Curved (Differential) Geometry
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All of the “approximations” that have been made in regard to a circles circumferential length (And that of curvatures) over the last two thousand years have been calculated using the formulae Pi. This formula was devised by the Greek mathematician Archimedes (287 – 212 BC) who resided for most of his life on the island of Syracuse, but he along with many other Greek students (e.g. Mathematicians Conon of Sámos and Eratosthenes of Cyrene) of the times was to receive his higher education at the Alexandrian Museum (Founded 336 BC) in Egypt.
However despite this higher education in what was perceived by the Greeks to be the world’s greatest centre of learning; Archimedes still found it necessary to devise his own formulae (Pi) for calculating what he believed to be was the closest approximation to obtaining the actual circumferential length of a circle.
Given this information and the fact that his formulae is still being used today some 2200 years after its event, we are able to deduce that;
- The Ancient Greeks did not have a standard mathematical formula for approximating the length to a circles circumference until Archimedes devised it.
- The Ancient Greeks did not have any other mathematicians in their ranks who were capable of confirming that Archimedes formulae was the closest approximation that could be made to a circles actual circumferential length
- The Ancient Greek mathematician’s belief that the length of a circle could not and cannot be found has persisted for more than two thousand years; though there is not one shred of mathematical evidence to support this belief.
The universities and schools of today continue to teach Archimedes formula Pi as if it is gospel; because they have failed to recognise that;
The “Square of a Diameter” (Any length of Straight Line) is the; Square of the Circle
The Diameter of the Circle has an exact "1 – 3” ratio to that of its; Circumferential Length
Click Here to download the proof
Please note: Pythagoras lived 582 - 500 BC; and therefore the dates above should have been given as 582 BC - 2011 AD; the latter being the year when I first had the above diagram placed on this Web page.
Despite more than two millennia of academic belief to the contrary; the above 3 x 120 centimetre diameter circle proves beyond any contention; that the circumference length to any circle is exactly three times that of its diameter length.
Therefore it follows: That as the Archimedean formulae Pi has been historically used for over two millennia, to approximate a circles circumferential length: It also lies beyond contention; that this exact method, is my Intellectual Property.
&
The above Pythagoras Theorem diagram also proves; contrary to more than four millennia of pandemic academic belief (As other civilisations e.g. Chinese, Egyptian, and Sumarian, had discovered this long before Pythagoras): That the area of the square on the hypotenuse is equal to the sum of the squares on the other two sides is wrong.
The area of the square on the hypotenuse of a right angle triangle; with base and vertical length each measuring 12 squares; is out to the tune of one additional square, relative to the sum of the two squares on the other two sides.
Further confirmation
Right Angle base length 24 sq's x 24 sq's vertical = 576 squares; therefore the sum of the area of the two squares is 1, 152 squares.
Hypotenuse length 34 squares (17 sq's + 17 sq's)
34 sq's x 34 sq's = 1, 156 squares which is an excess of 4 squares of area on the hypotenuse, to that of the sum of the two squares on the other two sides.
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Yesterday during a conversation in regard to the content of my web page, and only for the second time in the 17 years since I first worked out that there is an exact 3 - 1 ratio between a circle and its diameter; I was asked how I had managed to discover this.
Therefore following this conversation I thought not only might this be of interest to those logging onto this web page; but also it would allow me the opportunity to include a geometric mind imaging scenario that I had used during that conversation, in order to provide a mental picture that also served to define the 3 - 1 ratio between circle and diameter.
Back in 1995, I was measuring the diameter of a piece of metal tubing in order to obtain its radius, so that I could then use this measurement to circumscribe the circumference of the tube onto a piece of wood, prior to cutting a hole into the wood to receive it.
The diameter of the tube measured exactly one and a half inches, and so automatically knowing (From Pi) that a circle is approximately three times its diameter length; I calculated that the circumferential length was roughly four and a half inches, and then it hit me "roughly" it can't be; because a circle is perfectly symmetrical, and anything symmetrical can be sub - divided into equal parts, and this could not be achieved using Pi (22/7 or 3 & 1/7th or 3· 14) as it equates to being the lentgh of three and a bit diameter lengths.
This realisation then caused me to stop and evaluate the two measurements I had obtained, relative to each other and to the symmetry of the circle.
