You'll find plastered all over the American Armed Forces (run from the Pentagon, note) as well as about 40 of the national flags of the world:
The European Union, Greece, St Kitts and Nevis, and Vietnam ... never mind Old Glory (Stars and Stripes) etc...
This version is called the Drudenkreuz/ Drudenfuss/Witch's Foot - http://en.wikipedia.org/wiki/Drude and presented this way up is Devil or Goat (it looks like a goat's face). Where the chords cross are multiple phi points.Kepler (1596 AD) called phi a "precious gem":
"Geometry has two great treasures; one is the Theorem ofPythagoras; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of gold; the second we may name a precious jewel."http://en.wikiquote.org/wiki/Johannes_Kepler (MY
STERIUM COSMOGRAPHICAM).
Pythagrorean 3-4-5 (Euclid 47) is the first, the gold. and phi is the second, a "precious gem", figuratively.The Devil aka Lucifer once had a crown in which was set an emerald, the gemstone associated with Venus. Its broken (fallen) parts are associated with the Grail Chalice and the alchemically-linked Emerald Tablet of Hermes Trismegistushttp://en.wikipedia.org/wiki/Emerald_Tablet. I choose to identify the Kepler "precious gem" intersections of pentagrams/pentacles with the emerald theme associated with Lucifer, Venus, the Grail and the Tablet, both here on this page and elsewhere. This accords with both David Wood (GENISISet al)and Laurence Gardner (BLOODLINE OF THE HOLY GRAIL et al): there is a "precious gem" where his horns meet (his brow/crown* and another, the "Jewel of Venus", where her legs meet, both gems being emeralds. Boyd Rice calls the pentagram/pentacle the symbol of "Ari", the "Shining Ones".
The inverted version of the Devil/Goat is called Woman/Lady, and the Star of Isis,"the Egyptian goddess and her star"and "pentagram star ... Star of Isis, Star of Venus ..." http://homepage.ntlworld.com/fusniak/talisman/articles/isisofparis.htmlhttp://www.bibliotecapleyades.net/sociopolitica/codex_magica/codex_magica26.htm. I note here, though, that Sirius, the Dog Star, is perhaps more commonly associated with Isis than (the Green Planet) Venus but, also, I read, the Ancient Egyptians also identified Venus with Isis. A curiosity here is dice: 6 6 6 is a "Venus" whilst 1 1 1 is a "dog". Sirius = Canis = dog (= the soul of Isis - http://en.wikipedia.org/wiki/Sothis). On a dice, 1 mirrors 6. 666, of course, has other connotations - Devil. 111 and 666 are in the same 37 X table. The Star of Venus:
- and scroll down. It's all to do with pentacles and wisdom.
Quick (relevant) digression:
Below, though, some Tarot 15 versions*. This is called the Extended Pentagram and is perfectly parallel to the Star of Isis/Venus. It is dubbed by David Wood the "Isis" Star Union. It is a product of exactly the same straight edge and compasses classical construction that is used to draw regular hexagrams and pentagrams*:
*'Isis'- the shape/geometry so termed by David Wood - there on the forehead these first 3 Tarot XVs (the second being from the Rider-Waite deck) and visible in Wood's "Star Union" (right). Some other Tarot 15 (noting 666 is aften given -mistakenly - as the reciprocal/mirror of 15)representations have a regular pentagram ( fig. 4 above - "Baphomet", l'Abbe Constant) or, in one for instance, hexagram on the forehead of this 'The Devil'. This point totally eluded David Wood (GENISIS and, with Ian Campbell, GENESET ) . He/they used a regular 15-sided shape** (somewhat appropriately? and as in farthest right) to produce this Tarot 15forehead shape. It was claimed this was the only way to create this "Star Union"/"Extended Pentagram". There are actually quite a few (different and far easier!) ways***. "Isis" is the yellow plus the orange bits. I think "she" represents the marriage of Heaven (hexagon) and Earth (pentagram), Wisdom/Sophia, the Woman of REVELATION, the Bride of Christ and the New Jerusalem. "She" appears as part of my MOVING MENHIRS study. Her legs meet by Queenhill, River Severn. The Severn is a red river. In Wood and Campbell, Rennes-le-Chateau was the context.
* The vesica is where the two circles overlap (as in the Star Union, above). They share a common radius. The horizontal line between where they meet is a hexagram chord. This vesica is Square Root 3 geometry. Fancifully, perhaps, that's the square root of 1.5 + 1.5, the Square Root of Isis .... - or one of them ...
** A masonic ref.: the Winding Stairs? There are 3 + 5 + 7= 15 of them. A 15-sided (and segmented) regular polygon, a pentadecagon, will look like a 15-stepped spiral staircase. Biblical ref.: 24 Elders round the REVELATION throne - 360/15= 24 ... but the 24 can also be hours etc.
Back to the regular pentagram star:
The (first) pentagram shape below, Devil/Goat, below, is just a regular pentagon, joined up as a star, and nothing more sinister than that. If you turn it upside down - or tilt your head slightly - you'll see its mirror, complement and opposite: Star of Isis/Venus, Lady/Woman. You'll see pointed head, outstretched arms and legs. There is a 'precious gem' where her legs meet - and sometimes a candle/light where his horns do on Tarot XVs. It's an emerald - another one. Phi. And that's about as esoterically/ arcanely/hermetically frighteningly significant as it gets, really - for what you can do with a pair of compasses, straight edge, and pencil coupled (if you'll pardon the phrase) with vivid imaginations! If you look carefully you'll see that where-his-horns-meet and where-her-legs-meet are (essentially/non-geographically) exactly the same places - 5 of them in all - and are mirrors. If we superimposed an opposite on top we'd create decagonal maths and produce ten emerald phi-points. That's ten emeralds to our ten Tree of Life sapphires/sephira. Ten can be evocative of decagons.
GOAT LADY
The green circles are the (multiple) phi points. There are 5 each - making 10 ( if you put one atop t'other). The black line is common. Notice 'he' has a "precious gem" where his horns meet and 'she', where her legs meet.
A decagon is what happens when you the one atop the other. Masonic "Eastern Star" by-the-by:
*Brief digression - I recommend www.goldennumber.net here as a quite remarkable resource - which I drew from, here, in my brief digression, above, to an extent. Note also that the Tarot Major Arcana of 22 cards ends with card 21 (from card 0), 21 being a Fibonacci number (0,1,1,2,3,5,8,13...).
Dactyls (fingers) spring to mind. You have ten fingers, normally, and these have been assigned as right-hand = male and left-hand = female, with 'right' as dexter (smiths etc., as in dextrous), subject to the goddess, and 'left' as sinister and somewhat witchy and representatives of the goddess (See Robert Graves on Lemnos et al).
See the problem? I would expect a convention of sorts were there a tradition and I would expect it to fit to the Dactyls were it part of some esoteric 'stream': left would be female and right male. But mirrors is a recurring encounter in these pages I've posted - what if I'm supposed to see it from THEIR perspective. Adam/John the Baptist have Eve/John the Evangelist on their left, from their point of view. This possibly addresses the difference in the placing of the J and B Temple of Solomon pillars in terms of B J Tarot II to J B 'The Compass of the Wise' et al (where J is Solar/white/male/ Fire and Air to B's Lunar/black/female/Water and Earth). That just leaves the ask re. John the Baptist ..... water? 'Jesus' seems to be the (male) Fire Baptism to John's (female). Water? There are problems, I note, if you try to trowel on the Chakras and the Yogic systems - white normally becomes female and red male, for instance - but I do say 'normally' (it ain't set in stone, exactly!)*. Oh, well ... back to the plot:
If I drew a line from the centre below through a 'gem' to the inner circle, then the gem would "cut" that line, longer to shorter, and longer to whole length, in a phi ratio. Remember, the "gem" (emerald) is where-his-horns-meet and where-her-legs-meet - so we would go from the centre through the gem and to, say, halfway between 1 and 3 below. Let's call that point A. Were below a perfect pentagon, then 1-A and 3-A would be decagon sides and these would also be at phi (0.6180989-ish:1) to that line from the centre we first drew. Hence "multiple phi point". Phi is also what Venus gets up to in the sky. Remember that Venus is Lucifer (the Eos/ Eosphorus/Phosporous - note phosphorus/match/lucifer - Morning Star and the Hesperus Evening Star): Lady/Woman and Goat/Devil?* The pentagrams look it and Venus/Lucifer does it. This Female-Male idea appears on Golden Dawn Tarot 15 above - they are chained together.
