What are the E, pi, phi constants relations

[HallsofIvy]

Is that golden ratio constant the actual number, or an approximation?

The golden ratio constant is the actual number. In fact, it is exactly
\frac{1+\sqrt{5}}{2}.

I can't imagine any mathematical constant being an "approximation to an actual number"!

 

[moshek]

It was Hipasus of metapontum who discover the existence of irrational numbers. he find self similarity on the pentagon so he prove by this that the golden ratio is not a rational number . But for some reasoned Euclid wrote on his 10 th book only about the irrationality of the root of 2 by the classical prove but this Euclid make a confusion with what really happened
with irrational numbers.


Moshek

 

[MathematicalPhysicist]

Than you should reply to me
in some different way like:

Now i have more exact way
to ask my original question !

Best
Moshek

I invite you to read:

www.physicsforums.com/showthread.php?t=17243

i think i did it in first two pages of this thread.

 

[moshek]

I look but i did not see that you did it
anyhow it is really not the main point here.

Moshek

 

[epii10]

equation of unity involving Pi, e, Phi

Thought you guys might appreciate a little math I found concerning the numbers; Pi, e, and Phi as they relate to three unique right triangles. I call it the "Triple-Triangle-Theory" (TTT). I'm no mathematician so if anyone could tell me "why" the TTT works please feel free. (I think it has to do with the imaginary unit ie. "sqrt -1").

Here's the link:

http://www.gizapyramid.com/rick_howard research.htm

Rick Howard

 

[lavalamp]

That's a dead link.

Edit: Just try pasting the URL into the page, the forum should make it into a link automatically.

 

[MathematicalPhysicist]

Thought you guys might appreciate a little math I found concerning the numbers; Pi, e, and Phi as they relate to three unique right triangles. I call it the "Triple-Triangle-Theory" (TTT). I'm no mathematician so if anyone could tell me "why" the TTT works please feel free. (I think it has to do with the imaginary unit ie. "sqrt -1").

Here's the link:

http://www.gizapyramid.com/rick_howard research.htm

Rick Howard

he doesn't say how he arrived at the e proportion.
can someone tell me about it?
the pi and phi proportions are clear to me.

 

[epii10]

e proportion

Loop,

I found the e proportion just messing around with the angles of the Pyramid with my HP graphic calculator. Sort of an accident really, only (and this is going to sound weird) I loved the number e and would talk about it to anyone who would listen and had it in the back of my mind that I would find it in the Pyramid. Boy was I surprised!

My TTT paper (linked above) goes over the derivation of the e proportion but the first paper I wrote before discovering the TTT was all about the e proportion.. here is that link:

http://www.gizapyramid.com/ricks-e-proportion/rick-howards-research.html

I once had a real mathematical guy analyze the TTT and he said it was just a trick through the sustitutions.. (again, I'm no mathemetician) but simply because the equation embodies all three nearly congruent angles, and that coupled with the tetrahedral angle of 60 degrees being the only other solution to a specific question I pose along the way such that the output remains in the realm of "real" numbers, I tend to think it's just a little weird and still can't wrap my mind around it.

Pretty cool huh?

Rick

 

[MathematicalPhysicist]

howard have you tried plugging other numbers for the base of the triangle other than 1?

perhaps it's just a mistake but i notice that when the base is 1 then the side of the square (the base of the pyramid) is 2 and this number is in the proportion of e: beta/theta=e/2 perhaps there is a connection between the side of the base of the pyramid square and this proportion (and perhaps I am hallucinating who knows (-: ).

 

[matt grime]

there's nothing special at all in those calculations, and the thesis contains many unjustified statements.

1) what does "optimal" mean, other than "supports me theory"
2) why do you say irrational numbers are impossible to construct with any accuracy in the real world, with the implicit assumption that somehow rationals are constructible to some degree of accuracy, and if so that negates your statement as then phi is realizable as a diagonal of a pentagon?
3) The mathematical presentation of the paper is shockingly bad, such as anyone who looks at the first diagram is given the impression that the betas are all the same when they certainly aren't.
4) why on Earth is 2 so special to the point where you say no other integer will do it better?
5) the idea that you're going to produce a polynomial with phi as a root and 'wth the minimal number of terms' must be considered an ill advised boast since I'm sure i can think of one of degree 1 with phi as a root, and two if you must make me have integer coeffs, which must have fewer terms than the one you derive (a mathematically provable fact), though i didn't see it highlighted later in the text, but then that's because there's so much unnecessary waffle that it's not an easy task to extract information from the article.
6)the ideas of eqn 5.4 indicate a lack of understanding about raising complex numbers to exponents; again nothing special is going on there.
7) it would be beneficial to learn about polar representations of complex numbers to see why these coincedences occur.

 

[epii10]

TTT is an aesthetic thing

Matt,

Your feedback of my TTT paper is appreciated. I'm always glad to have a "math smart" person give it gander. Forgive me as I realize it is a poorly done paper full of too much extranious opnion.. what can I say, I'm an artist/musician and my approach to math is aesthetic. I never claimed to be a mathematician or even "good" at math for that matter, fact is, I pretty well suck at math.

end of apology...

I didn't set out in the TTT to solve a problem. Mathematicians do that, I am not one of them. I found a ratio in the outer geometry of the Pyramid ie. (the e proportion). And there was no denying that it was there. I thought it was interesting. I looked at the Pi and Phi proportions and had long been awed by their coincidental occurence in the Pyramid. Yes, I do know that coincedence is a reality. When I started playing with the angles I began substituting terms and ended up with an equation that was true. How could it be not true? My method was elementary and I was only dealing with identities and those identities led to an overall identity as opposed to a solution to a problem.

In the end I was looking at an equation with three unique angles embedded in it such that the equation was equal to "1". If the three angles in the equation could be anything else than what they are for the thing to equal "1" then I'd be interested to know what they would be.

That's all it is, just a curious correlation of three independent right triangles living together in a simple equation. But (and this is the kicker) three right triangles that are very nearly congruent.. only ever so slightly different in shape.. and that is aesthetic if nothing else.

Rick

 

[matt grime]

wow... so if i spot that things are accurate to some completely artificial level of accuracy that makes it note worthy in such eulogising prose? the square root of two is 14 tenths, if you accept certain tolerances...

 

[epii10]

I don't know how to respond to you Matt because I don't understand your thinking. Good luck in your endevours.

Rick

 

[matt grime]

but the number of days in a week divided by the number of fingers (and thumb) on one hand is almost equal to the square root of two, doesn't that suggest something to you about the people who set the number of days in a week?

 

[lavalamp]

I know that you're not going to like this, but you brought it up so I'm going to say it anyway.

Take the number of fingers (and thumbs) most people have, and divide it by the number of days in a week.

10/7 = 1.4286

Also as you said

7/5 = 1.4

But get this, find the mid-point between the two, and you get even closer:

(10/7 - 7/5)/2 + 7/5 = 1.4143

It turns out than now you're only 7.215 * 10^-5 out! Spooky!

 

[Gokul43201]

Or, the error is VERY NEARLY equal to:

(no. of days in week)/[(no. of fingers on both hands) ^ (no. of fingers on one hand)]

Oooooooooh !