You find a simple statement of fact to be "threatening behavior" and a "gratuitous personal smear"?
1) you have not provided a scintilla of evidence to refute anything I wrote.
I've demonstrated that the "Golden Mean", phi, and Fibonacci numbers are extensively used throughout Physics and other sciences. I'll prove it furthur, but you are obviously ignorant concerning this fact, and either in ignorance or outright deception attempt to portray these topics as fringe science.
2) you have provided NO evidence that the Math Depts. of the top 50 Universities teach technical courses in "Sacred Geometry," which should be trivially easy to do, if it is as Mathematically important as you keep making it out to be.
I don't recall ever stating that the subject was taught as a mainstream course. I did however state that it is obvious to anyone who has studied the history of Mathematics that "Sacred Geometry" is in fact related to Egyptian and Greek Mathematicians, and that this geometry relates to Universal constants and relationships. This matter of "vibrational resonance" which you harp and screech about is just one aspect of a definition which some people might have used to describe "Sacred Geometry", as there IS a metaphysical aspect involved as well. Whether or not YOU believe it possible, there ARE some things that Man doesn't yet understand. IF there are entities who have been here in the past and are visiting us now, THEY may have full working knowledge of that which we currently describe as "metaphysics".
3) your bloviating threats to "prove you to be a complete, total, utterly ignorant fool" don't impress me in the least.
Neither does your bloviating hypocracy impress ME.
4) and last, but not least, I decline your "invitation" to retract my statements because, how shall I put this...........
I already have a degree in Mathematics from a top-25 University.
Oooh, aahhh. Wow.... So are you proclaiming yourself to be a genius, a renowned expert, or another Isaac Newton, Einstein, or Tesla, simply because YOU have a piece of paper from some University? Give me a break.
Now that we can perhaps drop some invectives and go back to discussing the topic at hand, let me reiterate what I had initially stated.
"Sacred Geometry" is a term that describes Universal geometric relations and constants, and had originated in ancient times. The Egyptians and Greeks, amongst other ancient civilizations, utilized this knowledge extensively.
For a proper understanding of what is meant by "Sacred Geometry", follow the links below..
SACRED GEOMETRY OF CROP CIRCLES
Now that we have a better understanding of "Sacred Geometry", let us go back to the subject of the "Golden Mean", phi. Phi is a universal constant much like pi, which also dates back to the days of the Greeks. If you are claiming that phi is unimportant and obsolete, you might as well be saying that pi, the ratio of the diameter of a circle to its circumferance, is also an obsolete and archaic notion. This would obviously be a false and untrue statement, but it does appear that is exactly what you are saying.
Your extensive links on "phi" and it's relation to "Mandlebrot sets" and Fibonacci numbers, etc., merely reaffirms my previous objection: it, like all of "Sacred Geometry" is a Mathematical curiosity, a legacy of a mystical era in Mathematics, that today is nothing more than a hobby or curiousity for a few Mathematicians.
So again, let me just educate as to the importance of the Fibonacci numbers and phi...
Physics Links
B. Quantum Transport in Fibonacci Superlattices (Dr. Yong S. Joe) The general research objective is to study quantum effects on electronic transport in a Fibonacci superlattice. We plan to study the concept of the Fibonacci sequence and the `golden mean', and the effects of the conductance and transmission in a quasi-periodic structure. We will use a mathematical model describing potential barriers whose height or separation distances vary according to this sequence. A computer program will be modified so that it can calculate the conductance of this particular system. Finally, we will analyze the computer output and determine the conductance characteristics of this quantum-quasiperiodic system.
Properties of the peaks of second harmonic light through Fibonacci-class ferroelectric domains
From Theoretical Condensed Matter Physics Group
35. W. Salejda, P. Szyszuk: The Landauer conductance of generalised Fibonacci superlattices. Numerical results. Physica. A, 252, pp. 457-564, 1998. 36. W. Salejda, M. Kubisa, J. Misiewicz, K. Ryczko, M. Tyc: Landauer conductance of generalized Fibonacci type semiconductor superlattices. Acta Phys. Pol. A, 94, pp. 514-518, 1998.
Theoretical Solid State Physics Summer term 2002
Dynamical properties of three component Fibonacci quasicrystal
Electroabsorption spectroscopy of effective-mass Al Ga As/GaAs Fibonacci superlattices
Miniband transport in quantum Fibonacci superlattices with a modulated potential
A Golden Ratio construction of the 240-vertex E8 lattice from the 24-cell D4 lattice.
