**THE MAZZAROTH – PLATO’S NUMBER OF THE WORLD SOUL – THE NEW JERUSALEM**

**By Doug Krieger**

I am convinced that the Zodiac is not an invention of the Babylonians who allegedly concocted it from the Sumerians but that its origins are based on Hebrew revelations and secured from Job (the oldest book in the Bible), known as the ** Mazzaroth** which literally means “12 signs of the Zodiac.”

*“Canst thou bind the sweet influences of Pleiades, or loose the bands of Orion? Canst thou bring forth Mazzaroth in his season? or canst thou guide Arcturus with his sons? Knowest thou the ordinances of heaven? Canst thou set the dominion thereof in the earth?”* (Job 38:31-33 KJV) Answer: No – Job couldn’t muster; only the Creator who designed it could.

This underlying pagan subterfuge whose ego-centric effort to place mortals beneath the Zodiac’s sign thereby predicting one’s disposition, personality traits and on-going pursuits did incalculable damage to the original meanings of these divinely-commissioned symbols which are transcendent in their import. With stealth and deceit were these celestial constellations distorted by priestly fabricators – changing their divine origins into vulgarity and avarice. Though they knew, yet did they purposefully and with guile “exchange the truth of God for the lie, and worshiped and served the creature rather than the Creator” (Romans 1:25).

Yet did the Divine Mind persist as was the original intent for “He counts the number of the stars; He calls them all by name. Great is our Lord, and mighty in power; His understanding is infinite.” (Psalm 147:4-5)

The Scripture of Truth (Daniel 10:21) declares “Those who are wise shall shine like the brightness of the firmament, and those who turn many to righteousness like the stars forever and ever” (Daniel 12:3). It is with this rather ostentatious bombast void of Aquarian relativity that the Hebrew prophets descended upon Earth’s confining platform to announce and preserve for posterity these appointments in the heavens thereby confirming the Divine Intent, yes, and Ultimate Intention with the inexorable march of this Great Precessional – the Precession of the Equinoxes – the Mazzaroth, the Twelve Signs of the Zodiac.

These 12 constellations tell of Israel’s terrestrial journey throughout history past, immediate and future, with celestial validation – it can be unequivocally proven from the most ancient of writings – let alone the incredible discoveries found in Dead Sea Scrolls and the Septuagint (Greek version of Hebrew Texts translated by Jews in Alexandria for the world’s, at the time, most exhaustive body of knowledge ever assembled and viciously, in the main, destroyed by ignoramuses (would you believe, Julius Caesar), sad but altogether true – though some volumes were previously copied and spared from the Alexandrian Library’s burning and quakes, etc.).

Early Church Fathers like Hippolytus and his disputations with the pagans of his day declared the Zodiac’s origination derived its constellations’ names and symbols from the sons of righteous Seth, only to have its divine revelation distorted by men of baser talent who “changed the glory of the incorruptible God into an image made like corruptible man – and birds and four-footed animals and creeping things” (Romans 1:23).

The Fathers knew of the Mazzaroth’s original intent – that the heavens declare His glory – nevertheless, in the heat of battle, the Church eventually discarded the Sacred Nature of its message, condemning it under Gnostic intrusions into the early formations of the Church to the trash bin of history. It was only folks like Frances Rolleston who broke new but ancient ground to reclaim the spirituality of the Zodiac in the mid-1800s. He and the Anglican, E. Bullinger, and the Lutheran, Joseph Seiss and lesser lights, attempted to attribute these heavenly signs to the Life of Christ and the Church’s march through history – however, both their astronomy and their historicity lacked thorough research and credibility.

Much can be read and said of this topic by the reading of a superb text entitled: *Mystery of the Mazzaroth…Prophecy in the Zodiac* by Tim Warner, who has done, I believe, a masterful job in presenting the truth of the Zodiac as originally designed.

This “lead-in” to my immediate endeavor below – needs a final observation regarding the calculations of the *Mazzaroth* (and get accostomed to hearing that expression juxtaposed to *Zodiac* – it is designed to recapture its original meaning) and how these stunning calculations, though seen by cleric and witch (for Christianity and Paganism long have contended over these matters), are advised to do a double take at these calculations and their staggering extrapolations …extrapolations which validate the Mazzaroth’s ultimate message for humankind.

Why we branched off into the mysteries of the Mazzaroth has much to do with the underlying thesis that the ancients, and now those within the Sacred Geometric community (though well-intentioned, in the main) are, however, suffering from what can naught but be “pigeon-vision” leading to mathematical myopia. Naturally, I will veer on the side of Christian wisdom not to excoriate the natural mind of man in his/her efforts to represent magical alignments in number, etc., only to feign ignorance in order to achieve a greater reward amongst those seeking the rarity of truth that can and should and will be found in the Scripture of Truth. Indeed, Daniel the Prophet, found himself, like we of today, wholly contending with the astrologers, enchanters, sorcerers, soothsayers, diviners, magicians, channelers and Chaldeans and, alas, charlatans, in the courts of the King of Babylon – thusly, the more things change, the more they remain the same!

Setting in motion those mathematical endeavors which quite naturally lead us to greater profundities of spiritual import and intent!

**Greek Tetractys**

The Greeks most certainly knew these Sacred Tetractys (alluding to previous World Mysteries articles) embodied the essence of their mathematical fascinations of the meaning of the universe and nature – thus, much in every way the Great Pyramid of Giza exemplifies this ancient desire to express eternal truth(s).

In re-reading – in that I have read these materials in my research in bits, parts and pieces – I view these objects of geometry differently “than I used to” – having been sorely prejudiced by the dimensions of Paradise and their supremacy. The distinctive so noted that the Hebraic and, thence, Judeo-Christian world-view, is predicated on a relationship with the Almighty based on “deliverance” (i.e., Deliverer, Messiah) wholly outside man’s indefatigable quest to supplant his inadequacies by his own ingenuity – dispensing with God altogether as a figment of our rampant but conscious imagination (and fabrication) or using the divine order as established, running on remote and having no desire whatsoever for creation to interact with the Creator. Alas! Some otherwise brilliant cosmologists now suggest the death of God in that gravity constitutes innate energy from whence the entire universe is thereby derived and sustained.

Indeed, the Almighty’s condescension and quest for eternal relationship has consigned to those who are decidedly made “a little lower than the angels” (a somewhat inglorious understatement) to “freely explore” and discover a rather limited but sorely sufficient extant of this universe as an expression of cooperation (not that the Creator needs any) and discovery… having “others” (especially, ecclesiastical interference interpreting the divine mind “for us” has been and will continue to be a most prickly issue unto the End of Days – notwithstanding, no Scripture is of any “private interpretation” – it needs itself and injunctions of poor, puny man to, as told in Daniel, to “search anxiously to and fro throughout the Book” and with what can be derived there from, so as to “lead many to righteousness and to shine as the stars forever and ever!”

