The greats of math, science and geometry have long been fascinated with the Golden Ratio (Pi). Albrecht Durer, Descartes, Newton and a host of others were fascinated by infinitive nature of Pi and its relationship to the underlying fundamental basis of math, science and geometry. Albrecht Durer in particular used it to generate a number of complex geometric shapes which greatly influenced modern geometry. A number of which, including the rhombus and the equilateral triangle, are clearly depicted in these solutions to the trisection of the angle on the website listed below.

These great minds of geometry understood intuitively that the circle and Pi are infinite and from the interaction the circle and arc, and other geometric shapes, it is possible to generate the solution to an infinite number of complex mathematical problems.

As can be clearly seen in the diagrams on the indicated website http://pg.photos.yahoo.com/ph/edwardchesky/slideshow?.dir=/66d7&.src=ph it is possible, with the appropriate application of the circle and arc, to generate the solution to any number of complex geometric problems. In this particular case the solution to this problem also clearly demonstrates the universality of Pi.

In the future it is highly likely that advanced computing systems will be built around an operating system that incorporates an understanding of the universality of Pi. Whether or not this demonstrated universality of Pi, can be seen a proof of God or an intelligent design behind the structure of the universe still remains to be seen. This particular question has long frustrated the greats of geometry and is not likely to be definitively answered for some time to come.

Note I used a varient of the Quadratrix of Hippias to Trisect the angles depicted on the website. In terms of process I had to construct the geometric shapes first then use a varient of the Quadratrix of Hippias curve to perform the trisection. All work was done with a compass and straightedge. Not exactly the pure Greek solution to the problem but it fits within existing mathmatical theory. A discussion of the Quadratrix of Hippias is listed below.

Hippias's Quadratrix

This is a curve formed as the intersection of a radius and a line segment moving at corresponding rates. A square and a circle are drawn so that one corner of the square is the center of the circle, and the side of the square is the radius of the circle. The idea is this. A radius falls over from the side of the square to the base at a constant rate. At the same time, a line segment falls from the top of the square at constant rate. Both start moving at the same time, and both hit the bottom at the same time.

Thus, the ratio, change in arc length/ displacement of falling cross piece, represents the speed of the sweeping radius relative to the falling cross piece. Since both move at constant speeds, this ratio is always the same value. With some knowledge of "modern" trigonometry, it can then be calculated. The length of the arc swept out from beginning to end is pi/2 radians(90 deg.) time radius length. The distance the cross piece falls is simple the length of the square's side. But, since the length of the square's side is equal to the length of the radius, (pi/2) times radius length/side length= pi/2. Thus, the curve is a pictorial representation of the irrationality of pi.

Note: The quadratrix was discovered by Hippias of Elias in 430 BC, and later studied by Dinostratus in 350 BC (MacTutor Archive). It can be used for angle trisection or, more generally, division of an angle into any integral number of equal parts, and circle squaring.

I also note an Oxford Don also solved Alhazen's Billard Problem in 1997 by translating it into co-ordinates on an X and Y axis, an insight first obtained by Descartes in the 17th Century. My solution to the Billiard Problem is related to that created but never finished by Albrecht Duur, however was the result of independent research

Hi Edward, I came across a problem in my Atomic Mass paper which involves pi. I noticed that if lambda l in the deBroglie-Planck-Einstein equation equals zero, the equation falls apart. For example:

E = hc/ l(proton m) = ~(1-g)c^2

so if l = 0, the left side collapses to zero, so the right side means g, which is the proton-to-proton gravitational constant, defaults to g = 1, so the right side collapses to zero also. This means that E = 0, in effect there is no Energy.

Now here is pi comes in. In the conversion equation for figuring Newton's G from proton gravitational g, I used:

G^2 = gc^2 pi^2

But what happens if g = 1, as per above?

We get G^2 = (1)c^2 pi^2, where G = c. This is not in any known units, so numerical outcome only, though we may discover someday that G = c is a valid function for galactic black holes, or any place where all the surrounding ambient lambda cancels to zero. If there are no wavelengths on a point, then light ceases to function. (I had shown a simple kitchen experiment at one time, where a bowl full of water has a vibrator applied against the rim, like a back massager, so all the surrounding waves converge in the center of the bowl and cancel out.) So here is my question:

If all lambda cancels on a point, what happens to the pi function in the above gravity conversion equation? Does it collapse into zero also? In other words, what is pi on a zero point?