* Wiki carries "goat of lust" inverted pentagram as a mid-C19th AD fancy - and it also carries pentagrams as Ancient Greek "here to there" and "there to here" - otherworld places characterised by heroes entering Hades and returning with ... "wisdom". It is interesting, too, that Mercury can be associated with a hexagram.
It's a 5 : 8 relationship (phi-alike). It's not quite perfect but gets back to its exact start every 40 years - in the desert/ wilderness? Going round it is the counterclock-wise zodiac context: Scorpio atop, Taurus abottom, Aquarius left and Leo right. Move the context round 90 degrees counter-clockwise and you have the 4 Royal Watchers in their assigned NSEW stations of about 4-5000 years ago. In the Bible, these find expression as Calf/Ox, Lion, Eagle and Man/Angel - the 'wheels' on the fiery chariot, the merkabah/hod. Bull is Taurus, Lion is Leo, Eagle signals Scorpio, and Man, Aquarius : www.geoffss.plus.com/royalwatchers.htmNote that St John the Evangelist is identified as West/Eagle/Scorpio. This is of some importance in my study of the Perpetual Choirs of Britain/Moving Menhirs where the Lady and Goat pentagrams combine with Point St. John, Pembrokeshire. In Grail lore, Celtic tradition and Tarot suits there are Wands, Swords, Cups and Pentacles (Platters). Wands and Swords are male, Cups and Platters/Pentacles female.
ASIDE - SHA STAR: circle in a pentagram?
Caveat (geoffss, 12-09-09): "sha" exists in a number of languages with widely differing meanings, including the abbrev. astronomical SHA (below). We find it in Japan, in China and inHebrew et al. In Feng Shui, it seems to refer to various aspects, ominous and propitious.
In my notes, there's a reference to "sha star". The item is taken from a book I read some years ago which had extensive explanatory notes and which had an alchemical "thrust": THE ZELATOR by David Ovason is the source. Mention there is of sha as an Egyptian hieroglph, the "five-pointed star". No circle mentioned, though. But there IS one there on p. 332* as well as associations with the crocodile and reincarnation. See also the notes on Chapter 6, No. 3, pp. 584-585 (all page refs are to the paperback ed.). Ovason gives an academic source for the sha star as the star hieroglyph there plus notes a possible connection of it with the orans (worshipping position).
* "sha-star":
Elsewhere I read: "The five-pointed star within a circle has been a sacred symbol since ancient times. The five angles are said to represent the elements of Earth, Fire, Water, Air and Spirit, the circle represents Unity, Wholeness and God-Goddess or Divine Source". http://soul2soultreasures.com/properties.htm
Others say sha is plants and a pond whilst the five-pointed star in a circle is said (by Ford) to represent the goddess Neith*. There again, he writes dwt and not sha:
"The five-pointed star within a circle, dwt, or duat, is the ancient Egyptian symbol for the underworld or place of the soul's transformation. However, there are considerable differences of opinion amongst modern scholars as to the meaning assigned to the duat by the ancient Egyptians and the issue is by no means a settled one."
There again, earth, water, air, fire and spirit? Or the 5 planets, Mercury, Venus, Mars, Jupiter and Saturn? I even considered chucking in Vitruvian Man, Da Vinci .... or we could go Cyrillic where you have a symbol like E turned 90 degrees counterclockwise ( = sha).
There are 57 SHA stars - far bright stars*, the ones used by lunar astronauts, say, to fix position. These are stars that are used at the Spring Equinox (called "Ist point of Aries" still, despite precession) as Fixed (also despite precession) and astronomers measure their Sidereal Hour Angles (SHA).
*A number with mystic connotations if you care to check out why Heinz has "57 Varieties" or consider Saturn being symbolisedand as Heavenly Body number 7 in Ptolemy and Copernicus or consider (c/o BigBytes - my thanks) that the observable arc of the moon at the Equator is the St Johns' 23.5 of Tropics Cancer and Capricorn as above + 5 = 28.5 X 2 = 57 degrees ("grand total of variation of 57 degrees in the declination of the Moon". ... harvard.edu). 57 is the corollary of (masonic) 33, I note, in a right-angled triangle.
Here are three crests: Drury, St John and (St John) Sinjuns:
The last is the crest of a school endowed by Sir Walter St John: "Sinjuns". The Drury crest (noting Drury Lane and Freemasons Hall, above, wasoriginally the two stars, the tau being added after a trip to Egypt/and/or pilgrimage to Jerusalem (Nicholas Drury, early-mid C15th - he founded the Drurys of Hawstead circa 1453). His grandfather was a third son and his great X 6 grandfather, Drogo/Drieu of St Edmund was also = ? 2 mullets?).
Here is the US Military National Aircraft Insignia (1917-18 and1919-42):
I read that sha star denotes a death star of sorts. Feng Shui has a number of fate-and-fortune linked (prefixed) sha stars and I find these related to trigrams by some. It is possible that ideas related to Feng Shui have "contaminated" ideas connected with astronomy c/o "sha".
Sir Laurence Gardner points to the Rose Of Sharon and Elisha; sha means 'orbit' (to him - more commonly I find snw/shen/shenu given as orbit). This from p. 93 of one of his "GRAIL" series: "a sha being denoted by a circle .. = 360 degrees ... from sha-at-am ... 'a passing' ... can be related to the completion of an orbit ... about 275 BC ... Babylonian priest called Berossus ... recorded that an ancient sha was ... equivalent of 3600 years ... however ... Mesopotamian sha ... confirmed by Sir Leonard Woolley ... equivalent of 360 years ... ".* Keith (GHMB, 28-11-09 ... and my thanks) comments:
Dear Geoff,
... To begin, I would note the Sha-Star term that you mention. Now, there is an ancient time cycle of the value 3600 called a Sar - (Shar in Akkadian). This is signified by a large circle and is a 'princely' or 'royal' number. It also signifies a 'completed cycle' or 'perfect circle'. (I cite here references from Zecharia Sitchen). This may in fact be a direct tie-in.
If you have a copy of Ovason's Zelator, I would direct your attention to pages 349 to 354. On the first of these pages, Ovason mentions the importance of the number 72 as associated with the solar mysteries, and the sun. Now indeed, ideally, the earth once possessed 360 days per year - 1/10th of a Shar. I find it interesting that 360 / 72 = 5. You mentioned that Ovasion refers to 5 radiants (as in rays, possibly?). It this the answer?
Now, Ovason notes that in India, the mysteries of reincarnation are linked in to the Zodical Sign of Capricorn, the Makara. The Makara though is a crocodile monster. To go further (page 353) Ovason relates the Makara with the Liberia cap of the Mithraic rites. Of the cap, I quote from page 354 "...it is emblematic of completed work within the cosmos. The completing of the circle." Indeed, it is further suggested that people who wore such caps were 'completed men' who new the mysteries of reincarnation. This indeed, brings us all the way back to the 3600 value of Sitchen.
*(Note, 14-02-09, geoffss - this imagery reminds me of the snake tail-in-mouth ouroboros, aka endlessness, totality and completion - c/o Chambers.
Mind, others give consecrated/salvation/deliverance for 'sha' whilst Rose of Sharon associates with Astarte/Anath/ Ashteroth, "fruitful" and "sheepfold", and is twinned up/mirrored/alter egoed with Lily of the Valley. as Birth/Life v. Death imagery associated with the number 7 and a certa
So, circle in pentagram, "of/from", just an heraldic "mullet (signifying third son, my note) ... pierced of the field"? Possibly. Just maybe, though, something astronomical is also being displayed? Stars do seem to be somewhat thematic in my study - as are those who watch them! So, personally, I think the 'mullet' in some cases - like Drury and St John - identify Venus in conjunction with (transiting) the Sun.