Math Links
In an earlier post, you tried to bedazzle me with your mention of e^(i pi) = -1, which you failed to attribute to Euler. Another interesting relationship that Euler discovered was Euler's phi function. In fact, Euler also is known for Euler's Theorum , which is a special case of Lagrange's theorem.
Another nice treatise on Euler's phi-function is provided at Euler phi-function
Some more math links..
Golden Ratio, Fibonacci Sequence
Animation of Binet's formula for Reals
Phi in Nature and Biology Links
DNA "Grooving" Measureably Closer to PHI Embedding with Time?
Fibonacci Numbers and how they are related to flowers, pine cones, ...
Phi and the Golden Ratio in Art, Architecture and Music
Fibonacci Numbers and The Golden Section in Art, Architecture and Music
Music and the Fibonacci Series
Proportion and the Golden Ratio - Mathematics and the Liberal Arts
I've demonstated that phi, the Golden Ratio, and the Fibnocchi numbers are indeed widely utilized in everthing from Physics, Math, and are present in Nature and the Arts. The relationships are universal, and span everything from DNA up to planetary positions. Even the stock market utilizes the Fibonacci numbers for analysis.
For you to state that the Golden Ratio and the Fibonacci numbers are relics of a bygone era and are simply obsolete curiosities, I have to seriously wonder if you REALLY DO have a Degree in Mathematics, from a major university or otherwise.
Now on "Ignore Mode".
He's been walking the walk on this forum for longer than you've been here, for sure. Since I've been paying attention.
I see you've gone from bluster to outright fabrication.
Nowhere have I said what you attribute to me. I have not said on word about Fibonacci. What I DID say is that "Sacred Geometry" and it's "vibrational resonances" is simply not a mainstream topic in modern Mathematics, and you haven't provided a single piece of evidence to the contrary.
I have repeatedly asked you to show that top-50 University Math Departments teach "Sacred Geometry" as part of the Mathematics degree curriculum (not some non-technical "History of Math for Art Majors" course), and you've provided nothing, zilch. If it is such an important topic in Mathematics, why aren't there courses being taught in it at all the top schools?
Your massive links about Fibonacci numbers, etc., are a red-herring; I'm well aware of them and the fact that they come up in a variety of contexts. That doesn't make "Sacred Geometry" with it's "vibrational resonances" an important topic.
So, I repeat, they relevant indicator of the importance of "Sacred Geometry" is whether or not it is part of the course curriculum in well-regarded Math Departments; so I reiterate my challenge to you yet again; show me that the top-50 schools are teaching courses in "Sacred Geometry" including its "vibrational resonances" as part of the Math degree program.
Absent a showing of the Mathematical importance of "Sacred Geometry" with its "vibrational resonances", your assertion that Space Aliens are likely trying to communicate said "Sacred Geometry" including its "vibrational resonances" to us by squashing symbols in farmers' fields is ludicrous. It makes about as much sense as Earthlings travelling the galaxy to a distant planet in order to leave the imprint of a "Wonder Bread" advertisement in an alien meadow.
First, let me buy you a clue: real Mathematicians don't go around giving attribution every time they write down an equation somebody proved 200 years ago. Giving attribution the way you do is the signature characteristic of someone trying to impress people who don't know better.
Second, I have no interest in "bedazzling" you; in fact, I wasn't even thinking about you at all when I wrote it. I was thinking about the lurkers, and used it to illustrate my point, which was that e, i, pi, -1, and 0 are all important numbers in Mathematics, and are inter-related by the relation I posted. This is in contrast to your precious "phi" which notably is absent form Euler's relation.
Another interesting relationship that Euler discovered was Euler's phi function. [snip]
Another nice treatise on Euler's phi-function is provided at Euler phi-function[emphasis added]
FL, I hate to be the one to break the news to you: Euler's "phi function" ISN'T the same "phi" as the one in your precious "Sacred Geometry" with its "vibrational resonances." You do understand that Mathematicians use the same symbol to represent different things in different contexts, don't you?
No doubt you will protest that you never said it was.... which is true; but then the question becomes why would you post it in the first place unless you thought it was related to the issue at hand?