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A Book of Coincidence

A Book of Coincidence, and its more recent incarnation, A Little Book of Coincidence is a compilation of astounding geometrical relationships put together by John Martineau.  The first book is essentially out-of-print, but the second was published in 2001 and is available in most book stores [in the USA, Walker and Company, New York, 2001].

But a picture is worth a thousand words, and thus, consider the following pictures (and where thousands and thousands of words will not require being read -- well, maybe a few words):                          

In John Mitchellís famous construction, a 3-4-5 triangle (see Sacred Mathematics) can be the start of an 3:11 construction which compares the physical sizes of the Earth (+) and Moon (s) (mean diameters of 7,920 and 2,160 miles, respectively), so that the Earth squares the Moon (to over 99.9% accuracy).  Meanwhile, the extremes of Marsí (g) distance from Venus (f) -- furthest to closest -- yields the same 3:11 ratio (again to 99.9% accuracy).

Mercury (d) obviously has a thing for Venus (to 99.9% accuracy).  The three sided figure is also found in many church windows, and itís interesting to note that as a result of the shift from an earth-centered to a heliocentric cosmos, Venus and Mercury swapped positions in the order of things.  The second figures implies a simple geometric relationship between threeness and sevenness.  But itís also noteworthy that Mercuryís relationships to Venus, Earth, and Mars all involve either three or seven parts (from Mercuryís viewpoint).

Venus and Earth can be spaced with a pentagram (very Golden Meanish or Wiccaish) to 99.8% accuracy, or in an eightfold way to 99.9% accuracy.  And just as 3 and 7 have their own connections, so do 5 and 8 (both of which are Fibonacci Numbers).  

Of all the truly amazing relationships, perhaps the best are the proportions between Earth and Mercury, and the Earth and Saturn (j), where both the orbits and physical sizes of the planets are related (both to 99% accuracy) -- in one case a Phi-ve (five) pointed star, and a 30 pointed star for the other.  Multi-pointed stars might seem to be stretching the point, but 30 is the first number which can be divided by 2, 3, and 5, and is the number of the outer trilithon divisions at Stonehenge.  Coincidentally, Mercury and Saturn are the innermost and outermost of the medieval planets (those which can be seen with the naked eye).  But you can also do the latter with a fifteen pointed star (i.e. five times three).  So there!  

Furthermore, the diameter of a circle based on Mercuryís aphelion (closest point) to the Sun, also happens to be the distance between the mean orbits of Mercury and Earth.   

An even more famous coincidental arrangement is that Saturn takes the same number of years to go around the Sun as there are days between full (Earth) Moons (to 99.8% accuracy).  Score one for the Lunatics!  

Stonehenge, by the way, is the most visited place of any kind in Europe -- every year more people visit the site than were present on the face of the Earth at the time it was constructed.  Small wonder that visitors are drawn to the geometric masterpiece.  If for no other reason than that if Mars is sized so as to define the thickness of the inner bluestone horseshoe, then the Earth and Moon are sized as shown in the upper left figure. In the below left figure, all of the inner planets are sized (with Venus being slightly smaller than Earth, equivalent to the width of the main trilithon circle).  Meanwhile the right figure gives the orbits of Jupiter (h) and Saturn.  Note:  The architect(s) of Stonehenge apparently knew the physical sizes of the inner four planets!  Are there any questions?

The linear distances between Earth and Mercury, and Earth and Saturn, can also be used to create a threesome style geometry, while Venus and Earth have nested pentagrams (to over 99.9% accuracy.  

Meanwhile, Mars is doing its square dance with Jupiter, and (you guessed it!) a pentagram with Saturn (both to 99.9% accuracy).  The combination of Mars, Jupiter, and Saturn is one of will, expansion, and structure -- the stuff of which empires are built.  Four touching circles can also be used to space Chiron (()from Mars when viewed from the Earth!

Speaking of Chiron -- the object in a planetary orbit many astronomers wish to refer to as a comet -- Saturn does a seven circle thing (to 99.9% accuracy), similar to the Mercury and Venus thing (shown above).  Even more intriguing is when Jupiter and Uranus (k) -- and the multiple circles based on their closest, mean, and furthest distances from the Sun -- are combined with 99.7%, 99.6%, and 99.4% accuracies, respectively, Chironís mean orbit sits almost exactly at the geometric transition point.  Thus Jupiterís mean orbit is defined by Chironís by a pentagram with 99.5% accuracy.  (BTW, did we mention the connection between the pentagram and the Golden Mean?)