This is a detail from the Ace of Pentacles, Tarot. Can you see the (phi) Chalice? Number the top point 1, then go round clockwise 2-3-4-5. Join 3 to 4. See it now? Go 2 to 4 to 3 to 5 to 2. As in:
I say "roughly" (aka drawn crudely) - the chalice/cup is indicated in green and its pentagon "parent" in red. Some construction is indicated by the vesica and shared hexagram chord. Could this phi chalice be the Holy Grail (if the grail actually be a cup, of course)?
Note (added 03-08-07): geometrically speaking, every pentagon/pentagram has an implicit hexagram star - and you can also find 'gem' connections here to Star Sapphires (6s and 12s). Another name for sapphire is sephirot/sefirot. Plural: sephira, as in the Tree of Life, below. Pentagram is sometimes assoc. earthly/lower and hexagram spiritua/higher.
One of our Sts John of Jerusalem - the Evangelist - is portrayed by the symbol snake-in-cup/ chalice (there is a snake in this cup on the left! Look closely). Apparently he avoided a poisoning attempt on his life. But snakes are also associated with both wisdom and immortality - the two trees of Eden - and Durer, for instance, poses Adam, Eve, Tree and Serpent in a manner extremely suggestive of male pillar, female pillar, and central "wisdom" serpent/fruit/tree between them. The River Severn, aka Hafren, is a tad snakish in shape. I placed it in a pi chalice - and, appropriately, coloured it red. Snake is another word form worm or dragon. A red snake/dragon, kinda writhing? The Greek He Phren means lower mind/mind below. Hafren, He Phren? In both Greek gematria AND simple English letter count (x 9) the term values at 666 : H (8), E (5), P (16), H (8), R (18), E (5), N (14) = 74 (same as J + E + S + U + S - 10 + 5 + 19 + 21 + 19). 74 X 9 = 666. The mirror of 74 is 47 (J + O + H + N). Oh - and the river in the circle - foetal/with child? Plotted on an OS map, a line from the centre of the chalice base through the centre of its lip will reach the coast at Point St. John.
Representations of the Tree of Life sometimes come with a serpent rising from Earth to Heaven c/o all the ten sephira; some representations of the crucifixion replace Christ with a serpent, an image reprising Nehushtan, the brazen serpent Moses nailed to a pole.
Snakes, in "gnostic" representation, are largely UPwardly mobile - and they seem to represent the river of the water of life' (is this river' partly an allegory for Time, with the 12-sign zodiacal ouroboros either side of the 'street' of it?). Yet the Fall serpent gets kicked out of Paradise/Eden = DOWN*, Heaven to Earth. This Heaven to Earth pathway is called the Lightening Flash - the enlightened snake in reverse. Both sequentially visit all the ten "Gates of Light" and "Shining Ones", as the sephira/sephirot are known. To the 22 pathways connecting these are assigned both the 22 letters of the Hebrew alphabet and the 22 cards of the Tarot Major Arcana**.
* Onesuch gnostic snake is Ophis - not kicked out but deliberately going to earth to encourage the eating of the (pentagram) apple/wisdom.
** Note re. 22. It is 11 + 11. 11 is 7 + 4 (and 4 + 7!). "John" in masonry is the Tropics of Cancer and Capricorn. These are are Lat's 23.5-ish ... and 23.5 X 2 = 47. The letters that comprise John sum to 47 (c/o alphabet place positions. That's a 4 and a 7. The "mirror" of 47 is another 4 and 7: 74. Jesus = 74 (and 9 X 74 = 666).. Now Jesus + John = 121 ... which is 11 X 11. At one time, the multiply sign X was written as . so we could write 11 X 11 as 11.11. 11.11 is known by some as "insight". If we allow the Gemini II sign to indicate the masonic pillars Jachin and Boaz then we could represent Gemini as II II (noting Aleister Crowley's Atu of Thoth is Major arcana is 11 + 11, 22 cards numbered 0-21).
To the sephira are assigned names, numbers, qualities, the "Heavenly Bodies" (and their sigils/glyphs), geometrical shapes, colours, angels .... The High Priestess/Papesse ("JOHN") card, Tarot II, gets to 'live' at non-sepirot II, Da'ath. The snake goes through there, too. To detail some: top left (the male pillar) is sephirot 3, Saturn, triangle, black; middle-right (the female pillar), 4, Jupiter, square/pyramid, blue; middle left, 5, Mars, pentagram, red; 6 (miiddle pillar), Sun, hexagram/cube/ truncated pyramid, yellow; 7, Venus, hepta/septagram, green; 8, Mercury, octagram, orange; 9, the Moon, nonagram/ enneagram, purple; 10, Earth, dekangle, 4-coloured quarters of a circle. This Earth-centred, Ptolmaic, universe conceptualisation, was known to people like Pico della Mirandola, C15th AD. But it was also known to St. John: his 'seven seals' that needed breaking on the way to enlightenment. The idea was that the heavenly bodies were 'guards' on the snake-path to sephira 1, the Crown/Throne of Heaven/Bethel. We are looking at "Jacob's Ladder'. Notice also that the 7 listed polygrams combined with the 5 Platonic solids in Metatron's Cube make 12. 12 'Fruit' of the Tree of Life? Another nicety is that the central pillar sums to 26 - as does MM (hence Mary Magdalene and Master Mason interest?). I looked here at the SONG OF SOLOMON "I am the Rose of Sharon ... lily of the valley" because of the association of red rose with lowest sepiroth. It was striking that lily is Jacob's Ladder, a Tree of Life term, and, as Iris, it is the rainbow. A rainbow spectrum is 7. The combination is White: alchemy is about turning red into white (apparently). Gary Osborn mentions the male red to female white as mirrors and complements (Graham Hancock Mysteries Forum) and alchemical Mercury and Sulphur also come to mind. But female is usually black ... cold/wet ...
A related idea to enlightment is that Fall/being cast out of Paradise is the 'Word made Flesh', a Fall from Grace/Logos/ Spirit to the Earthly and carnal pleasures, this characterised as going from 1 to 10 either by the Lightening Flash or directly Crown-Sun-Moon-Earth. Ker-splat! Earth is also 'Bottomless Pit' - not a nice place for seekers after intellectual and spiritual enlightenment to hang out. Not nice at all! Omar Khayyim, late C11th-early C12th AD knew of this stuff from the bowels of the Earth, he wrote, ... rose to sit on the Throne of Saturn. Ptolmaic. This is to be compared with Copernican and alchemical 'turning Lead (Saturn) into Gold (Sun). Under the Babylonian/Ptolmaic system, the 7 Heavenly Bodies (Earth doesn't count) fit to a 'fat' heptagram star in the Tree sequence - and then along came Copernicus, late C15th - mid C16th AD and messed the whole thing up with his heliocentric stuff - never mind the discovering of Uranus, 1781, Neptune, 1846 and Pluto, 1930-2006)! In a chakra allied systems, the 7 became Saturn (base) - Jupiter - Mars - Venus - Mercury - Moon -Sun Copernican (having been Moon - Mercury - Venus - Sun - Mars - Jupiter - Saturn Ptolmaic).* The idea of Saturn as an inverted (black) triangle and lowest chakra is evocative of something. I wonder what?**
* An oddity ... the 10 sephira of the Tree of Life have these 7 assigned as 3-9, descending 3 (Saturn), 4 (Jupiter), 5 (Mars), 6 (Sun), 7 (Venus), 8 (Mercury) and 9 (Moon) BUT "enlightenment" runs the other way: from 333 akraisia up to 999. Two alternate systems collide.
**Stop press: Agrippa and the 'marriage' of Magic Squares to Ptolemy. 3 gets to be Saturn counting inwards to 9 being the moon. Sun is (Hexagonal) 6. 6 and 9 are mirrors - quite deliberately symbolically so. Agrippa published 1510 AD, possibly from earlier sources - but Magic Squares don't arrive in Europe until 1300 AD. I've posted a (very minimal) history of Hindu-Arabic number development on another page - e.g. 6 and 9 as against say VI and IX, not mirrors.
Besides pentagonal geometry, phi is also to be found via an equilateral triangle and a square via very simple compass, straight edge and pencil construction. So it is a feature common to the developments equilateral-hexagon (Seed/Flower of Life), square-octagon and pentagon-decagon - as well as all derivatives and developments of these. From simple Isis/decagonal geometry, you also get to trisect a pentagon and deliver Wood's 15-sided pentadecagon. This last seems to me to be far more likely a constructional outcome than an input!