For that matter, why is there a pi function in the conversion equation in the first place? Here is how it works out:

G^ = gc^2 pi^2, which is:

52.41E-22 m^6 s^-4 s^-4 kg/kg = (5.9E-39 m^-4)(9E+16 m^2 s^-2)(9.87), which taking the square root gives us: G = ~7.239E-11 m^3 kg/kg s^-2, where the mass (kg/kg =1) is implied as kg.

I've been thinking about this for some time, but don't have a meaningful answer. I think this implies that all galaxies will have a black hole, which is maximum gravity (G = c) at their center if all the ambient light from the surrounding galaxy cancels on a point. But then what happens to pi on a point? Does it simply disappear, or is its collapse to zero leaves pi, but is rendered meaningless?

Ivan

Ivan,

Good question on Pi,

With regards to the blackholes at the center of Galaxies. I believe that, excluding odd things like Stellar Clouds, all major Galaxies will have blackholes at the center of them. As to Pi, like the Kline bottle and Mobious strip http://mathworld.wolfram.com/MoebiusStrip.html you will find Pi still exists in a form that we may not yet be capable of understander. It is my opinion and feeling that Pi has trans-dimentional charactersistics that we are only begining to understand. In support of this hypothesis, I cite the mobious strip and kline bottle as examples of trans-dimentional constructs that still contain Pi as a integral component of them. The website listed above discusses the relationship of Pi to these trans-dimentional and multi-dimentional objects. I have also included another website on this same subject http://en.wikipedia.org/wiki/Mobius_Strip

I have given a lot of thought to blackholes as part of multi-dimentional theory and believe that at a base level all blackholes are linked and form a construct that is multi-dimentional and trans-dimentional in nature and that we are just begining to understand this aspect of them.

During my career as a former cryptographic analyst I have run accross data that could possibly support the concept of multi-dimenational theory and interaction with our reality. Cryptographic officers occasionally when looking for patterns in seeming random sets of numbers find causal realtionships that defy probability yet tend to re-occur. These relationships always occur yet can not exactly be reproduced in the same form. I note the Bible Code as one example of this, althought I have great reservations about the Bible code myself. I do note that there has been at least one study performed and documented using a computer that defied probability and one in Germany with students that also defied probability. When you run into one of these situations it tends to be rather scary and is the reason I have gotten involved with the study of Pi and trans-dimentional constructs and trans-dimentional effects.

I also note that bsaed on my study of the Bible I have taken the position that it contains a lot of information on possible trans-dimentional interaction with our reality/dimension. In particular incident I cite the example of St. Paul talking about living in a pattern. I believe that what St. Paul was trying to say, but lacked the word was that he witnessed/was invovled in a trans-dimentional interaction that defied probability. However, lacking the words he put it in the context of what he could understand. I also note the story of the conflict between St. Paul and the magician where the sun darkened.

If we accept as a discussion point the possibility of a micro blackhole existing in the center of the sun and the accuracy of what was observed and reported in the Bible, what could be described in the Bible could be a trans-dimentional interaction that defied the laws of probility, hence why it was included in such a document in the first place.


I also liek you table top experiment, with wave forms what I think you created should be further expored in terms of multi-dimetional theory, like the Kline Bottle and Mobious strip I think you will find Pi still exists. I do note that I have had the same question on wave cancelation you have had while serving as an electronic warfare officer. In specific I always wondered what happend when you matched frequences during radio-electronic comba to the energy of the jaming signal when the waves match and cancel each other out? This type of resoning is what gave rise to the stories about the Philidelphia experiment.

My Best Ed

Thanks Ivan,

I hope you have a great trip. Excuse the spelling errors in my previous posting. I work late and have a hectic schedule and I have noticed a direct correlation between spelling errors in my postings and lack of sleep. I tend to post these things after a long day in the early morning hours.