Diameter = one and a half inches = 3 half inch lengths
Circumference = four and a half inches = 9 half inch lengths
An exact 1 - 3 ratio between the circles diameter length and that of its circumferential length
I then also considered the sub divisions that are applied to clocks, sun dials, and of course a 360° protractor; and in each and every case the circle has to be, and is being sub - divided into identical and equal lengths of sub - division of the circle (Which is extremely interesting? as it is impossible to achieve this mathematically using Pi; for confirmation refer back to the diagram of the 120 centimetre diameter circle, at the top of this page);
Which served to confirm that the circle is indeed perfectly symmetrical; as it is being and can only be equally sub - divided; by use of identical and therefore equal sub - divisions of measurement.
Further (Minds - Eye Visualization) Proofs
1.
In your minds eye, imagine one whole unit in the form of a circle; then choosing a number e.g. (Any number from 1 - 9) the number 3 sub divide the circle into 3 equal lengths of arc.
Now try this same mind imaging exercise; using 31/3rd ; and of course it cannot be done because the circle can only be equally sub - divided, by use of equally/matching whole units of length.
2.
a. Imagine in your minds - eye; a perfect circle and give it a pale colour
b. At the 360° position on the circles circumference at the top of the circle, place a small black dot
c. Extending from this position, imagine sub - dividing the circle into three exctly equal lengths of arc
d. At the distal end of each of the two arcs extending from the 360° point at the top of the circle, place another small black
e. In your minds eye you should now have a pale circle with three small black dots, spaced equally in a triangular formation on the circles circumference.
f. Next join the three dots together with three straight black lines
g. In your minds - eye you should now have a pale circle divided into three exact lengths of arc; with the three pointed tips of the equilateral triangle touching (Sitting on) the circumference of the circle.
h. Therefore the three arcs of the circle are exactly equal in length; as are the three straight lines that were produced from them, in order to create the shape of the equilateral triangle (The product of Symmetry/equality is Symmetry/equality).
i. Now imagine adding in a small amount of length to any one of the three lines of the equilateral triangle; and the result will be that the line will extend beyond the circumference of the circle.
j. Now imagine adding the same small amount of length to each of the three lengths, of the equilateral triangle; and the result will be; that all three points of the equilateral triangle will extend beyond the circles circumference of the circle;
Because any increase or decrease to the length of any or to all three of the straight lines (Dimensions) going into the make up of the equilateral triangle; will subsequently cause a change in the volume/area/size of the equilateral triangle; and thus the symmetrical relativity, that formerly existed between the circle and the perimeter of "its" own equilateral triangulation.
And note some 15 years later, while looking up "Geometry - Estimating the Wealth" in the Encyclopedia Britannica; I was overjoyed to discover; that despite all of the disbelief and the resultant flack that I had to take over the previous 15 years; that indeed both the Ancient Sumerians and I had/have both got it right.
And despite the fact that there are now academics (And for many, English being a secondary language) logging on in 66 countries', of the 206 recognised countries' of the World (And most if not all States of the USA, especially throughout California);
I have yet to receive an E mail, seeking to contradict or disprove the fact; that the length of a circles circumference, is exactly three times the length of its diameter.
The Little Man
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Updates
23rd of January 18 40 hours: Re; 18 "Nine Spheres of the Sun" the font style has been changed to arial black and revisions and corrections made to the text.
