005, 06:46 GMT


Re: Re: Re: Re: Re: Re: Re: What do you know about the golden ratio?
Zeroko  Account Info
(Web Page)

Mathematics is supposed to be elegant, & "1*Phi" is not, so there must be a better (that is, more elegant) equation. Maybe e^(pi*i)+1/Phi+phi^2=0 (& then it even includes 2, which all geeks know is important).

Reply to this comment    13 May 2005, 01:21 GMT

Re: Re: Re: Re: Re: Re: Re: Re: What do you know about the golden ratio?
Zeroko  Account Info
(Web Page)

Now all it needs is 42. :)

Reply to this comment    13 May 2005, 01:32 GMT


Re: Re: Re: Re: Re: Re: Re: Re: What do you know about the golden ratio?
Zeroko  Account Info
(Web Page)

Here is a better one: e^(pi*i)+1/Phi+phi^(42/(3*7))=0
This includes the important mathematical constants, 42 (the answer to Life, the Universe, & Everything), 3 (to represent the Trinity), & 7 (also important in Christianity & Judaism). Obviously, it looks better written in "textbook"/pretty print fashion.

Reply to this comment    13 May 2005, 04:33 GMT


Re: Re: Re: Re: Re: Re: Re: Re: Re: What do you know about the golden ratio?
Ben Cherry  Account Info
(Web Page)

but then we do have phi twice in all of these... Isn't there a way to make phi show up only once? No, I guess not...

Reply to this comment    13 May 2005, 04:50 GMT


Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: What do you know about the golden ratio?
Zeroko  Account Info
(Web Page)

Phi & phi both appear so the equation is especially beautiful. :) Actually, there may be a way to get rid of one of them, but it would probably ruin the layout &/or mess up the other numbers. No powers of Phi are integers.

Reply to this comment    13 May 2005, 05:12 GMT


Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: What do you know about the golden ratio?
Ben Cherry  Account Info
(Web Page)

but phi can be computed with integers.

Reply to this comment    14 May 2005, 06:02 GMT


Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: What do you know about the golden ratio?
Zeroko  Account Info
(Web Page)

Infinitely large ones, or infinitely many of them...I do not want to add an infinite sum, infinite product, or limit to the equation.

Reply to this comment    14 May 2005, 14:33 GMT


Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: What do you know about the golden ratio?
Ben Cherry  Account Info
(Web Page)

jvdthwip wrote (9 May 2005, 18:24 GMT:

I'll be the 1`st to answer:

== GOLDEN RATIO ==
(1+sqrt(5))/2, approximately 1.61803, which happens to be the ratio of a diagonal of a pentagon to its side. This constant shows up in many metrical properties of the dodecahedron and icosahedron just as the square root of 2 shows up in the metrical properties of the cube. A golden rectangle has sides in this ratio. A golden rhombus has diagonals in this ratio.

So all we have to do is find out how to involve that in the equation...

Reply to this comment    14 May 2005, 22:14 GMT


Re: Re: Re: Re: Re: Re: What do you know about the golden ratio?
calkfreak83  Account Info
(Web Page)

Can anybody solve that for Phi, so we can get a formula for Phi in terms of e?

Reply to this comment    14 May 2005, 02:54 GMT


Re: Re: Re: Re: Re: Re: Re: What do you know about the golden ratio?
Zeroko  Account Info
(Web Page)

I assume he meant e^(pi*i)+Phi=1/phi (or with the (P/p)hi's reversed, which would be the same thing), which yields 0=0 upon attempt at solving for Phi, so, unfortunately, no.

Reply to this comment    14 May 2005, 14:31 GMT


Re: Re: Re: Re: Re: Re: Re: Re: What do you know about the golden ratio?
calkfreak83  Account Info
(Web Page)

No.. the equation is e^(pi*i)+Phi=1/Phi [both with capital letters].

I can get to:
Phi^2+Phi*e^(pi*i)-1=0

-e^(pi*i) + sqrt(2e^(pi*i)+4)
------------------------------ = Phi
2

That looks way too nasty though..

sqrt(2e^(pi*i)+4) - e^(pi*i)
----------------------------- = Phi
2

Reply to this comment    14 May 2005, 17:08 GMT

Re: Re: Re: Re: Re: Re: Re: Re: Re: What do you know about the golden ratio?
calkfreak83  Account Info
(Web Page)

Or all on one line as:

Phi = .5 (sqrt(2e^(pi*i)+4) - e^(pi*i))

Reply to this comment    14 May 2005, 17:10 GMT


Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: What do you know about the golden ratio?
calkfreak83  Account Info
(Web Page)

Dammit.. It dont work.. Oh well.. I tried.

Reply to this comment    14 May 2005, 17:12 GMT

Re: Re: Re: Re: Re: Re: Re: Re: Re: What do you know about the golden ratio?
Zeroko  Account Info
(Web Page)

You are right, his equation does work as e^(pi*i)+Phi=phi (or with phi replaced with 1/Phi, of course). Sorry & thanks for the correction.

Reply to this comment    18 May 2005, 02:40 GMT


Re: Re: Re: Re: Re: Re: Re: Re: Re: What do you know about the golden ratio?
Zeroko  Account Info
(Web Page)

You are right, his equation does work as e^(pi*i)+Phi=phi (or with phi replaced with 1/Phi, of course). Sorry & thanks for the correction.

Reply to this comment    18 May 2005, 02:40 GMT


Re: Re: Re: Re: Re: Re: Re: Re: Re: Re: What do you know about the golden ratio?
Zeroko  Account Info
(Web Page)

Oops...double post.

Reply to this comment    18 May 2005, 02:41 GMT

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