Reaching the outer reaches, we can note the fascinating dance between Jupiter and Saturn where from the viewpoint of Earth, we get Golden Mean relationships, Star of David combos, and threesomes.  And of course, we can connect Jupiter with Neptune (l) with a multi-pointed star dressed to the Nines.  Keep in mind that Jupiter and Neptune are both on the column of Mercy in the new and improved version of the Tree of Life, and that a nine pointed star is just a triangular shape squared.  

Uranus, Neptune, and Pluto (;) have a very straightforward relationship with the Golden Mean -- Pluto and Neptuneís outer orbits to 99.5% accuracy, and Pluto and Uranusí inner orbits to over 99.9% accuracy.  Chiron and Plutoís outer orbits are in a proportion similar to the Golden Mean nested twice (to 99.7% accuracy).  Alternatively, Uranus and Pluto can be easily related by ten circles -- but then again, ten is just double five (i.e. Phi-ve).

Ceres, the preeminent asteroid, is also connected to all of this.  On the one hand, Venus, to over 99.9% accuracy, and on the other hand, acting as a midpoint for a very curious set of relationships between their orbital radii -- those given as:

Venus times Uranus = 1.204 Mercury times Neptune

Mercury times Neptune = 1.208 Earth times Saturn

Earth times Saturn = 1.206 Mars times Jupiter

Venus times Mars - 2.872 Mercury times Earth

Saturn times Neptune = 2.976 Jupiter times Uranus

Venus x Mars x Jupiter x Uranus = Mercury x Earth x Saturn x Neptune  

Finally, we should point out two other relationships.  The first relates wholly to Earth and is based on the Earthís tilt of 23.4 degrees from the plane of its orbit around the Sun.  The set of three rings was used as the base scale for medieval astrolabes and is generated by imagining oneself to be standing at the South Pole, and then seeing the tropics and the equator as they appear projected on the flat sheet of the equator.  According to Martineau, ďThis diagram rewards study.Ē

But if youíre in a hurry, please note that Keplerís attempt to space the orbits of Mars and Earth with a dodecahedron, and Venus and Earth with an icosahedron, was very close to the mark.  The dodecahedron and icosahedron are related Platonic Solids (i.e. they create the other from the center of their faces), while Venus and Mars have been having relationships in many diverse forms for millennia.

All of these incredible figures -- used by permission from the author, John Martineau -- must inevitably demonstrate the fundamental geometric nature of the universe in placing the planets in their orbits.  The quantization of the orbits is simply not a matter of chance!  Furthermore, an understanding of the process could greatly simplify the search for new planets, both those belonging to Sol and to other nearby stars.  In effect, there are just so many orbital radii possible.  If you know a couple, then the rest should be predictable.

Meanwhile, just relax in the knowledge that everything is mathematical (not to mention aesthetic), and that we can sleep well tonight knowing that the mainstream astronomers are dutifully searching the skies for those pesky Near-Earth Objects which are threatening to annihilate the Earth, pummel it back to the stone age, or just destroy civilization as we know it. 

(5/25/06) In fact, a comet (SW-3) has just crossed Earth's path -- missing a collision by a few million miles. There were some expecting some significant action, but apparently the Earth doged another bullet (aka rock from outer space).

At the same time, there is always 2012-2013 A.D. and the End of the Mayan Calendar. This has been given some planetary emphasis by Graham Stevens in his aptly entitled Jupiter's Dance. It seems fundamentally obvious that planetary geometries (to which Astrology might ascribe) are having significant effects -- the kind of effects which tend to result in earthshaking events.

Alternatively, one can fall back on:

Harmony of the Spheres         Sacred Mathematics         Kepler

Unless youíre still game for more, in which case...

Satellites of Jupiter         Hyperdimensional Physics        Connective Physics

Meanwhile, you can find a bit more of John Martineauís observations embedded in...

Days of the Week         Calendars

   

(IIc) (_d) (+) (^) (f) (g) (h) (i) (e)

  

               

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