My Best

Ed

Application of Transdimentional Technology,

If you check the link
http://en.wikipedia.org/wiki/Mobius_Strip
you will find discussion of the application of transdimentional Technology using the mobius strip.

I quote from the websight,

There have been technical applications; giant Möbius strips have been used as conveyor belts that last longer because the entire surface area of the belt gets the same amount of wear, and as continuous-loop recording tapes (to double the playing time).

A device called a Möbius resistor is a recently discovered electronic circuit element which has the property of cancelling its own inductive reactance. Nikola Tesla patented similar technology in the early 1900s, US#512,340 "Coil for Electro Magnets" was intended for use with his system of global transmission of electricity without wires.

I raise this point related to the disscussion we have been having with wave cancelation and multi-dimentional theory. Its my premise that in the circuits mentioned above we may have the beginings of a breakthrough in the application of multi-dementional technology, which could lead us to additional breakthroughs in energy technology, computing and structural materials as we begin to exploit these types of constructs. I also beleive that was we explore these trans-dimesional constructs we will begin to get a much better understanding of multi-dimentional space and how things like waves and energy act in such spaces....like the question you had regarding the existence of pi in a null space....

My Best

Ed

I note that in trisecting the angle I found it linked to the generation of a hexagon....

When you do things like this you are conscious of people out there that have some very hateful thoughts.... I include the following from a website that has a different sort of spin on the hexagon

Update: November 11th 2003 ~ New Age Alchemy: Two Eclipses and One Hexagram
On November 8th 2003, the planets Saturn, Jupiter, Mars, as well as the Sun, Moon, and the asteroid Chiron all align to form what is called a 'Hexagram in the heavens,' the Star of King David which is to imply the Messiah. The uniqueness and power of this alignment has astrologers all over the world lining up to expound upon its occult significance. The Hexagram being formed however is, in the Western Esoteric system, a symbol that expresses the concept of 'As Above, So Below.' It is also a representation among ritualistic magicians for the completion of 'the Great Work,' (appearance of Antichrist), whom they believe will lead them into a unparalleled new world age, a global utopia based on sorcery and magick. The hexagram itself is comprised of three sixes (666); six, within a six, within a six: [Count the sides of each triangle facing the clockwise direction, the sides facing counter direction, and the sides of the inner hexagon]. We have also seen an exceptional number of unique heavenly signs in 2003 seemingly leading up to something larger. There was a unique blood red moon eclipse in early May, then another more unusual solar eclipse in late May. In August, Mars came closer to earth than in the last 60,000 years (see Mars' relation to the quatrain above).

By November 2003, we had another unprecedented dual event within the same month, two Eclipses (occult 'two into one'), one lunar, one solar. The lunar eclipse took place on November 8th 2003 (which is the same night as the above mentioned 'Hexagram in the sky)' and seen by millions across the world as a large blood red moon, an esoteric portent symbolizing the occult Moon Goddess Diana and her flowing blood or blood line being cast to the earth (yet in Scripture, the red moon is a prophetic sign pointing to the end of the world). A Total Solar Eclipse then took place fifteen days later on November 23rd which peaked at 11:08am [22:08 GMT] and was quite unique in that it was the first eclipse ever in recorded history to have it's shadow cast over Antartica. In between the timeframe of those two Eclipses was the so-called occult 'Rebirth of the Phoenix' (the Phoenix rising from the ashes is another symbol of the Biblical Antichrist; resurrection into the tenth Stargate) whereby a number of incredibly massive solar flares were being recorded as eminating from the Sun. The eleventh then twelfth and final Stargate yet awaits the one who would be King, yet once that last portal has been crossed the world will have been changed right along with him, for these doorways into the occult lead all into One and he will again be the Light of this world, and likewise it's Solar King.

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And there shall be signs in the Sun, and in the Moon, and in the Stars and upon the Earth distress of nations, with perplexity; the Sea and the waves roaring...for the powers of Heaven shall be shaken. And then shall they see the Son of Man coming in a cloud with Power and great Glory.
Luke 21:25-27


When you discover a breakthrough in Geometry you tend to wonder about things like this.....and the people that come up with it

The rest of this can be found at

http://www.heart7.net/knights-templar-conspiracy.htm