Is there a progression from equilateral to square to pentagon (and on) that is constructional and resides in the properties of the Vesica Piscis-based Seed/Tree of Life? Here is Robert Lawlor, SACRED GEOMETRY (p.43):
This image is (almost) the Albrecht Durer classic "showing the construction of a pentagon from a Vesica Piscis and its union with the hexagon" (the hexagon is implict here in the bottom circle). It is accomplished in the same way as the Creator traditionally designed the universe, 'with the compasses unchanged' (Michell, Street, or both). Durer, 1471-1528, was a noted engraver, woodcut designer, painter and astrologer. What Lawlor has done here is add in an equilateral triangle and a square to the Durer geometry whilst dropping 5 of the 6 hexagon sides). His point is that the Seed of Life will deliver regular polygons, all with the same base length so all are equally-sided in the length of all their sides. What's more, equilateral delivers hexagon delivers dodecagon (by geometry) as pentagon delivers decagon delivers .... Lawlor notes that the Vesica's Square Root of 3 is the 'formative power' than gives 'rise' to these polygons. An extended diagram shows the polygons (rather like a scallop shell, don't you think?) fanning out:
If you replaced the polygons with their describing circles you'd have a kind of Round Table based on the Square Root of (1.5 + 1.5) geometry! Note the central column - and how similar the 'building blocks appear. It's almost as if there is an incremental rise from one polygon to the next, isn't it? But it's an illusion (and I note Lawlor, himself, doesn't claim equal increments). The Lawlor approach delivers some polygons, it seems, but not heptagon ... nonagon ... I looked at the (inviting) idea of using a common base combined with an constant increment gain generating regular polygon centres - doesn't work either - but then so much of this stuff looks good at A4/Trig. free level. One logical outcome of Lawlor: phi. It is necessarily the relationship twixt the equilateral (and common side) and the decagon centre-to-corner (radius, given describing circle).
Whilst is is obvious that an octagon can be same-sided (lengthwise) as a square - as in Lawlor, above - you need a common describing circle base for an octagon and square to 'live together' on a Seed/Flower of Life geometric development. The octagon sides will have to be smaller than the square's but the radius will be X2 - and hence the describing circle will be X2 in circumference (a Seed/ Flower 'fit'necessity). Lawlor's diagram above might be miscontrued (but not by him!) as indicating Seed/Flower. For my purposes, however, the common side above is abandoned in favour of a common bottom - and (two) circles tangential to each other at it containing two related polygons. One will have a radius of 63 miles (with an inscribed decagon) and one will have a radius of 50.4 miles (with an inscribed octagon), noting that 50.4 is 8/10ths of 63 and that 63 miles is 504 furlongs. Allowing Pi to be 22/7 (which it ain't), we would have circumferences of 316.8 miles (octagon) and 396 miles (decagon) - and our decagon perimeter will (again with 'stylised' 22/7) be 6.66 miles less than the 396 circle circumference. The centre of the octagon circle will fall on Lat. "Pi (22/7)", Elmore Back, River Severn: calc. 7/5.5 = 1.27272727r. The Elmore Back site is on Lat. 51.8428, tan. 1.272728 ...This is very close to the Great Pyramid of Giza gradient. If this latter were on a 9:10 gradient (10/9 = 1.11r), corner to top, say, then the angle would be 51.8442 .... 5184 is a number that is interesting to some: 25920 is the Platonic "canonical" number of years it takes Earth to precess completely through the zodiac (the 12 "Ages" of ...). X 2 = 51840. It is the "Great Year". 5184 is also 72 squared, 72 being a pentagonal and decagonal angle and 1/3 of 2160 ( = 25920/12 = a "canonical Age", itself, aka Great Month). We are looking at some of Bonnie Gaunt's, say, "magnificent numbers" ... this in the octagon and decagon, both. Others include 108, 144, 288, 396, 432, 792 864, 3168, (all 36 X table stuff and you add 0s to each to get interesting (stylised) results: 1080 = Moon's radius, 7920, Earth's diameter, and 864000, Sun's diameter ... and the number of seconds in 10 days, etc.). Note: you have to have "mile" and "second" to get 1080, 7920 and 864000 ... Mile and second appear to be utterly arbitrary man-made quantities of time and distance - but, without them, the "canonical" values attached to moon, earth and sun, and a pi of 22/7, this beautiful but stylised system of number falls apart.*
* Take the inch: 198 make a rod/pole/perch (22 X 9) and 198 is half 396, above, our decagon circumference, supposed Ancient Solfeggio healing frequency and Earth radius. Then there's the cricket pitch chain: 792". There has to be a start measure that others are multiplications or divisions off (you might usefully take a look at CIVILISATION ONE, Christopher Knight and Alan Butler, here - thanks Michael!). I note, by-the-by, a fairly standard 51.84-ish Pi: Take Planet Earth and shove the Moon atop it tangentially, run an axis from centre Earth X-section to centre Moon Xsection and run a horizontal at 90 degrees to that through the Earth centre/axis bottom, then join up the angles from centre Moon to where the horizontal cuts the Earth circumference, et, voila, Great Pyramid http://genesis.allenaustin.net/pyramid.htm
Now, let that square have sides of earth 7920. The perimeter will be 4X that = 31680. But bottom earth to top moon = 7920 + 2160 = 10080. Were we to draw that as the diameter of a circle the circumference would also be 31680. And 3168 was a number we saw above centred on Elmore Back, River Severn, Lat. Pi.
Given Khafre indicates a Pythagorean 3-4-5 theme, it is perhaps not unreasonable for maths to also be identified with its big brother. Khufu, aka the Great Pyramid at Giza?
Note 21-11-12: I've done some further work on this for Gary Osborn, partly involving the freemason Frank Higgins. You need page 15, Figs 6 and 7 http://www.glbet-el.org/bet-el%20livres/The_Apron[1].pdf The context is the masonic apron. Higgins appears to be saying that the masonic apron carries 2 well-known geometries: the Pythagorean 3-4-5 triangle and the 51.84 degree Great Pyramid. It doesn't. Higgins takes a chess board and puts his 3-4-5 4 squares in (top centre) and 3 down (generating a hypotenuse of 5). So a Euclid 47/Pythagoras 3-4-5, indeed. But that leaves the tan 5/4 for the "Great Pyramid) - and that's circa 51.34 degrees, and not a (schoolboy) Pi of 7/5.5. Whereas 5/4 is 1.25 is circa 51.34 degrees 7/5.5 is 1.2727 ..... is 51.842 ... degrees (noting the Great Pyramid's 51.83-5-ish slope). HOWEVER, were that a Mer triangle at the top - 4 across the top again but angled at 36 degrees down (from the corner) - then the remaining triangle would be close to 51.85. It's circa the tan 1.2735 (near 51.856, where 4/true pi is circa 1.27324 = circa 51.854). Now the Great Pyramid context ranges from phi possibilities to pi: a triangle circa (phi values) 1-1.272-1.618 will have an angle of 51.827-ish but is often given as 51 50 (51.8333r) whilst the Great Pyramid often identified with 51 51 (51.85). Perhaps this range of possibility and the possible import is why Higgins wrote (ibid, 11):
"it gradually dawns upon the student that innumerable figures in question are based upon mathematical and geometrical propositions so ingeniously managed as to betray no notion of their real character to the unaided perception." ?? See more of Gary Osborn @ http://www.garyosborn.moonfruit.com/#/the-masonic-apron/4570384355
At Elmore Back, River Severn, the entire range of phi-pi latitude possibilities above is covered by about 1.863 miles across the river. Milton has the virgin, Sabrina, drowned in the river - Lat. 360/7 cuts across the mouth of the Severn and this value is known as "virgin" - 515 "parthenos" in gematria (with 360/7 = 51.42857 ...). 515 is also the tilt of the moon and the relationship between pi and phi: http://www.515.org.uk/numerology.swf
Back to our model - and the common 'bottom'? It will beat another actual geographical placeon a map, too: just by Great Bottom, WhiteSheet Hill, ST813351, Lat 51.115 (a mirror - of sorts). And the 'precious' gems of Lady and Goat? Well, I gave you Shenstone for Goat/Devil. Lady/Woman is just by Berkeley on the River Severn - a spot from which you might have been able to here the screams of Edward II re. "fundement" and "salamander". Berkeley indicates birch:
"Birch is associated with the element of water, is a tree of the sun and the planet Venus, and its Herbal Gender is feminine ... Birch is considered to be a Goddess tree, the symbol of summer ever-returning."
