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Home :: Community :: Surveys :: What do you know about the "golden ratio?"
Results
Not only do I know what it is, I have a good chunk of it memorized! 29 15.4%
I know of it, and where it sometimes occurs 96 51.1%
Never heard of it 48 25.5%
Ratios don't have colors! 15 8.0%

 Survey posted 2005-05-09 15:20 by Jon. Contribute ideas to surveys by sending a mail to survey@ticalc.org.

Re: What do you know about the golden ratio?
Paul Houser
(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
(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

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

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

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
(Web Page)

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

Re: Re: What do you know about the golden ratio?
Zeroko
(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
(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

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
(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
(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
(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
(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
(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
(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
(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
(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
(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
(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
(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
(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
(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
(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
(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
(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
(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
(Web Page)

Oops...double post.

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

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