Relating π to Φ

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A unit circle is a circle with radius 1 rather than a diameter of 1.
 
MarkFL said:
It seems you may have some axe to grind with the mathematics community, and/or are a crank. At any rate, I have stated why I dismissed your impossible claim.
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A moderator name-calling? Really? Are you also into the identity politics of slandering people as "cranks" who don't agree with you?

MarkFL said:
Yes, both \(\pi\) and \(\phi\) are irrational, but \(\phi\) is an algebraic number while \(\pi\) is not; it is transcendental. The number:

[MATH]\frac{4}{\sqrt{\phi}}[/MATH]
is a root of:

[MATH]f(x)=x^4+16x^2-256[/MATH]
A transcendental number can never be a root of a non-zero polynomial in one variable with rational coefficients. This is one reason many here will likely dismiss your claim at a glance.
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Is nonsense: because Φ is itself geometric, as long as it is coupled to π,
(which it is, by way of being the very base of it) that π is "transcendental" is irrelevant.
The geometric portion always holds: like imaginary numbers acting on real ones.

(π+π√5)/2π is a valid representation of Φ, and as Jeff pointed out:

JeffM said:
A unit circle is a circle with radius 1 rather than a diameter of 1.
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MY error was designating the circle corresponding to the unit square as a unit circle, when in fact it is not, rather r=2, so
thank you to Jeff for pointing that out - was the most helpful response. I take it no further contention despite orthodoxy.
 
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This whole thread is a quintessential example of beating a dead horse. Who cares?
 
Romsek said:
Found this little tidbit. You'd think OP would have found it if they were at all serious about the topic.

https://johncarlosbaez.wordpress.com/2017/03/07/pi-and-the-golden-ratio/
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Well how nice of you to have been researching the topic.

The problem is summarized:

"by approximating the circumference of a circle using a regular 96-gon... "

1. Using straight-line polys to approximate a curve is stupid, and
2. Archimedes was obviously unaware of the relationship between Φ and π, however I know he is an idol upon mathematicians.

I already found what I was looking for:

pibyphimh2.jpg

However please continue to worship the dead Archimedes and his poly "approximation".

How can humanity be this stupid, and for so long?

What Φ is to image/linear, π is to likeness/curvature.

In whose image and likeness are the skies and the terrains created?
As well as the Eve (π) who is derived from Adam's (Φ) own rib?

pka said:
This whole thread is a quintessential example of beating a dead horse. Who cares?
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Romsek said:
Found this little tidbit. You'd think OP would have found it if they were at all serious about the topic.

https://johncarlosbaez.wordpress.com/2017/03/07/pi-and-the-golden-ratio/
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Romsek

Thank you.

First, a demonstration of how to present a demonstration.

Second, a proof that the OP's specific conclusion was wrong, which as Mark pointed out, was known from general principles.

Third, something that should (but probably will not) please the OP: an exact relationship between pi and phi using an infinite process.
 
One of the moderators or an administrator , please lock/close this thread ASAP. You have seen what it has
devolved into.
 
JeffM said:
Romsek

Thank you.

First, a demonstration of how to present a demonstration.

Second, a proof that the OP's specific conclusion was wrong, which as Mark pointed out, was known from general principles.

Third, something that should (but probably will not) please the OP: an exact relationship between pi and phi using an infinite process.
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The fundamental premise of the "proof" is false: you simply can't use straight-edged polys to find a curve to exactitude: you will always be short, infinite process or not. The surface of a sphere if/when represented on a 2D surface requires some "backwards" curvature apparatus to measure the circumference which can not even be represented visually, let alone "approximated" by a straight line. You can't "bend" a "straight" line such to capture the area under the curve: however, you can use a "bent" line which is scale-invarant, which is precisely what the golden spiral is.

However the four golden triangles fixes this problem due to the proportions cancelling out such to only be left with a function of √Φ
as Φ naturally produces the curve we need to measure the entire circumference.

lookagain said:
One of the moderators or an administrator , please lock/close this thread ASAP. You have seen what it has
devolved into.
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You're missing an entire portion of the circle if you use lines. This can only be overcome by the association of the line-to-curve that the golden spiral and associated golden triangle provides. This is all the proof does: uses a curve to measure a curve. What is the problem?
 
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The last post (which had been #31) was reported. I requested the deletion of said post, the repeated request to lock this thread,
and the banning of user nothing. Thank you.
 
lookagain said:
The last post (which had been #31) was reported. I requested the deletion of said post, the repeated request to lock this thread,
and the banning of user nothing. Thank you.
Click to expand...

pi by phi flower.jpg

Here is a flower - will you calm down?

All I did was copy/paste the golden spiral, doubled it each time and bulged the interior such to reveal the internal symmetry.

Isn't it pretty?
 
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