I want to post a special note of thanks here to George Firsoff, now, sadly, deceased. I corresponded extensively with George during his time in Stoke and he 'kept me honest' whilst keeping me keen. George's mathematical help - and his spirit and humour - were much-welcomed props. I miss them. Amongst other things, I note, George was the long, white-haired 'Druid' who tangled with English Heritage over access to Stonehenge at the Solstices. Bless all his surds and pseuds!
I parked this here but it's not exactly relevant to the above! 7s and 12s - notes:
Something that I noted years ago was a John Michell reference to the relationship between 7 and 12. I forget which way round, but apparently one is the other, esoterically. Thoughts were the Seed of Life - the 7 circles generate both 6-sided hexagon and 12-sided dodecagon (as the fitting of the Tree of Life can demonstrate - 7 disciples of 12 catch 153 fish seems pertinent and indicative of Sq Rt 3), another Square Root of 3 possibility in meaning 7/4 with 12/7 (where 3 + 4 = 7 and 3 X 4 = 12), a music scale of 7 notes (of 12) in an octave*, or something to do with the 12 zodiac signs/months and the 7 heavenly bodies, but Nigel Pennick touches on a possibility that not only fits to the 'ask' but also to the basic geometric building blocks of vesica/equilateral/square. I knew that basic church floorplan design was just an unbundled cube (six squares - and sometimes with snake or rose), but apparently two constructional techniques - Pennick nominates Freemasonry (he calls them "the two Masonic traditions) here - are ad triangulum and ad quadratum, threes and fours. Put another way, vesicas, equilaterals and squares. Pennick says the 3 and 4 combination of running both systems together generates a 12, of sorts: "effectively a twelve-fold symbolically associated with the zodiac". And 3 and 4 make 7 (and 12, of course ... 3 X 4). Here's his demonstration of a Glastonbury floorplan:
There are a number of things 'going on' here that we have met with already. You can easily make out the circles, equilaterals and squares - and possibly you can see the hexagons, both explicit and implicit. But there are also the implicit pentagons/ pentagram stars - we're looking at Vesica/Seed/Flower of Life geometry. And that means we're looking at "Isis" - in exactly the same way as on my Flower of Life/Tree of Life graphic, Isis twixt J and B and in the Wood-Campbell 'Star Union' from GENESET. Pennick actually superimposes one of these on the other to effect. For the second graphic and an excellent write-up go to www.isleofavalon.co.uk/history/pennick.html
I was aware of this author in the context of the 'thin' Templar (7-sided) Star he proposed existed in France, made of cathedral-sites, and also the Royston Cave/omphalos idea, which interested me because it was just by the Icknield/Ermine "Rosy Cross" (well, Roisia de Vere's, actually) - and Old Ways figure large in my study (in fact, Ermine is the only one - of the Big 4 - not immediately picked out by the geometry I explored:MOVING MENHIRS).John Michell and Chris Street (drawing on Michell) also demonstrate hexagonal maths in the context of a Glastonbury church, whilst one or more also show pentagonal, hexagonal, heptagram and dodecagram (7 and 12, note) geometry in the Stonehenge design.
A note re. 7 and 12: it could be said to be a way of coding 3-4-5, the most famous of the right-angled triangles, perhaps. 'Isis' gets to be feminine/horizontal/negative (gematria 1080),Osiris male/upright/positive (gematria 666) and Horus is the hypotenuse.7 and 12 is a fairly simple Square Root 3-alike (1.714 ... to 1.732...). Better, perhaps: Sq Root 3? Mean 7/4 and 12/7 - you get 194/112 - 1.7321.... 7 (4 + 3) and 12 (4 X 3) again ... Also 774(2) : 447(0) ...*. Note that 666/1080 i a fairly useful "phi" whilst added they are gematria 1746, agrain of mustard seed (from which sprang the tree of the universe), the parent number:
Another note: Gnostic texts (Nag Hammadi) tell of the 12 disciples of Jesus and 7 women followers. Then there's the 2 X 2 X 2 cube: 8 small cubes generating one larger one (so 9 in total). There are 24 facets of which 12 are interfaces - but, if you dismantle the large cube and line up the 8 then there will only be 7 interfaces.
Note (26-12-08, Morph, GHMB, re 7, 12 and cubes/dice/dies ... and thanks):
"... sacred cubes, as relative to the sacred objects (ladders/Milky Way/perfect ashlar/perfected initiate if later Masonic considerations are anything to go by). Of course, 2 cubes each numbered 1-6 have a sum value of 42 and an average value of 7.
This does of course harmonise 12 the number of Divine ordering with 7, the number of mysterious change .... or so tradition would have it."
Paul Ashworth
My notes (re REVELATION numbers): 3 1/2 (7/2) REV. 11, 9 and 12, 14.3 1/2 days is 84 hours (is 42 X 2) is 5040 minutes (and 504 is our 63 mile radius X 8 = in furlongs rather than miles) and 302400 secs. 42 months - REV. 13, 5 and 11, 2 - is 3 1/2 years. 42/3.5 = 12.. 1260 - REV. 11. 3 and 12, 6 - seems to tie in: 1260/3.5 = 360.n Horus child of Isis of 7 results from the 'coupling' of an Osiris of 4 with an Isis of Sq. Rt. 33. Sq. Rt. 3 alike 153 : 265 is 51 X 3 : 53 X 5. Whilst this 'stuff' (I call it "messin' with maths") fits to an equilateral/ hexagon (sided 3, generating a right-angled triangle hypotenuse 3 and one side 1.5) it so nearly/almost fits to decagons (as Michael Behrend points out in his Perpetual Choir study -he posits hypotenuse 5 plays side 1.5 or, more accurately, 3/2 - the rather grandly titled Institute of Geomantic Research and carried in the quarterly, PENDRAGON, in an article by Fred Stedman-Jones detailing Behrend's 10 CPC vertices and his - Behrend's - qualifications of John Michell's original dimensions). Rather thematically, too, we can use 4 and 7 (c/o Euclid 47) to generate a hypotenuse of Sq. Rt. 65, which is 5 X 13. Differently sided right-angled triangles seems to be thematically generative somewhat! 5 and 13 also figure with 13 equal sized spheres where one is central and the other12 surround it perfectly, each of the 12 touching 4 others (and 4 + 1 = 5).The idea is said, by some, to be redolent of the zodiac (+ centre) and other12s + 1 (Jesus, Arthur, Charlemagne ...).
*On the 7 note scale in a 12 note octave, I discussthis elsewhere as of fairlyrecentorigin.
In correspondence with me several years ago, Fred told me his own research into the CPC idea threw up a recurring 'fugitive stag' theme. For an explanation of this alchemical symbol (and others on this 1618 AD Emerald Tablet) go towww.alchemylab.com/smaragdina.htm
Of note to us here is the Merian placing of things: Fire and Air get to be left and daytime (our J pillar) and associated with the revenant phoenix; Water and Earth get to be right and night-time (our B pillar) and associated with the Aquila eagle:
The hexagram is said to symbolise alchemical salt - union of (male) Fire with (female) Water. The same idea obtains in Durer's Adam and Eve. Note that 'Adam' is to the right of 'Eve' - from their perspective.
15 is 3 5s - and some run these together - 555 - to generate a 'Sacred geometric pattern' consisting of pentagon/lady pentagram combo. with a larger goat pentagram between them. 555 is also termed 'master number' - but not by me!!! (555 "literally means "Highest Death" - http://www.whale.to/b/5_h.html - etc.). The Washington obelisk is 555' high (that's 6660").