So getting back to this Greek enthrallment…there are, at once, at least 12 Equilateral Triangles present; however, this second design presents the original 12 and with the “Shield of David” in dotted lines creating at least an additional 12 Equilateral Triangles (can you see them?). There are, of course, other triangles, but not within the 60° + 60° + 60° mode (equilateral). Thus, the 180 degrees within each triangle (again, our little 18 NJS – New Jerusalem Standard) is amplified with two sets of 12 = fascinating in that 12×12 = 144 the Wall of the New Jerusalem and/or 12 Patriarchs and 12 Apostles or the 24 Elders.

What is of interest are these sets of 180° or 18 = 12`?`

x18 = 216 (or 72, 72, 72 = the Name of God – as from our previous exchanges as well as the diameter of the Moon (2160 miles) and the circumference of the earth in nautical miles (21,600)) and 12×18 = 216 or 216 x 216 = 46656 = 27 – the number 27 is so ubiquitous in the New Jerusalem Matrix for one peculiar reason – it amplifies the Messiah in the Christian Canon – 27 books. Likewise, the Moon’s radius is 1080 miles or 18 or we could see 180 as well = our equilateral triangles so amplified. Two sets of 2160 x 2 = 4320 = 4x3x2 = “24″ – this number set is highly representative of the composition of the New Jerusalem’s only two Proper Nouns: 12 Patriarchs/Tribes of Israel (gates) and the names of the 12 Apostles of the Lamb (foundations) as the Church = 12 + 12 = 24; and these two sets of “12” constitute the “Wall of the New Jerusalem” as in 12×12 = 144 (Revelation 21:17).

Even so, let’s take a closer look at this issue of these sundry triangles.

Firstly, the New Jerusalem Standard measurement of 18,000 Linear Miles (12 of her cubed edges) = “18” or 18 NJS. This New Jerusalem Standard (one edge of the New Jerusalem according to Revelation 21:16 is 12,000 furlongs with 1 furlong = 660′ x 12,000 furlongs = 7,920,000 Imperial Feet/5280 (Feet in a Statute/Imperial Mile) = 1,500 miles x 12 edges of the cubed New Jerusalem = 18,000 miles = “18″ the standard of the New Jerusalem.

Now, with that as an exceedingly brief but necessary introduction we view what is known as the “Creation Holograph Component: Genesis Triangles” from the good folks at Bible Wheel. The claim is made that there are “36 counters” or 3 sets of 36 in each light blue equilateral triangle – in other words, each of the sides of these three “upper triangles” is 36, including their base; there being a total of 1998 “counters” in the three top triangles; therefore, 1998/3 = 666 per equilateral triangle.

Each of the three triangle sides constitutes 36 or for each triangle = 36 x 3 = 108 or the radius of the moon as per 1080 miles and, of course, 18 NJS with three sets of such 18s (three separate equilateral triangles) or 18 + 18 + 18 = 54 or Plato’s Optimal Number 5040/2 = 2520 the Sacred Cubit and the total degrees of earth’s seven-day rotation week – 1 day being 360°) with a total of 1998/3 = 666 per triangle (the heaven) and with the “purple” triangle constituted as 703 (the earth) and rows of “37″ x 3 (sides of the lower triangle) = 111; therefore, 666 + 111 = 777 (see anything there?). 1998 + 703 = 2701 = (2 + 7 + 1) = 10 Perfect Number (as you have it).

As we examine these triangulations we notice that there are 73 on each of its legs or 3 x 73 = 219 or 2x1x9 = 18 NJS. Also, 3×36 = 108×3 = 324 (top triangles) + 3×73 = 219 + 324 = 543 = “12″ (as in 5 + 4 + 3 = 12) or 219×324 = 70956 = 27 (Sacred Christian Scriptures = 27 Books of N.T.) or 3×36 = 108×3 = 324 (top triangles) + 3×37 (bottom triangle) = 111 and 324 + 111 = 435 or 4 + 3 + 5 = “12″ or 4x3x5 = “60″ (seconds, minutes, etc. or 6 = man’s number).

Or – we can combine all of the triangles as in: 324 (top 3 sets of 108′s) + 111 (bottom 37 triangle) + 219 (overall 73 counter triangle 3 sides) = 654 = 6 + 5 + 4 = “15″ (New Jerusalem Edge – 1,500 miles) and 6 x 5 x 4 = 120 or “12” – The multiplicity of “12″ so generated could connote the dynamic of the “12″ of the New Jerusalem 12 Gates, 12 Foundations, 12 Pearls, 12 Angels at the Gates, 12 Manner of Fruit, 12 Stars as the Woman’s Garland, etc.)…this can be amplified by multiplying 324 and 111 and 219 as follows: 3x2x4x1x1x1x2x1x9 = 432 = 4x3x2 = “24″ as per the 12 Patriarchs of Israel and the 12 Apostles of the Lamb or the 4 and 20 Elders of the New Jerusalem or two sets of 12 or 12×12 = 144 New Jerusalem Wall.

The total counters = 2701 or “27″ and “1″ = 27 Sacred Revelation of Christ in the New Testament and “1″ the One True God.

Furthermore, these sets of 180 degree triangles wherein there are actually 3 atop, 1 below and one overall to bring us to “5″ and this is the result: 180 degrees per triangle x 5 (in that there are a total of 5 triangles counting the overall triangle) = 60° + 60° + 60° = 180 degree equilateral triangle or 6x6x6 = 216 x 5 (triangles) = 1080 = 18 NJS (assuming all 5 triangles are equilateral).

Now, with this backdrop – let’s go back to this:

…We discovered that there were 12 Equilateral Triangles (discounting the overall Triangle itself constituting the 13th) in your first Sacred Tetracty and with the superimposition of the Shield of David (six-pointed star) we have an additional 12 Equilateral Triangles (six at the points and 6 large triangles skipping from point to point – every other point) – giving us a total of 24 Equilateral Triangles – not only is there the 12 + 12 but the following is quite astounding: Each triangle as noted above is 60° + 60° + 60° = 180° or 6x6x6 = 216 = 216 x 24 (or 12 original equilateral triangles + an additional 12 in the Magan David) = 5184 = “18″ New Jerusalem Standard; if, however, we add the 13th – i.e., the overall triangle – we arrive at 5184 + 216 = 5400 or the 5040 of Plato’s Optimal Number/2 = 2520 or the Sacred Cubit = which is the measurement of the Divine Geometer! Or, 5400/2 = 2700 or the 27 of Messiah’s Revelation in the Christian Scripture (27 Books).

An expansion of the “Genesis Triangle” appears as follows:

Here you clearly have the three (666 counters) and “in their midst” the 777 counter. The calculations are the same, but with the clear avoidance of the upper/center triangle spared a trapezoid embarrassment in that an additional 1 counter has been added on either side of the overall triangle to account for the 703 sum. Interesting – in each of the 666 triangles the “base” of the triangles is equal to 36 counters but the legs of the “703 triangle” are all 37 counters to arrive at the 703 (thus, the openings of the 3 counters on each of the points of the purple triangle of 703).