25th of January; update to the above re; super heated rocket thrust
26th of January 13 00 hrs; revision of last paragraph + additional text
31st of January 18 00 hrs; update to 18 "Nine Spheres of the Sun"
18th of February; Addendum to 15th of February update to First Law of Physic's above
1st of March 01 20 hrs; Addendum to the "First Law of Physics" above
I6th of March addendum to Archimedian and Pythagorian diagams; and revision to some of the text re - First law of Physics
5th of April see; Fundamental Truth's 02 Three Times the Radius Squared; Religion and Politics
9th of April see; "Relativity and Four Dimensional Time" 17 Geometric Geophysical Age of the Known Universe
14th of April see; 01 Squaring the Circle; Addendum dated 14th of April in red font
28th of April see/scroll down to; Nine Spheres of the Sun - Content below
30th of April; Revision to the Addendum of the 13th of April; please scroll down and find this addendun highlighted by the use of a blue font
6th of May; As above, scroll up to this date highlighted by use of blue font
17th of May; Continuing revision of 19, 4D Geometry
19th of May; Refer to 19, Introduction to 4D Geometry and Natural Geometry
19th of May; Refer to 17 Geometric Geophysical Age of the Known Universe; Einstein's Theories (New Section) Gravity and Curved Space
17 Geometric Geophysical Age of the Universe - Content
1. In Search of Infinity and Eternity
2. Einstein's Theories
Einstein's Theory of Relativity and Time
Relativity the Emperor's New Cloak of Physic's
Relativity and Four Dimensional Time
Time
The Source of Einstein's Genius
Einstein's Theory of Relativity
Gravity as Curved Space 19th of May 2012
Debunking E = mc2
3. Alpha Omega Particles - Dark Invisible Matter - Gravity
4. Speed of Light
5. Gravity and Inertia
6. Gyroscopic - Centrifugal - Inertial Force
7. Gravitational Centralisation
8. Overview of Magnetism
9. Magnetism and Gyroscopic/Centrifugal Force
10. The Origin and Mechanism of Centrifugal Force
11. Infinity and Eternity
12. Distinguishing Eternity from Infinity
13. Infinity Eternity re Big Bang
14. Genius
18 Nine Spheres of the Sun - Content
1. Whats in a Number
2. The scope of the Metaphysical Universe
3. Bio-rhythmic Context
4. Imperial Numerical Time
5. Bio-rhythmic - Biological - Geological Time = 360° of Terra firma Rotation
6. How the mechanism of Gravity; relates to that of a Hydrogen Gas filled Balloon
7. Mechanism of Balloon Buoyancy - Lift off + experimental proof
8. The source of expansive heat/pressure = force
9. Mechanism of Hot Air Balloon Lift
10. Heated air displacement
11. Rocket Propulsion in Outer Space
12. Rocket Thrust + Resistance = Rocket Propulsion
13. Cold Air Thrust
14. Super Heated Atmospheric Thrust
15. Aerodynamics
28th of April 2012: Please note in regard to the latter; 15 Aerodynamics
I have not added to this for some time, as I am neither happy with my use of a plough in this explanation or my getting into a long-winded explanation of streamlining: Therefore at a later time I may delete this text; and move straight into explaining the mechanics of atmospheric Rocket thrust and then outer space thrust.
You will have also noted that I have not added to either Whats in a Number or 4D Geometry for some time; however in regard to the latter 4D Geometry, I still have to gain the computer skills to be able to transfer my diagrams onto the web page; and in regard to additions to the web page; my mind is eclectic and so I am unable to predict what I may be considering from one day to the next:
Also as you can imagine from the wide ranging content of this web page, I have and do need to spend a very great deal of my time in deep thought, in order to be able come up with answers that satisfy my curiosity; but the tasks and problems of everyday life also take up time and cannot be ignored:
Therefore I will make no apology for what many, may quite rightly; consider to be a rather disorganised and frustrating web page.
For E mail address please scroll down
Note for those persons logging on to this web site for the first time:
For those of you who are mainly interested in differential geometry, and differential geometry as it applies and can be applied to the subject of time; I suggest that you may find it more interesting and certainly quicker in regard to satisfying your questing mind in regard to this subject; to firstly address each of the 18 main diagrams which appear at the top of each page, in their order of succession, 1 through to 18; and then 19 introduction to four dimensional geometry (Which is a work still under revision and in progress) before becoming involved (If you wish to do so) in other subjects e.g. the physics posted on pages 17 and 18.
First "Law" of Physics
Energy cannot be Created or Destroyed = Energy Cannot Be "Destroyed" OR "Created"
Therefore: When Georges Lemaitre, decided to Play God and abracadabra "Destroy the Entire Energy of the Holism of the Universe"; and then abracadabra none - empirically Create a Primeval Particle/Energy out of Nothing and Nowhere:
He was not only Playing God but also expressing a Heretical belief (To that of Science); that served to both contradict and negate, the most empirically demonstrated/demonstrable and fundamental Law of the Sciences the "First Law of Physic's".
However regardless of whether one chooses to believe as he proposed in a None - Sentient Primeval Particle; or a Sentient God; or an Intelligent Universe/Creator:
Each one (1) of the Three choices is as with e.g. a Single Galaxy - a Single Star - a Single Planet - a Single Atom,
Is but A - Single - Unit of Energy/Quanta/Mass/Holism/Thing:
Therefore as each is one single whole Unit of Energy; we can prefix any one of the three; with the number/numeral 1 e.g.