You'll find the ideas with simple searches. My interest is that 666 and 555 are multiples of 37 (2 X, which is, quite literally, 'Jesus' - add up the letter values)! And I note the common misconception that the mirror (reciprocal) of 15 is 666 (it's 0.0667 to 4 dec. places) ... and that takes us neatly back to Tarot 15, the Devil card. 15 comprises 5 + 5 + 5 and 555 = 37 X 15. 37 is also the 5th 'lucky prime', the 1st 'irregular prime' and the 3rd 'unique prime', I read (Wikipedia). How can the third be unique?
A fascinating site carrying the kabalistic sun as 3-7-12 (22 - the Hebrew alphabet). Note implicit 3-4-5:
*Following the sides of a triangle/12 hour clock lines takes you into the 1 3 5 interplays possible: 3.15 is 15.15 (clockface), for instance, where 3 is 1.5 + 1.5 - 'Isis'? A
Note: (geoffss, 11-11-09). 666 is 151 + 515. The Grand Lodge of Freemasonry, Great Queen Street, London, in pretty much sited on Lat. 51.515 (to 3 dec. places).
*666 = 531 + 135, and 666/531 is very close to 360/7, the Virgin Latitude (where - on/by the River Severn) an octagon of 50.4 miles radius can be posited, atr least on a map. 504 is 351 + 153. All those 1s, 3s and 5s ...
Oh well! I find it posited that Roslin's Latitude is both 55 51.5 (?is it?) and related whilst 55 50 somehow ties to St. John. The Michell CPC 'Croft' site - Enderby, really! - sits on "St Johns" (Fosse), by the River Soar burial place of King Llyr (father of our topical Bran the Blessed who. like St. John was. notice, beheaded), and on no interesting Lat. whatsoever.The Longitude, however, appears to be circa 1 11 11. The site appears to be called Grove Park, by the King's Peace road, the Fosse Way (and B4114). There is a St John's Dayceremony annually nearby and the possibility of a Abbey site at Lubbesthorpe, also nearby. Older maps of the area (I've seen)seem to indicate it was all Abbey land once. Curiosity Note (geoffss, 05-12-08): Re Foundation = 12 (3 + 4 + 5 Pythagoras)
3 sq + 4 sq = 5 sq - and this is implicit in the High Priest breastplate,Jerusalem with its 3 vertical rows of 4. Ifyou take the order of birth of Jacob's 12 male children together with theorder of jewels listed in REVELATION 21, 19-20 (as against EXODUS 28, 17-21, thusstarting Benjamin (jasper) = 1 (and do this in the context of the REVELATION New Jerusalem gates/tribes), then the oddest thing happens:
Levi (3, 3 = 6) gets kicked into the centre whilst Joseph (5, 11 = 16)goes missing completely. Sons Ephraim and Manasseh arrive instead. We get 6 (Levi/centre)-7-8 (no 9) 10*-11-12 13-14-15 (no 16) 17-18-19.
*Assuming Ephraim and Manasseh are the 10 (5 + 5), then the "missing values" are 3 sq. and 4 sq .... possibly implying 5 sq (25)? Try (c/o PMac - and my thanks) adding 1st to last etc. - all = 25 (6 +19, 7 + 18 etc. etc. in 12 pairings)!.The missing values of 3 sq. and 4 sq add to 5 sq. which is both the area of a 5 X 5 square and the squared diagonal of a 3 X 4 (High Priest breastplate) rectangle (Euclid 47/Pythagoras 3-4-5 triangle).
Values:
1 Benjamin Jasper,2 Issachar Sapphire, 3 Levi Chalcedony,4 Judah Emerald, 5 Joseph Sardonyx, 6 Reuben Carnelian, 7 AsherChrysolite, 8 Zebulun Beryl, 9 Dan Topaz, 10 SimeonChrysoprase,11 Napthali Jacinth, 12 Gad Amethyst.
Birth order:Reuben (1), Simeon (2), Levi (3), Judah (4), Dan (5),Napthali (6), Gad (7), Asher (8), Issachar (9), Zebulun (10), Joseph (11),Benjamin (12).
Gateorder: East - Judah, Issachar, Zebulun. South - Reuben, Simeon, Gad. West - Benjamin, Manasseh*, Ephraim*. North - Dan, Asher, Napthali (with Levi in the middle).
(Of interest?9, 16 and 25 are the magic squares of Saturn, Jupiter and Mars. Note alsothat 24 elders round a throne = 25. Note too EXODUS gives a different order to REVELATION.)
The analysis above rests on a rather massive "might"*. This only workswith one version of what gem identifies what tribe - and there are many.See also Ezekiel 48, 30-34 for a different who has which gate. Note toothat Philo and Flavius both identified the 12 breastplate stones with thezodiac (apparently).
'G', the letter of 'God', the 'Great Architect', the 'Geometer', for G is the 7th letter -
The Square and Compass is aligned horizontally to revere the direction in which the Sun as well as the 'Sun behind the Sun' - the Star of Set, or Sirius which is also included in the layout as the White House is not only at the left side of the Compass, but it is at the bottom of the averse pentagram aligned with the North.
The Star Sirius is a binary star, and the lesser star - Sirius B - is depicted as the smaller star to the bottom left; 'The Pentagon'. Even the hieroglyph of Sirius contains the predominant elements of the architecture;
the Obelisk (Washington Monument), the 5 pointed star, and the Dome (The Capital Building).
11. Proverbios 25:11:MANZANA de oro con figuras de plata Es la palabra dicha como conviene.
The letter G symbol of freemasonry traces back to the Hebrew letter gimel and interestingly links to the serpent as well. It is said that the letter G also represents the ouroboros, the snake eating it’s tail which represents immortality/resurrection.
LA SERPIENTE QUE SE MUERDE LA COLA SIMBOLIZA A LA VIDA ETERNA Y AL LINAJE DE CRISTO Y MARIA MAGDALENA. ESE ES SU MENSAJE ESOTERICO. ESO EXPLICA LA RELACION CON LA MAQUINA DEL TIEMPO
Ecuaciones de Einstein
Las Ecuaciones de Einstein son el centro de la relatividad general. Proporcionan una formulación precisa, utilizando el lenguaje de las matemáticas, de la relación entre la geometría del espacio-tiempo y las propiedades de la materia.
Distancias correspondientes a 30 grados a diferencia de longitud, en diferentes latitudes, sobre la superficie de la tierra.
Estas ecuaciones se formulan utilizando el lenguaje de la geometría riemanniana, en la que las propiedades geométricas de un espacio (o espacio-tiempo) son descritas por una cantidad llamada métrica. La métrica codifica la información necesaria para calcular las nociones geométricas fundamentales de distancia y ángulo en un espacio curvo (o espacio-tiempo).
Una superficie esférica como la de la Tierra proporciona un ejemplo sencillo. La ubicación de cualquier punto de la superficie puede ser descrito por dos coordenadas geográficas: latitud y longitud. Sin embargo, a diferencia de las coordenadas cartesianas del plano, las diferencias de coordenadas no son lo mismo que las distancias en la superficie, tal y como se muestra en el diagrama de la derecha: para alguien en el ecuador, moverse hacia el Oeste por 30 grados de longitud (línea magenta) corresponde a un distancia de aproximadamente 3300 kilómetros; para alguien mucho más al norte, a una latitud de 55 grados, al moverse 30 grados de longitud hacia el oeste (línea azul) se cubre una distancia de sólo 1900 kilómetros. Las coordenadas, por lo tanto, no proporcionan suficiente información para describir la geometría de una superficie esférica o la geometría más complicada del espacio-tiempo: se necesita información adicional para convertir las diferencias de coordenadas a distancias reales. Este es, precisamente, la información codificada en la métrica: se trata de una función definida en cada punto de la superficie (o espacio, o espacio-tiempo) que describe hasta qué punto el espacio se curva o estira en el entorno de ese punto. Todas las demás cantidades que son de interés en la geometría, tales como la longitud de cada curva, o el ángulo en que dos curvas se encuentran, se puede calcular a partir de esta función métricas.[15]
La cantidad de curvatura que hay en cada punto de un espacio (o espacio-tiempo) determina la curvatura del espacio. Más precisamente, la función métrica y la rapidez con que cambia de un punto a otro se puede utilizar para definir una cantidad geométrica llamada Tensor de curvatura de Riemann, que describe exactamente la forma en que el espacio (o espacio-tiempo) es curva en cada punto . En la relatividad general, la métrica y el tensor de curvatura son las cantidades definidas en cada punto en espacio-tiempo. Además, el contenido de materia del espacio, como se ha indicado, define otra cantidad, el tensor energía-impulsoT, y el principio de que "el espacio-tiempo le dice a la materia cómo moverse, y la materia le dice al espacio-tiempo cómo curvarse", significa que estas cantidades deben estar relacionados de alguna manera. Einstein formuló esta relación usando el tensor de curvatura y la métrica para definir otra cantidad geométrica G, que ahora se conoce como el tensor de Einstein, que describe algunos aspectos de la forma en la que el espacio-tiempo se curva.La ecuación de Einstein entonces se establece que
es decir, hasta un constante múltiple, la cantidad G (que mide la curvatura) se equipara con la cantidad T (que mide el contenido de materia). Las constantes que participan en esta ecuación reflejan las diferentes teorías que se usaron para deducirlas: G es la Constante de gravitación universal que ya está presente en la gravedad de Newton;c es la velocidad de la luz, la clave constante de la relatividad especial, y π es una de las constantes básicas de la geometría. La aparición de π en la ecuación se asocia con la zona (4 π) de la unidad de materia, mientras que las constantes c y G se necesitan para convertir la cantidad T (que tiene unidad físicas) en unidades puramente geométricas.