What I’m saying in all of this has everything to do with viewing these geometric objects from the perspective of the measurements of the New Jerusalem – then they begin to make profound sense!

Meanwhile, the New Jerusalem Matrix continues to consume – oh, and by the way – take this into consideration regarding the Magan David, Shield of David, Star of David and its utterly profound prophetic import (for the Hebrews alone have given us the prophets – not philosophers, law-givers, military commanders, business leaders, so-called holy men, teachers, etc. but THE PROPHETS)…

…here we have at its points 6 equilateral triangles of 60 degrees x 3 = 180 degrees and supplementary angles of 120 degrees in that 60 + 120 = 180 (straight line); therefore, as you view this profundity you must calculate as follows: 3 sets of 60 = 180 degrees x 6 = 1080 degrees + 12 ea 120 degree supplementary angles or 12 x 120 = 1440 Degrees (the 144 Wall of the New Jerusalem) and, of course the 18 of the New Jerusalem Standard measurement of the 1080 miles of the Moon’s Radius) and what do we have: 1080 + 1440 = 2520 = The Sacred Cubit Measurement! Tell me now – these 2520 degrees constitute the 70th Week of Daniel’s Prophecy? Of course they do – therefore, everyone/ everything bearing the Star of David in this manner demonstrates the prophetic fulfillment yet to be – tell me, DO YOU SEE IT? If not, perhaps you do not wish to see it? Yet, if you do…then you have, I believe, embraced the Scripture of Truth as did Daniel the Prophet…

**PS**

Unless one is driven by the simplest of math with what I believe is designed to purposefully communicate to a greater mass of people profoundly sacred truths, then most of this material will be boring to most but intensely gratifying to others.

I leave a rather mysterious series of calculations entitled *MAZZAROTH – EARTH – MOON – SUN – THE DIMENSIONS OF THE NEW JERUSALEM.*

This rather simplistic attempt to ingratiate sundry measurements whereby orbits, diameters, circuit, years and distances merge is in keeping with John Michell’s “Heavenly City as Eternal Standard” (*The Dimensions of Paradise, Sacred Geometry, Ancient Science, and the Heavenly Order on Earth*) – as if “borrowing from an self-declared Pagan Occultist somehow discredits the connectivity here – I reject outright! The man was on to something and he had many things spot on.

When it is finished, the ** New Jerusalem Matrix** will be supplemented by

**. The extant of the NJ’s number value systems are also reflected in other disciplines beside these rudimentary astronomical configurations and calculations – music, other math disciplines, architecture (applied mathematics and calculus), chemistry, biology, the human anatomy (physiology), city and social planning, as well as other sciences.**

*The Dimensions of the New Jerusalem and their Relationship to Earth – Moon – Sun – Inner/Outer Planets and Dwarf Planets of the Solar System***Plato and the Aggregate Number of “The World Soul”**

Platonic scholars for some 2,000+ years have labored – inconclusively – to establish “an exact numerical composition of Plato’s world soul” apprising its matrix with extreme value in that a “ruler would have the benefit of a constant mathematical standard as guide and reference in all things.” (*Dimensions of Paradise*, p. 180, Michell).

“Plato give no apparent clues as to the numbers comprising the physical world, but its aggregate number is likely to be the same as that of the world soul, since the two were designed to fit together.” (Ibid.)

The seven basic numbers of Plato’s “world soul” (384, 768, 1152, 1536, 3072, 3456 and 10368 – derived from multiples of 64×6 = 384 – therefore, 1×384 = 384; 2×384 = 768 and so forth with numbers 3, 4, 8, 9 and 27) total 20736 (thusly, was it practiced in Plato’s Academy). Interestingly enough this figure sums to 18 NJS (2 + 7 + 3 + 6 = 18).

“Plato clearly implies that it (world soul) was first and foremost a code of number” – not simply a scale of music. Notwithstanding, Plato developed two series of number representing a musical scale in the traditional Dorian mode so recommended in his Republic whose impact would have a “most beneficial effect on societies and the individual soul.” In any event the “number of the soul” is constructed of two series of number. The second series involves 18 sets of numbers, with the first set consisting of 17 number sets for a total of 35 sets of number.

It must be noted here that the “world soul” is in reference to the mythical “Journey of Er” via reincarnation (the doctrine of metempsychosis) – in that Plato affirmed the immortality of the soul (final disclosures in *The Republic*). Plato’s theories of the universe were advanced and embodied in the Socratic dialogue of *Timaeus* – the pinnacle of his impact for the past two thousand years upon Western Civilization. In both works the Creator is viewed via arithmetical and harmonic means to progress the “world soul” into its ultimate destination in the heavens – the “third heaven” being the ultimate reward. Through “sound philosophy” and “habits of justice” the soul is perfected – “human happiness” can be found, not at its extremities but through moderation life’s greatest achievements are accomplished. In this quest, this journey toward perfection, the “world soul” must be measured by an “exact numerical composition” – an ultimate standard…Michell summarizes the brief history of creation in *Timaeus* as the essential knowledge that Plato wrought through his distillation of various sciences:

*“Among its contents are the canon of musical harmony that determined the forms of government in the ancient world, the scientific cosmology that gave it stability, and, above all, the basic formula behind that mathematical standard from which ancient philosophy and every branch of art and science were derived and developed.” (Ibid. p. 180) Thus, decoding the musical and mathematics of creation have set scores of philosophers, scientists, physicists, astronomers, mathematicians and lovers of the arts in pursuit of the aggregate number of the world soul allegedly maximizing its journey to the stars – “For those that are called immortal (“world souls”) when they reach the top (of the heavenly whorls as revealed to Er), when they reach the top, pass outside and take their place on the outer surface of the heaven, and when they have taken their stand, the revolution carries them round and they behold the things outside of the heaven.” (from Plato’s Phaedrus)*

This veiled illusion of Plato is emblematic of Daniel 12:3 wherein “Those who are wise shall shine like the brightness of the firmament, and those who turn many to righteousness (i.e., “right standing”) like the stars forever and ever.” It is at this juncture, again, that the perfection of the soul – with its harmonic quest via number so dignified in all of the aforesaid sciences – natural and social – can achieve that heavenly destination “descending from heaven” – but by what means can this be achieved? Indeed, the aggregate number must add up! The journey is there – but is human perfection derived from the soul’s ultimate effort? Herein lies the rub – for we who see “through a glass darkly” are persuaded that the likes of Er who would aspire to such heights, is ill-equipped, no matter how determined and in harmonic balance he is with the proportions so given out by his Creator . . .