1 Universe
1 Primeval Particle
1 Creator
And if we then make a choice e.g. Universe; and then sub divide it by 2
1 Universe (Whole Unit - Holism) ÷ by 2 = 1/2 of a Universe
1/2 of a Universe ÷ by 2 = 1/4 of a Universe
1/4 of a Universe ÷ by 2 = 1/8 of a Universe
1/8 of a Universe ÷ by 2 = 1/16th of a Universe
This sub - division process continues on endlessly as it travels on into infinity because; any whole number represents a whole unit of energy, and therefore it follows; that just as we cannot sub divide a whole number down into oblivion (Nothing = No - thing = No Unit/Energy); neither can we sub - divide the Holism (Whole Number/Unit) of the Energy of the Universe down into oblivion, or destroy or create any sub - division of that Holism:
Ergo; the First Law of Physics;
Energy Cannot Be "Destroyed" OR "Created"
Is an Absolute:
And so it follows that the Abracadabra Theory of the Big Bang's origin (If it were indeed possible to term nothing and nowhere as being an origin) is no more plausible; than that of the story of Aladdin’s Magic Lamp.
Therefore the only logical explanation that remains for the origin of the Big Bang (As with Nova's and Supernova's) is that a gravitational focal point of the Universe, reached such a point of density that it became a critical mass that served to end an ancient part of the Universe by blasting its overly confined energy into an outwardly driven and expanding sphere of fundamental and chaotic/turbulent energy (Sphere of Activity); which over billions of years re - coalesced to form the holism of the Universe as we see it today.
Thus the Omega point of that ancient part of the Infinite Universe; became the Alpha/Genesis Point of our own current neighbourhood; within the ever changing Cycles (Infinite and Eternal - Alpha and Omega; Circles of Energy) of the Infinite and Eternal Universe.
And it should be noted; regardless of any and all assumption's theories or beliefs to the contrary; if the first law;
Energy Cannot Be "Destroyed" OR "Created"
Cannot be mathematically or empirically negated; then it follows that;
The Universe "IS" Both Infinite and Eternal - And Thus The Creator
Of
All that has been - All that is - All that will be
Inclusive of all intelligence's:
And as you can no more take the "Scope of Intelligence out of the Universe"; than you can take the "Universe out of the Scope of Intelligence";
So it follows that the geometrically and Mathematically Rational Universe (Creator of All None Sentient and Sentient Units of Energy), Is;
Sentient
And given; that there are only two choices between Sentient or None Sentient in regard to the fundamental nature of the Universe;
So it also follows; that as the unsupported/empty belief of the atheists of the physical sciences cannot provide any logical, rational, mathematical, or empirical proofs in support of their empty belief;
Niether can they contest against the logical, rational, mathematical, empirical content and presence of the Universal Sentience/Intelligence; of which they we and each every other intellegence of the holism of the Universe, is but an infinitesimal part of the (Infinite and Eternal) whole.
Addendum 13th of April - Revised 30th of April
Perhaps more simply put; the very fact that we seven billion humans and tens of billions of other intelligent creatures exist of and upon this infinitesimal grain of sand we call planet Earth; so it follows in logic, that as the Earth was not the beginning nor is it the centre of the vast (Infinite and Eternal) Universe that surrounds it:
That as with any Mother; the vastness of the holism of the surrounding Universe exists of intelligence, and its interstellar oceans (As with our own oceans here on Earth) exist in order to promote and give life to many other forms life, and their intelligence.
And indeed if it did not possess intelligence; it would have less (None) ability to be able create our own levels of intelligence, than an amoeba has to create a computer or a www.
In sum: None - Sentient Energy (E.g. A rock or a stone) can neither create nor give birth to a sentient/intelligent being.
And indeed; if neither the Universe or its living creatures possessed intelligence; then the Universe could not exist; because there would no form of psyche/intelligence present, to recognise or note its existence.
The Little Man
Refer to; 02 Three Times the Radius Squared: Fundamental Truth's "Mystique"
13th of April
The depth of thought that exists between Creationist and Atheist, equates to the distance that exists between Yes and No, or Heads and Tails.