Esta ecuación es referida a menudo en plural como ecuaciones de Einstein , puesto que las cantidades G y T son determinados por un conjunto de diez funciones de las coordenadas del espacio, y las ecuaciones equiparan cada una de estas funciones componentes. Sin embargo, a causa de la libertad de cambiar las cuatro coordenadas en las que las ecuaciones se expresan, en realidad hay sólo seis ecuaciones físicas que deben cumplirse en cada punto en espacio.[16] describe una geometría particular de el espacio y el tiempo. Por ejemplo, la primera solución que se encontró, apenas un mes después de que Einstein publicara su teoría, fue la métrica de Schwarzschild, que describe la geometría esférica alrededor de una única masa no giratoria, como una estrella o un agujero negro, mientras que la solución de Kerr describe un agujero negro giratorio. Otras soluciones pueden describir una onda gravitacional o en el caso de la más compleja solución de la Métrica de Friedman-Lemaître-Robertson-Walker, la expansión del universo. La solución más sencilla es por supuesto el espacio-tiempo plano o espacio de Minkowski, que es el espacio-tiempo descrito por la relatividad especial.[17]
NOTABLE LA RELACION DE G, CON EL NUMERO PI=3.1416..
PYRAMID / MARY
MARY MAGDALENE DAY=22/7 =3.1416 =EXPERIMENTO FILADELFIA (MAQUINA DEL TIEMPO= "AGUJERO DE GUSANO")
LA MISMA SANTA CENA ES UNA REFERENCIA A LA "MAQUINA DEL TIEMPO" EN EL MARCO A SU RELACION CON LAS 12 HORAS DEL RELOJ, 12 CONSTELACIONES DEL ZODIACO, 12 CICLOS LUNARES, 12 CICLOS PRECESIONALES, ETC,ETC
De izquierda a derecha: Galileo Galilei, Marie Curie, J. Robert Oppenheimer, Isaac Newton, Louis Pasteur, Stephen Hawking, Albert Einstein, Carl Sagan, Thomas Edison, Aristoteles, Neil deGrasse Tyson, Richard Dawkins y Charles Darwin.
EL ORO REFINADO ES EL GRIAL MISMO
714. Mateo 23:17: ¡Insensatos y ciegos! porque ¿cuál es mayor, el ORO, o el templo que santifica al ORO?
ISRAEL = JACOB= VENCEDOR= ESTRELLA DE DAVID O 6 PUNTAS= RELOJ
ISRAEL = ISIS - RA- ELOHIM
IS-RA-EL =(OJO DE RA= OJO DE RA-QUEL) = NACIMIENTO DE BENJAMIN =LOBO=PERRO= CHACAL = CAN MAYOR = SIRIO = GOD= DOG = GOLD (MANZANA DE ORO) =7-4 =4-7 (CUARTO MANDAMIENTO CON REFERENCIA AL SEPTIMO DIA)
EL MISMO SIGNO PESO, QUE TIENE REFERENCIA A LA SERPIENTE O LETRA S, TIENE NEXO CON EL SABADO, OSEA EL SEPTIMO DIA.
EL UNICO SABADO QUE RESPONDE EL PATRON 4-7 (CUATRO FASES DE SIETE DIAS) ES EL LUNAR, CODIFICADO EN LA MISMA SANTA CENA, DISEÑADA EN FUNCION A LAS 12 TRIBUS DE ISRAEL, EN FUNCION A SU UBICACION ALREDEDOR DEL TABERNACULO. (ESTE- OESTE- NORTE -SUR)
LA MISMA SANTA CENA ES UNA REFERENCIA A LA "MAQUINA DEL TIEMPO" EN EL MARCO A SU RELACION CON LAS 12 HORAS DEL RELOJ, 12 CONSTELACIONES DEL ZODIACO, 12 CICLOS LUNARES, 12 CICLOS PRECESIONALES, ETC,ETC
De izquierda a derecha: Galileo Galilei, Marie Curie, J. Robert Oppenheimer, Isaac Newton, Louis Pasteur, Stephen Hawking, Albert Einstein, Carl Sagan, Thomas Edison, Aristoteles, Neil deGrasse Tyson, Richard Dawkins y Charles Darwin.
1. Génesis 9:18: Y los hijos de Noé que salieron del arca fueron Sem, Cam y Jafet; y Cam es el padre de Canaán.
2. Génesis 9:22: Y Cam, padre de Canaán, vio la desnudez de su padre, y lo dijo a sus dos hermanos que estaban afuera.
3. Génesis 9:25: y dijo: Maldito sea Canaán; Siervo de siervos será a sus hermanos.
4. Génesis 9:26: Dijo más: Bendito por Jehová mi Dios sea Sem, Y sea Canaán su siervo.
5. Génesis 9:27: Engrandezca Dios a Jafet, Y habite en las tiendas de Sem, Y sea Canaán su siervo.
6. Génesis 10:6: Los hijos de Cam: Cus, Mizraim, Fut y Canaán.
7. Génesis 10:15: Y Canaán engendró a Sidón su primogénito, a Het,
8. Génesis 11:31: Y tomó Taré a Abram su hijo, y a Lot hijo de Harán, hijo de su hijo, y a Sarai su nuera, mujer de Abram su hijo, y salió con ellos de Ur de los caldeos, para ir a la tierra de Canaán; y vinieron hasta Harán, y se quedaron allí.
9. Génesis 12:5: Tomó, pues, Abram a Sarai su mujer, y a Lot hijo de su hermano, y todos sus bienes que habían ganado y las personas que habían adquirido en Harán, y salieron para ir a tierra de Canaán; y a tierra de Canaán llegaron.
10. Génesis 13:12: Abram acampó en la tierra de Canaán, en tanto que Lot habitó en las ciudades de la llanura, y fue poniendo sus tiendas hasta Sodoma.
11. Génesis 16:3: Y Sarai mujer de Abram tomó a Agar su sierva egipcia, al cabo de diez años que había habitado Abram en la tierra de Canaán, y la dio por mujer a Abram su marido.
12. Génesis 17:8: Y te daré a ti, y a tu descendencia después de ti, la tierra en que moras, toda la tierra de Canaán en heredad perpetua; y seré el Dios de ellos.
13. Génesis 23:2: Y murió Sara en Quiriat-arba, que es Hebrón, en la tierra de Canaán; y vino Abraham a hacer duelo por Sara, y a llorarla.
14. Génesis 23:19: Después de esto sepultó Abraham a Sara su mujer en la cueva de la heredad de Macpela al oriente de Mamre, que es Hebrón, en la tierra de Canaán.
15. Génesis 28:1: Entonces Isaac llamó a Jacob, y lo bendijo, y le mandó diciendo: No tomes mujer de las hijas de Canaán.