“The aggregate number of Soul is indicated in the description of how the Creator portioned out its material so as to form the strip that he later bent into circles….Since he used up all the Soul material by removing variously proportioned parts of it, the sum of the numbers represented by those parts must be equal to the total number of Soul. If those component numbers could be identified, the recovery of the traditional formulas of creation would be virtually accomplished”…and thus, with supreme clarity, the “world soul” would achieve its fulfillment and ultimate heavenly placement. (Ibid. 181)

So close – and yet so far…the sum of the numbers must equal the total number of the Soul…for, apparently, the Creator has enabled the soul these numeric proportions sufficient to progress it to its ultimate destination – any distortions in the calculations disturbs the world soul’s progress – thus, incessant reincarnations make the journey’s end achievable . . . eventually “things add up.”

“Neither the number of terms, thirty-five, nor their sum, 108,551, is of any particular mathematical importance, and there is no reason why Plato should have called attention to either number (i.e., 35 sets whose sum is 108551).” (Ibid. p. 185). As a result of this open-ended affair, philosophers and mathematicians have struggled over the conclusion of the matter – adding and subtracting various number sets to arrive at an optimum. Platonist Michell’s final, yet inclusive, conjecture for the “world soul” arrives at (from a multitude of reasons) 36 optimum number sets with the most likely addition tallying 114048 (whose “number sum” tallies to 18 NJS). I concur in that 114048 if expressed as a circle with a circumference of 11,404,800 having a diameter of 3,628,800 which matches the perimeter in inches of the GPG (36,288” – itself a “testimony” or “reflection of the New Jerusalem’s dimensions) and accords to the 144 Sacred Cubits of the Wall of the New Jerusalem (144 x 25.20 = 36288); likewise, the diameter of Earth’s Moon at 2,160 miles x 5280’ = 11,404,800’ (i.e., 114048) = 18 NJS.

Michell’s hypothesis that 114048 was intended to be the aggregate number of the world soul is, nevertheless – and in spite of all its integration – an unsatisfying self-conclusion to the matter; however, the original seven basic numbers of Plato’s “world soul” tally to 20736 + 114048 = 134784 = “30” which in the New Jerusalem Matrix constitutes “Messiah” (age of Messiah’s ministry commitment…if we add back in the original seven into the 114048 total). But, the original thirty-five set of “world soul” numbers sum of 108551, when added to the original seven, 20736 = 129287 = 29, a rather insignificant number set, aside from 2 x 9 = 18 NJS. To arrive at Michell’s 114048 (juxtaposed to 108551) he added in a number set (or sets) totaling 5497 (making the sum of number sets at a minimum of 35 + 1 = 36 sets…although, Michell does not disclose how he added in the 5497, a rather peculiar number set whose sum equals to “25.”

Notwithstanding his apparent hesitation, he sets forth a most stunning modification using 114048 as the original base and subtracting out 5184 to arrive at 108864. Could this indeed be the aggregate number of the world soul? Thus, he set out to express this geometrically via a diagram “illustrating the Creator’s subsequent dealings with the Soul material.” By adding together the original 7 numbers we discover: 108864 + 20736 = 129600 = 18 NJS (though these seven numbers are included within the 108864). It is this sum which adds credibility to Michell’s hypothesis and affirmation that 108,864 (though its sum is “27” – which sum, incidentally, holds extreme credibility within the New Jerusalem Matrix as “Messiah’s Revelation in the Christian Scriptures” – 27 books of the New Testament); thus, we have BOTH within the 108864, i.e., Messiah’s imprint as well as the ultimate manifestation of the New Jerusalem – the Lamb’s Wife or the Groom and the Bride = wherein “eternal relationship” is altogether the supreme goal of the Divine Mind – not, sorry to say, the human perfection of the “world soul” – although that quest for perfection is, nevertheless, realized in the dimensions of Paradise…it is the purpose for that perfection that concerns and the “wherewithal” to effect that perfection that is fundamental to the New Jerusalem Matrix juxtaposed to the Journey of Er and the “heavenly whorls” so revealed to Er.

What adds credibility to the 108864 or 108,864 as the summation to Michell’s ultimate number – and the profound meaning of the New Jerusalem associated thereto – is the following: When viewing 108,864 we see TWO peculiar number sets – “108″ and “864″ stand out. These “number sets” are derived, as I will later explain, from a most unusual calculation and from the metrology of a world-famous object of antiquity – both the calculation and the object validate the ultimate intent of the Almighty’s quest that these “sacred calculations” are not the exclusive purview of the occult.

Firstly, in “108″ and “864″ we naturally see two sets of “18″ – or validation of the Standard of the New Jerusalem as in 18,000 miles on her 12-cubed edges. Secondly, their total of “27″ (as in: 1 + 8 + 8 + 6 + 4 = 27) which is the number of volumes in the Sacred Christian Canon wherein Messiah, as Jesus, is fully revealed – but that He is revealed as Very God in that the two sets of “18″ are equal to 36 as in 18 + 18 = 36 and 36 is but a fractal (a smaller or larger number set resembling itself) – for 36 is a fractal of 360 degrees of a circle, having no beginning or ending for the Eternal God is so represented.

Likewise, and as so promised, how this calculation is derived and from what object of antiquity is most gratifying. The base measurement of the Great Pyramid of Giza, which we affirm to be that Monument or Pillar unto the LORD at the Border (lit. Giza) of Egypt (Isaiah 19:19-20) – past, present and future – is 756 Linear Feet (a calculation which has been decisively proven again and again by leading metrology figures like Sir William Matthew Flinders Petrie). Taking this 756′ (which is as well another “18″ for 7 + 5 + 6 = 18) and multiplying it by 12 (for the cube of the Great Pyramid of Giza is reflective of the cube of the New Jerusalem’s 12 edges) = 756′ x 12 = 9072 Linear Feet x 12″ (to arrive at a cubed linear inch GPG calculation) gives us 9072′ x 12″ = 108,864″ = the very calculation and ultimate number sought after by John Michell but discovered herein attesting to the Divine Intention (27 and 36) of the New Jerusalem “18.” Even so, 27 x 36 = 864 (which again attests to the fact that the Almighty (36) through the Son (27) fully intends to secure the New Jerusalem (864) or 18 for Himself.

I am somewhat bemused and astounded that Michell’s 108,864 confirms not only the totality of the sum of all the numbers suspected of achieving his goal, but that this summation is attested in the Imperial (British) calculations found in the measurement/dimension of the Sacred Cubit and of the radius of the Earth’s Moon (1080 cf. to the 108 of the 108864) and of the 864 as the diameter of Earth’s Sun (for 864,000 miles is the diameter of Earth’s Sun); therefore, 108,864 attests to the Moon as the reflection of the Sun and the “Sun of Righteousness” (Malachi 4:1-2). And, 1080 Miles x 5280′ (number of imperial feet in an imperial mile) = 5,702,400 Linear Feet = “18″ as well (5 + 7 + 2 + 4 = 18) and 864,000 miles x 5280′ = 4,561,920,000 = “27″ which attest to the Messiah’s intention as the Sun of Righteousness in securing the New Jerusalem as His ultimate prize!