24th of February
It is both interesting and ironic to note; that wherein the Easter Islanders were wiped out due to their destruction of every tree on the island; we are heading the same way, by turning billions of life giving trees into billions of tons of unwanted, misleading, and useless junk mail.
Thought of the day; 4th of February
To look into the face of the most aggressively virulent plague ever to exist; as a constant and unrelenting threat to every form of life on this Earth;
Simply Look In The Mirror
7th of January
There has never been nor will there ever be; a greater degree of human hypocrisy invested in, or mistruth applied to a single word; than that of the word Humane.
And the word "Sorry" runs a very close second to the latter.
Please note:
E mail: UniAlphaOmega@hotmail.com
Based on intuition rather than, and going against my better judgement (That tells me not to bother); I have decided to provide the above E mail address to allow questions to be asked, or to allow for "Constructive Critiscism or Comments" to be given.
However please take note given the controversial nature of my work, and the fact that it flies in the face of establishment and orthodox thinking; I expect to be inundated with e mails, and therefore I expect that 99% at least will go unanswered as I really wont have time to answer them all.
It should also be noted that in regard to any abusive e mails; they really will be a total waste of time as 1. You cannot insult me because I am ignorant. 2. Only those I respect (Who are very few) can hurt my feelings; and any that ever have, have either been thanked for being honest and straight forward; or they have descended in my estimation.
As to any attempts at cyber bullying; 1. I am not easily intimidated. 2. Being a little man I have faced bullies all my life, and I have always found great satisfaction in dealing with them one way or another. 3. As to physical threats; well Cybor wise they are obviously ineffectual, so only a moron would choose to make them; supernatural curses witchcraft etc; every so called witch and warlock on Earth can cast a spell or curse me if they so wish, I really could not care less; But if they choose to do so, they had better pray that I am unable to find them in the hereafter, and I am pretty damn sure that I will be able to do so; and I already have a very long list of miscreants for whom payback still remains, and will remain pending (Especially in regard to those unethical miscreants who belong to my own profession, and those that they also involved in their nefarious and undeserved machinations of some 13 years ago; who I have neither forgotten nor forgiven) until I leave this mortal coil, and I am not so outnumbered.
1st of November:
I noted today on the monthly Internet security report, two threats (Their term not mine) made against my web page made on the 6th and 11th of November.
Therefore I say to the person or persons concerned; you like all (In no particular order) Hackers, Terrorists, Board members, Dictators, Politicians, Criminals, Cult Leaders, Sociopaths etc:
Believe that because you carry out your nefarious activities in isolation, or anonymously and by proxy as a member of a larger group, gang, committee, corporation, political party, authority (Same thing): That this protects you from discovery and therefore any form of retribution:
However you should consider that not only are you responsible for your own initial and ill thought out actions, you are also responsible for "all" of the subsequent consequences that stem from your cowardice and ill will towards others:
And regardless of discovery or not within this physical realm; you cannot delete nor wipe clean the memories of your self - serving activities from your own mind (Hard Drive) or conscience, as you can with a computer.
And as all of our memories (Mind - Id - Soul - Report Cards) are all that we can take with us and answer for; in regard to all that we have done and all that we have learned within this mortal coil, before going to meet our maker.
It will not be of any use in the face of the "Ultimate Intelligence" to state "I was only following orders"; because the consequences of all we have done in our lives will have already come to pass and travelled ahead of us; and therefore be undeniable.
As to those cowardly terrorist's who plant bombs; in full awareness of the terror and horror that they will cause, as they rip through and slaughter innocent women, children, and the unborn; and the ongoing physical suffering and mental anguish that will be ongoing for all the remaining years of those who survived, and their loved ones.
I would say that I would rather be one of the victims than I would be one of the terrorist's.
Because one thing I am certain of; is that I certainly would not be rewarded in Heaven for having committed such a cowardly and vile act against innocents; and the alternative I am certain; does not bear thinking about.
So I would suggest to the person or persons involved; go and do something that's actually useful with your lives; instead of wasting your time on what is no more than irresponsible and childish behaviour.
E mail: UniAlphaOmega@hotmail.com
Please do not expect a reply to E mails as a matter of course, as I expect to be either answering (Or thinking about) the most interesting of these on this web page; or deleting the least interesting among them.
17.