The “Moon beneath her feet” in Revelation 12 connotes that “The Woman” who is “clothed with the Sun” (Revelation 12:1) dominates the Moon and reflects “off the Moon” the “Sun” who provides her clothing – thus, Moon and Sun are engaged (108 and 864) – for this Woman, we affirm, is the same Woman whose Seed would one day crush the Serpent’s head and the same Woman throughout Holy Write who in the final frame of time shall descend from heaven as the Bride: “Come, I will show you the WOMAN, the Lamb’s Bride…and he carried me away in the Spirit to a great and high mountain, and showed me the Holy City, Jerusalem, descending out of heaven from God” (Revelation 21:9-10).

Likewise, her garland of 12 stars, representative of the 12 constellations of the Mazzaroth are her “crown” – for all 12 attest the 7 (Israel’s history) and the 5 (the Church’s history) throughout the Great Precessional’s 25,920 Years, which in turn, attests to the New Jerusalem’s ultimate intention in this history for 2 + 5 + 9 + 2 = “18.” Furthermore, the 7 constellations connoting Israel’s history are equal to 2160 (1/12th of the Great Precessional in years or 1 “star” of her garland) x 7 = 15120 years (and 1512 is a fractal of the Great Pyramid of Giza’s 2 edges as in 756′ x 2 = 1512′ and 1512 in Greek Gematria is equal to the word Apocalypsis foretelling of the End of Days (and, of course, even the calamities of the “End of Days” is the precursor of the New Jerusalem in that 1512′ x 12″ = 18,144 = “18″ (New Jerusalem Standard) and “144″ (Wall of the New Jerusalem) or 1 + 8 + 1 + 4 + 4 = “18″ New Jerusalem Standard. And, the remaining “5 stars” constitute the Church’s history or 5 x 2160 = 10,800 and need I say more for the “18″ dominates the Church’s ultimate destination as the Bride of Messiah – but, as well, so does Israel, for the Church has been brought into the “Commonwealth of Israel” (Ephesians 2:12)

Ladies and gentlemen – let me be so bold to declare that the “Number of the Soul” so sought after by Plato and scholars who have labored inconclusively to establish the “exact numerical composition of his world soul” has, I believe, been discovered – “for therein is a great prize.” it involves both Moon and Sun and, of course, the New Jerusalem – it is 108,864. As a validation or “proof” of this, I only have John Michell himself in which he attempts to measure, by use of the “function of the universal pole” to extract the “area of the New Jerusalem.” Mitchell postulated that since “12 is the number that measures the New Jersualem, the radius of the central dot is taken as 12 units in length (please visualize a huge circle with a dot in its center constituting 12 units of measure as its radius) and “why the radius of the circle surrounding the center dot is taken to measure 72 feet.” (The Dimensions of Paradise, John Michell, pp. 39-40).

Mitchell places this “dot” within what he calls his “New Jerusalem diagram, the symbol of divine order on earth.” Eventually, there is a 12-sided figure and a series of 12 circles surrounding 12 interior triangles within the 13th and enlarged (the 12 other circles on its circumference) – well-suited for explaining the dimensions of the New Jerusalem, for when the “central dot” consists of a radius of 12, its area is considered 1 unit; thence, the small circle around the “central dot” has a radius of 72 in area or 36 units. These dimensions are extrapolated until we arrive at the Earth’s radius of 3,960 miles and if Pi is equal to 22/7 then we would arrive at 108,900 New Jerusalem Units; however, if we use a higher calibrated and “a more perfect calculation” to arrive at the measurement of a circle’s circumference – as in 864/275 for Pi, then using the earth’s radius of 3,960 miles, we will arrive at 108,864 units (or New Jerusalem Units). Here, Mitchell’s “Jerusalem Unit” is determined by using Pi as 864/275 instead of the “more inaccurate” 22/7 (i.e., 3.14181818181818 vs. 3.14285714) wherein instead of arriving at 108,900 New Jerusalem Units and 1,440 acres of a square with a radius of the Earth’s 3,960 (but in feet), he now arrives at 108,864 New Jerusalem Units and 1,440 acres of a square with a radius of the Earth’s 3960 – imperceptible, however, and, although the 108,900 does manifest the “18″ of the New Jerusalem, not only does the 108,864 manifest two sets of “18″ it also declares the Moon (1080 radius) at 108 and the Sun (864,000 miles diameter) at 864 but manifests the 18 + 18 = 36 (or 108 = 18 and 864 = 18) or the 360 degrees of the Eternal God (as in 18 + 18 = 36 = 360). Thus, the “more accurate” Pi of 864/275 with its “18″ repeats” is superior.

Mitchell contends that the 108,864 New Jerusalem Units can be achieved by the radius of the earth @ 3,960 feet (which it is), doubling it to arrive at its diameter (7,920 miles/feet as fractal) and multiplying it by Pi (using Pi at 864/275 or 3.14181818181818 – a slight testament that “18″ dominates here in this Pi calculation), giving us a fairly accurate circumference of the Earth at 24,883.2 (which interestingly enough equates to “27″) (i.e., 7,920 x 3.14181818181818 which is, in fact, the Greek calculation of the Earth’s Circumference as in 12 x 12 x 12 x 12 x 1.2 = 28,883.2; thus, the Earth’s circumference bears the stamp of the full revelation of Messiah (27) as expressed in the volumes of Christian Sacred Canon. Furthermore, Mitchell affirms the New Jerusalem’s 144 or 1,440 wherein 7920′ fractal surface around the earth (squaring the earth) is equal to: 7920′ x 7920′ = 62,726,400 sq. feet / 43,560 (sq. feet in 1 imperial acre) = 1,440 acres.

In Michell’s top simplicity there are 22 squares each having an area of 5184 (which is likewise 18 NJS, i.e., 72^{2 }, giving the two rows of 11 squares each a total area of 114,048 (the original aggregate number = 18 NJS as well). Since each square is 72 x 72 its width is 144 and its length is 72×11 = 792 = 18 NJS and a fractal of Earth’s Diameter of 7920 miles. Four out of the 22 squares are taken up by the original seven numbers of the world soul or 4×5184 = 20736. Also, the area of the 22 squares (144 x 792) is equal to 114,048 = 18 NJS.

In order to arrive at 108,864 he must eliminate 5,184 from 114,048. He manages to do this when the 22 squared-strip is divided down its middle forming two strips of 11 squares each, which are laid across each other (disregard the blank squares – only the squares within the dark lines are considered the two strips of 11 squares each). The “superficial” area created when the two strips are bent upwards into circles and joined at the top to each other, appear to form a cross (shaded area) and to occupy an area equal to six of the original world soul squares; however, when so bent each of the cross’ extensions loses an area 72 x ¼ or 72 by 18 – i.e., 72 x 18 = 1296 (also 18 NJS) and this, of course, must be multiplied by 4 (four extensions of the cross) = 5,184. What to me gives Michell’s diagram such credibility is his simple statement whereby the “diameter” or one of the four sides of this “square within the square” or the outer extensions of the shaded areas is equal to 252 or the measurement of the Sacred Cubit of 2520 – derived by adding the full 72 from three squares or 3 x 72 = 216 + two of the 1/4^{th} or the squares adjoining on either side of any given side or 72/4 = 18 x 2 (on either side of any three squares in a row) = 36. Thus, taking the three squares on one of their sides and adding it to the ¼ of each adjoining square we get the following calculation: 72 + 72 + 72 + 18 + 18 = 252.

Thus, perhaps unwittingly, or by design, Michell has separated out the 5,184 from 114,048 to achieve 108,864 by the use of the measurements of not only the total dimensions of 252 (the Sacred Cubit) but having 216 (the Name of God in the New Jerusalem Matrix) and several 18 NJS – a truly astonishing accomplishment. The total area in question, as well, is 252 x 252 (the outer reaches of the square within the square, counting the blank squares or portions thereof) which equals to 63,504 = 18 NJS. Likewise, its perimeter is 252 x 4 = 1008 = 18 NJS. The 11 sets of 72 = 792 linear (which is a fractal of one of the sides of the New Jerusalem as in 12,000 furlongs x 660’ = 7,920,000’/5280’ = 1,500 miles – likewise 792 is the Earth’s diameter 7920 miles). Also, taking Michell’s 792 drawing of the 72 by 72 squares (one square) and, therefore, the entire area of 792 x 792 = 627,264 (the square area of the entire diagram – thereby not discounting the blank squares). If this were the New Jerusalem it would match this number, being its fractal. As the New Jerusalem is based upon the Sacred Cubit (for its wall is 144 cubits or 144 x 252 = 36288 = the perimeter in inches of the base of the Great Pyramid of Giza), therefore, 627,264 can be divided by 4356 (as in 43,560 sq. feet per acre) = 627,264/4356 (dropping zero) = 144. The 144 is the measurement of the Wall of the New Jerusalem as 144 cubits, etc.

Manipulating the diagram of John Michell which strangely enough conforms to the dimensions of the New Jerusalem, I am fairly sure, was not his original intention; however, he has made it terribly appealing to do just that! And, since it was Dr. Michell’s supreme desire to accurately and persistently discover the Dimensions of Paradise – I hope that we have in measure achieved that posthumously on his behalf.

Finally, if we “add back in” the original seven numbers to their new aggregate of 108864 + 20736 we arrive at 129600 = 18 NJS (or 1x2x9x6 = 64, a number when multiplied by itself = 64×64 = 4096 = 18 NJS). But just to be sure: 1 x 2 x 9 x 6 = 108 = 18 NJS. So am I convinced that the aggregate number of 108864 is the sum of the “world soul?” Well, let me see: 108864/144 = 756 = 18 NJS and 756 is one base side of the Great Pyramid of Giza, a clear reflection of the New Jerusalem. Still not quite convinced: 108864/25.20 (Sacred Cubit) = 4320 which is the radius of the Sun as in 846,000 miles/2 = 432,000 miles – and, indeed, the Sun is a full reflection of the New Jerusalem in every way. Well, as an aside: 108864 x 33 (Messiah’s Number) = 3592512 = 27 which is Messiah Revealed in the 27 books of the New Testament. One more test: 108864 = 1 x 8 x 8 x 6 x 4 = 1536 = 18 NJS!

(May I add here that the Sacred Canon of the Hebrews and that of the Christians tally some 66 books (omitting Apocryphal writings, most of which are either of dubious origin or fail to meet historical acceptance by Jewish and/or Christian councils or Early Church Fathers – notwithstanding Catholic claims to the contrary). These texts are broken into two sets of Sacred Text: 39 from the Israelites and 27 from the Church; thus, 39 + 27 = 66. These numbers bear incredible worth, and, I affirm convey spiritual revelation assigned to their completion by the Creator – given to humanity for our edification; to wit: The number set “27” appears frequently in NJMatrix patterns which produce products of 27. The number is the total Books of New Testament canon = 27. Products/sums generated with 27 x 33 (Messiah’s Number) = 891 = **18 NJS** and 39 x 33 = 1287 = **18 NJS**. The sum of the two products (891 + 1287) = 2178 = **18 NJS**; likewise: 891 + 1287 + 2178 = 4356 = **18 NJS**. By themselves (891 and 1287) and with their product sum (2178) – all three bear the 18 NJS; therefore, 18 x 18 x 18 = 5832 = **18 NJS. **Also, 3 x 18 = 54 or 5040 Plato’s Perfect Number/2 = **2520 SCM. **“Full product manifestation” = 6 x 6 (66 Books of the Bible) x 3 x 9 (Hebrew Scriptures) x 2 x 7 (Christian Scriptures) = 13608 = **18 NJS. **Finally, 66 x 33 = 2178 = **18 NJS **and 66 x 39 x 27 = 69498 = 36 = 3 x 6 = **18 NJS. **The Two Testaments: 3 x 9 x 2 x 7 = 378 = **18 NJS**.)

As I have previously stated, the repetition of these number sets either proves that one can prove anything by number or that certain numbers, as many of us, including Michell, Plato, etc., bear repeated reflection in that they communicate to humanity the Creator’s full intentions. As Nicomachus of Gerasa in the first or second century CE states:

*“[Number] existed before everything else in the mind of the creating God, like some universal and exemplary plan, relying upon which as a design and archetypal example the Creator of the universe sets in order his material creations and makes them attend to their proper ends” ( Introduction to Arithmetic, 1, 6 and 4). *

Or as John Michell postulates: “Yet there is one system in which all numbers and proportions and every disparate or incommensurable element coexist and function together in perfect harmony, and that system is the universe.” Whereas, I would humbly add, “that universe is calculated in proportion with the Dimensions of the New Jerusalem.”

I’m to the point that these sacred dimensions permeate the universe…a rather extraordinary, if not supernatural accomplishment, whereby it is safe to say…world mysteries for sure now unraveling before us…and if you can’t see the fish swimming around in these three-dimensional drawings, subtle as they are – look harder, they’re there, just relax and pop, they appear!

Copyright 2011 Doug Krieger

www.the-tribulation-network.com

{ 12 comments… read them below or add one }

The chart is more than all the religions created from the hebrews or christians or muslims or the jews some just have interperation the wheel exodus jerusalem look secure true knowledge from the star gods forward spin.

Mr. Krieger, I wondered why you would publish such an aritcle on this website until I read the comments. Good work on both the article and the choice of websites. If only I could wrap my mind around your very thorough work. Best regards from a David Flynn admirer.

Thats for sure divine intent peace be with you.The seal of the living god 144,000 ascending/rapture,in other ways the pagan worship for earth reverse heart.

Why, thank you for your kind remarks – aren’t you glad we still have the freedom to express ourselves like this – incidentally, the so-called God/Spirit is not incompatible with the tech – in point of fact, the tech wholly substantiates the God/Spirit, – if I understand what you’re saying…I will continue to irritate people concerning these matters to substantiate the Divine Intent which is everywhere around you – in point of fact, every second, every minute, every hour, every day, every week and month and year points to God’s Ultimate Intention – and, guess what, you’re livin’ in it!

See below on the matter of TIME.

and, by the way, I’m glad you have included me in your “consciousness” – sorry about those passages in the Apocalypse which exclude the following from the New Jerusalem: “But outside are dogs and sorcerers and sexually immoral and murderers and idolaters, and whoever loves and practices a lie” Rev. 21:15). And, of course, the whopper of THE LIE was that we could be “like God knowing good and evil” and that, of course, we would do the good over the evil – hasn’t worked out too well there, has it? Incidentally, again, I didn’t write the book…and the notion that the Dimensions of Paradise exclude such is not something I would have put in there – but then again, I didn’t write the book – but thank you for letting me in – now, I don’t mean to hurt, either, but amorphous relativism doesn’t seem to be what we Jews and Christians and Islam are/is into – but thanks in any event.

a message from christ, marked just for knowing the truth over the lie here what a mistake peace in the rapture event worship and say your prays, 000.

Why, thank you for your kind remarks – aren’t you glad we still have the freedom to express ourselves like this – incidentally, the so-called God/Spirit is not incompatible with the tech – in point of fact, the tech wholly substantiates the God/Spirit, – if I understand what you’re saying…I will continue to irritate people concerning these matters to substantiate the Divine Intent which is everywhere around you – in point of fact, every second, every minute, every hour, every day, every week and month and year points to God’s Ultimate Intention – and, guess what, you’re livin’ in it!

See below on the matter of TIME.

and, by the way, I’m glad you have included me in your “consciousness” – sorry about those passages in the Apocalypse which exclude the following from the New Jerusalem: “But outside are dogs and sorcerers and sexually immoral and murderers and idolaters, and whoever loves and practices a lie” Rev. 21:15). And, of course, the whopper of THE LIE was that we could be “like God knowing good and evil” and that, of course, we would do the good over the evil – hasn’t worked out too well there, has it? Incidentally, again, I didn’t write the book…and the notion that the Dimensions of Paradise exclude such is not something I would have put in there – but then again, I didn’t write the book – but thank you for letting me in – now, I don’t mean to hurt, either, but amorphous relativism doesn’t seem to be what we Jews and Christians and Islam are/is into – but thanks in any event.

Hey Doug, I have a spreadsheet showing a pattern based on calculations from the number 144. The interesting part is that in the pattern are numbers that reference the moon cycle, the geometric influences of the zodiac (Feb 14 is one of note) specific days of the year and likely much more. If you are interested in reviewing it I would be glad to send it via email reply.

It is all to easy to spend hours, days, months, years of your life searching for information that supports your own agenda/ideas….doesn’t make it valid. All I can say is the real truth lies within YOU….until you’ve searched there and mastered yourself, you won’t have any answers….

Speaking of spending seconds, minutes, hours, days, weeks, months, etc. – please consider this – and, then enjoy the FACT that you’re living in my reality every second, ever minute, etc. of every day and year, etc. and, no, I’m not sorry about that – somebody out there has set this up so that we can know the truth that alone can set us free within – to that I concur! Here’s just a little bit of that inward reality or “waste of time” which is not wasted one bit!

Everyday that you and I are alive is a testament to the Divine Intent – in that:

Seconds in a minute = 60 secs. x 1 hr. = 3,600 seconds x 24 hrs. = 86,400 x 7 days in a week = 604,800 or 86,400 x 30 days in a prophetic month = 2,592,000 or 86,400 x 360 days in a prophetic year = 31,104,000…

3,600 = 36 = 360 Degrees in a Circle = The Eternal God without Beginning or Ending

86,400 seconds in a day = 8 + 6 + 4 = “18″ which is the cardinal number alerting us to the ultimate measurement of the New Jerusalem’s 18,000 mile 12-edged perimeter and 864,000 Miles is the diameter of the Sun – who is the Sun of Righteousness (Malachi 4) and it is He Who clothes the Woman of Revelation 12. also, 2,592,000 = 2 + 5 + 9 + 2 = “18″ which again tells us that every month – every second of every month – God has but one purpose in view: the New Jerusalem! And, 31,104,000 seconds per prophetic year x 30 years (which was the year in which the Levite priest commenced to minister and the age of Jesus when he commenced His ministry – and what was the 30-years of preparation for? 31,104,000 x 30 years = 933,120,000 seconds in 30 prophetic years = 9 + 3 + 3 + 1 + 2 = “18″ – All His preparation was but for one thing: The New Jerusalem!

Indeed, Jesus ministered for 3.5 years (3 1/2 years) – if you take 31,104,000 seconds x 3.5 years, you arrive at 108,864,000 seconds of “ministry” and when you see that “108″ = “18″ and “864″ = “18″ and then recognize that 108 is a fractal of 1080 Miles (the radius of Earth’s Moon) and 864 is the fractal of Earth’s Sun’s diameter of 864,000 miles – then, you realize that the Woman, clothed with the Sun, with the Moon beneath her feet in Revelation 12 is a PROFOUND expression of the Divine Intent – EVERY SECOND OF JESUS’ MINISTRY from His baptism to His crucifixion on this earth was but for one purpose and one purpose only: His Bride, the New Jerusalem!

There are 60 minutes in each hour and there are 24 hours in each day x 60 = 1,260 minutes in each day – this 1,260 is equal to the number of days in Daniel’s 1/2 Week – i.e., 1,260 days = each of these time frames is exceedingly significant – the 42 months = time, times and half a time, 1,260 days or 3.5 years/3.5 days. This is the time of Great Tribulation, testing and testimony as well.

1,260 minutes in each day x 7 days (one week) = 8,820 which is also “18″ – therefore, each week bespeaks of God’s intention of the New Jerusalem and, furthermore, 1,260 x 30 days (one month) = 37,800 minutes per month (i.e., prophetic month) which is also equal to “18″ (3 + 7 + 8 = “18). and 12 months x 37,800 = 453,600 minutes per every 360-day prophetic year which also equals to “18″ as in 4 + 5 + 3 + 6 = 18. God has but one thing in view: The New Jerusalem!

Likewise, 30 years of minutes is equal to 30 x 453,600 minutes = 13,608,000 or “18″ (1 + 3 + 6 + 8 = “18″) and 3.5 years of minutes is equal to: 1,587,600 = “27″ which is wholly the number of New Testament texts connoting the full revelation of Messiah in the New Testament – indeed, every minute of his 3 1/2 years of ministry…and if you’re not sure about that just add: 13,608,000 minutes (30 years of minutes) to 1,587,600 minutes (or 3.5 years of ministry) = 15,195,600 = “27″ (1 + 5 + 1 + 9 + 5 + 6 = 27).

Also, there are 24 hours in one day and 7 days = 168 = 15 (1 + 6 + 8 = 15) and this “15″ is the first mention of “15″ of the edge of the New Jerusalem as in 12,000 furlongs on one side of the NJ (1 furlong = 660′) and 660′ x 12,000 furlongs = 7,920,000 Linear Feet / 5280′ (in one Imperial Mile) = 1,500 miles x 12 edges = 18,000 Miles = both “15″ (as in 1,500 miles) and “18″ (as in 18,000 Miles).

Also if there are 24 hours in one day x 30 prophetic days in a prophetic month = 720 hours per every 30 days = 72 is precisely the number in Hebrew to connote the Name of God and 360 prophetic days in every prophetic year = 360 x 24hrs. = 8,640 hours in every year, which in turn, is equal to “18″ (8 + 6 + 4 = “18″) and 864,000 is the diameter of the Sun, etc.

And, in 30 years there are 8,640 hours (each year) x 30 years = 259,200 hours in 30 years = 2 + 5 + 9 + 2 = “18″ – Therefore, every second, every minute, and every hour of His whole life was for one purpose: THE NEW JERUSALEM! And 3.5 years of ministry on this Earth = 8,640 hours per year x 3.5 years = 30,240 hours and when this is added to His 30 years = 30,240 hrs + 259,200 = 289,440 = “27″ which is the full revelation of Christ in the New Testament’s 27 books of Sacred Canon!

And, insofar as “prophetic days” concern – 360 prophetic days per year x 30 years = 10,800 days – DO YOU SEE IT? “18″ – His entire preparation, every second, every minute, every hour, every day was but for THE NEW JERUSALEM!

And, 3.5 years x 360 prophetic days per year = 1,260 days – which is the 3.5 years of His ministry and the 1,260 days of “our ministry” in the Last Days (Revelation 11).

I’m waiting to see the Möbius Strip….

Nancy – you bet – there’s MOST DEFINITELY something here as well – all such absolutes have unique and remarkable characteristics which have, I believe, a message to us – even so…I only wish I could show you what it looks like but you apparently can find that out on the internet – it’s marvelous!

Mobius Strip Square

The Möbius strip, also called the twisted cylinder (Henle 1994, p. 110), is a one-sided nonorientable surface obtained by cutting a closed band into a single strip, giving one of the two ends thus produced a half twist, and then reattaching the two ends (right figure; Gray 1997, pp. 322-323). The strip bearing his name was invented by Möbius in 1858, although it was independently discovered by Listing, who published it, while Möbius did not (Derbyshire 2004, p. 381). Like the cylinder, it is not a true surface, but rather a surface with boundary (Henle 1994, p. 110).

The Möbius strip has Euler characteristic chi=0 (Dodson and Parker 1997, p. 125).

According to Madachy (1979), the B. F. Goodrich Company patented a conveyor belt in the form of a Möbius strip which lasts twice as long as conventional belts. M. C. Escher was fond of portraying Möbius strips, and they appear in his woodcuts “Möbius Strip I” and “Möbius Strip II (Red Ants)” (Bool et al. 1982, p. 324; Forty 2003, Plate 70).

A Möbius strip of half-width w with midcircle of radius R and at height z=0 can be represented parametrically by

x = [R+scos(1/2t)]cost

(1)

y = [R+scos(1/2t)]sint

(2)

z = ssin(1/2t),

(3)

for s in [-w,w] and t in [0,2pi). In this parametrization, the Möbius strip is therefore a cubic surface with equation

-R^2y+x^2y+y^3-2Rxz-2x^2z-2y^2z+yz^2=0.

(4)

Moebius gears

The illustration above shows interlocked turning gears along the length of a Möbius strip (M. Trott, pers. comm., 2001).

The coefficients of the first fundamental form for this surface are

E = 1

(5)

F = 0

(6)

G = R^2+2Rscos(1/2t)+1/4s^2(3+2cost),

(7)

the second fundamental form coefficients are

e = 0

(8)

f = R/(sqrt(4R^2+3s^2+2s[4Rcos(1/2t)+scost]))

(9)

g = ([2(R^2+s^2)+4Rscos(1/2t)+s^2cost]sin(1/2t))/(sqrt(4R^2+3s^2+2s[4Rcos(1/2t)+scost])),

(10)

the area element is

dS=sqrt(R^2+2Rscos(1/2t)+s^2(3/4+1/2cost))ds ^ dt,

(11)

and the Gaussian and mean curvatures are

K = -(4R^2)/({4R^2+3s^2+2s[4Rcos(1/2t)+scost]}^2)

(12)

H = (2[2(R^2+s^2)+4Rscos(1/2t)+s^2cost]sin(1/2t))/({4R^2+3s^2+2s[4Rcos(1/2t)+scost]}^2).

(13)

MobiusStripArcLength

The perimeter of the Möbius strip is given by integrating the complicated function

ds=sqrt(x^(’2)+y^(’2)) =[1/(16)w^4cos^4(1/2t)+{[R+wcos(1/2t)]cost-1/2wsin(1/2t)sint}^4+{Rsint+1/4w[sin(1/2t)+3sin(3/2t)]}^4]^(1/2)

(14)

from 0 to 4pi, which can unfortunately not be done in closed form. Note that although the surface closes at t=2pi, this corresponds to the bottom edge connecting with the top edge, as illustrated above, so an additional 2pi must be traversed to comprise the entire arc length of the bounding edge.

Cutting a Möbius strip, giving it extra twists, and reconnecting the ends produces unexpected figures called paradromic rings (Listing and Tait 1847, Ball and Coxeter 1987) which are summarized in the table below.

half-twists cuts divs. result

1 1 2 1 band, length 2

1 1 3 1 band, length 2

1 Möbius strip, length 1

1 2 4 2 bands, length 2

1 2 5 2 bands, length 2

1 Möbius strip, length 1

1 3 6 3 bands, length 2

1 3 7 3 bands, length 2

1 Möbius strip, length 1

2 1 2 2 bands, length 1

2 2 3 3 bands, length 1

2 3 4 4 bands, length 1

A torus can be cut into a Möbius strip with an even number of half-twists, and a Klein bottle can be cut in half along its length to make two Möbius strips. In addition, two strips on top of each other, each with a half-twist, give a single strip with four twists when disentangled.

The topological result of attaching a Möbius strip to a disk along its boundary is a real projective plane, which cannot be embedded in R^3. However, there are three surfaces that are representations of the projective plane in R^3 with self-intersections, namely the Boy surface, cross-cap, and Roman surface.

TietzeMoebiusColoring

Any set of regions on the Möbius strip can be colored using only six colors, as illustrated in Tietze’s graph above. (Sorry, couldn’t get the graphs in but it’s beautiful!)

All the above compliments of my good buddy in math – Wolfram

http://mathworld.wolfram.com/MoebiusStrip.html

yeah, who you helpin cept you? why dont you talk the god/spirit , without the tech? You are detrimental to any development of uself…

The immanent development of consciousness in all will include you despite your nonsense… have a nice day, we are getting there, you cant refuse, we are all included.Dont mean to hurt, only to move forward.