16. Génesis 28:6: Y vio Esaú cómo Isaac había bendecido a Jacob, y le había enviado a Padan-aram, para tomar para sí mujer de allí; y que cuando le bendijo, le había mandado diciendo: No tomarás mujer de las hijas de Canaán;
17. Génesis 28:8: Vio asimismo Esaú que las hijas de Canaán parecían mal a Isaac su padre;
18. Génesis 31:18: y puso en camino todo su ganado, y todo cuanto había adquirido, el ganado de su ganancia que había obtenido en Padan-aram, para volverse a Isaac su padre en la tierra de Canaán.
19. Génesis 33:18: Después Jacob llegó sano y salvo a la ciudad de Siquem, que está en la tierra de Canaán, cuando venía de Padan-aram; y acampó delante de la ciudad.
20. Génesis 35:6: Y llegó Jacob a Luz, que está en tierra de Canaán (esta es Bet-el), él y todo el pueblo que con él estaba.
1. Se juntaron a Jesús los fariseos, y algunos de los escribas, que habían venido de Jerusalén;
2. los cuales, viendo a algunos de los discípulos de Jesús comer pan con manos inmundas, esto es, no lavadas, los condenaban.
3. Porque los fariseos y todos los judíos, aferrándose a la tradición de los ancianos, si muchas veces no se lavan las manos, no comen.
4. Y volviendo de la plaza, si no se lavan, no comen. Y otras muchas cosas hay que tomaron para guardar, como los lavamientos de los vasos de beber, y de los jarros, y de los utensilios de metal, y de los lechos.
5. Le preguntaron, pues, los fariseos y los escribas: ¿Por qué tus discípulos no andan conforme a la tradición de los ancianos, sino que comen pan con manos inmundas?
6. Respondiendo él, les dijo: Hipócritas, bien profetizó de vosotros Isaías, como está escrito: Este pueblo de labios me honra, Mas su corazón está lejos de mí.
7. Pues en vano me honran, Enseñando como doctrinas mandamientos de hombres.
8. Porque dejando el mandamiento de Dios, os aferráis a la tradición de los hombres: los lavamientos de los jarros y de los vasos de beber; y hacéis otras muchas cosas semejantes.
9. Les decía también: Bien invalidáis el mandamiento de Dios para guardar vuestra tradición.
10. Porque Moisés dijo: Honra a tu padre y a tu madre; y: El que maldiga al padre o a la madre, muera irremisiblemente. (EL QUINTO MANDAMIENTO, QUE TIENE RELACION CON LA TIERRA (CANAAN), ES EL NEXO CON LA ESTRELLA DE 5 PUNTAS CON SIRIO)
11. Pero vosotros decís: Basta que diga un hombre al padre o a la madre: Es Corbán (que quiere decir, mi ofrenda a Dios) todo aquello con que pudiera ayudarte,
12. y no le dejáis hacer más por su padre o por su madre,
13. invalidando la palabra de Dios con vuestra tradición que habéis transmitido. Y muchas cosas hacéis semejantes a estas.
14. Y llamando a sí a toda la multitud, les dijo: Oídme todos, y entended:
15. Nada hay fuera del hombre que entre en él, que le pueda contaminar; pero lo que sale de él, eso es lo que contamina al hombre.
16. Si alguno tiene oídos para oír, oiga.
17. Cuando se alejó de la multitud y entró en casa, le preguntaron sus discípulos sobre la parábola.
18. El les dijo: ¿También vosotros estáis así sin entendimiento? ¿No entendéis que todo lo de fuera que entra en el hombre, no le puede contaminar,
19. porque no entra en su corazón, sino en el vientre, y sale a la letrina? Esto decía, haciendo limpios todos los alimentos.
20. Pero decía, que lo que del hombre sale, eso contamina al hombre.
21. Porque de dentro, del corazón de los hombres, salen los malos pensamientos, los adulterios, las fornicaciones, los homicidios,
22. los hurtos, las avaricias, las maldades, el engaño, la lascivia, la envidia, la maledicencia, la soberbia, la insensatez.
23. Todas estas maldades de dentro salen, y contaminan al hombre.
24. Levantándose de allí, se fue a la región de Tiro y de Sidón; y entrando en una casa, no quiso que nadie lo supiese; pero no pudo esconderse.
25. Porque una mujer, cuya hija tenía un espíritu inmundo, luego que oyó de él, vino y se postró a sus pies.
26. La mujer era griega, y sirofenicia de nación; y le rogaba que echase fuera de su hija al demonio.
27. Pero Jesús le dijo: Deja primero que se sacien los hijos, porque no está bien tomar el pan de los hijos y echarlo a los perrillos.
28. Respondió ella y le dijo: Sí, Señor; pero aun los perrillos, debajo de la mesa, comen de las migajas de los hijos.
29. Entonces le dijo: Por esta palabra, ve; el demonio ha salido de tu hija.
30. Y cuando llegó ella a su casa, halló que el demonio había salido, y a la hija acostada en la cama.
31. Volviendo a salir de la región de Tiro, vino por Sidón al mar de Galilea, pasando por la región de Decápolis.
32. Y le trajeron un sordo y tartamudo, y le rogaron que le pusiera la mano encima.
33. Y tomándole aparte de la gente, metió los dedos en las orejas de él, y escupiendo, tocó su lengua;
34. y levantando los ojos al cielo, gimió, y le dijo: Efata, es decir: Sé abierto.
35. Al momento fueron abiertos sus oídos, y se desató la ligadura de su lengua, y hablaba bien.
36. Y les mandó que no lo dijesen a nadie; pero cuanto más les mandaba, tanto más y más lo divulgaban.
37. Y en gran manera se maravillaban, diciendo: bien lo ha hecho todo; hace a los sordos oír, y a los mudos hablar.
'G', the letter of 'God', the 'Great Architect', the 'Geometer', for G is the 7th letter -
11. Proverbios 25:11:MANZANA de oro con figuras de plata Es la palabra dicha como conviene.
1. Job 9:9: El hizo la Osa, el Orión y las Pléyades, Y los lugares secretos del sur;
2. Job 38:31: ¿Podrás tú atar los lazos de las Pléyades, O desatarás las ligaduras de Orión?
3. Amós 5:8: buscad al que hace las Pléyades y el Orión, y vuelve las tinieblas en mañana, y hace oscurecer el día como noche; el que llama a las aguas del mar, y las derrama sobre la faz de la tierra; Jehová es su nombre;
1. Jueces 3:25: Y habiendo esperado hasta estar confusos, porque él no abría las puertas de la sala, tomaron la LLAVE y abrieron; y he aquí su señor caído en tierra, muerto.
2. Isaías 22:22: Y pondré la LLAVE de la casa de David sobre su hombro; y abrirá, y nadie cerrará; cerrará, y nadie abrirá.
3. Mateo 16:19: Y a ti te daré las LLAVEs del reino de los cielos; y todo lo que atares en la tierra será atado en los cielos; y todo lo que desatares en la tierra será desatado en los cielos.
4. Lucas 11:52: ¡Ay de vosotros, intérpretes de la ley! porque habéis quitado la LLAVE de la ciencia; vosotros mismos no entrasteis, y a los que entraban se lo impedisteis.
5. Apocalipsis 1:18: y el que vivo, y estuve muerto; mas he aquí que vivo por los siglos de los siglos, amén. Y tengo las LLAVEs de la muerte y del Hades.
6. Apocalipsis 3:7: Escribe al ángel de la iglesia en Filadelfia: Esto dice el Santo, el Verdadero, el que tiene la LLAVE de David, el que abre y ninguno cierra, y cierra y ninguno abre:
7. Apocalipsis 9:1: El quinto ángel tocó la trompeta, y vi una estrella que cayó del cielo a la tierra; y se le dio la LLAVE del pozo del abismo.
8. Apocalipsis 20:1: Vi a un ángel que descendía del cielo, con la LLAVE del abismo, y una gran cadena en la mano.
INICIACIÓN A LOS NÚMEROS DE LA ARQUITECTURA O DE COMO DARLE FORMA A UN EDIFICIO
Los números pueden estar explicados matemáticamente en la “red” pero el problema que plantea el conocimiento de la arquitectura es: ¿cómo se le da forma con esos números a un edificio?. En arquitectura los números operan a partir de los polígonos estrellados formando concatenaciones, tal y como a continuación vamos a describir.
NÚMERO DE ORO - PENTÁGONO
El número de oro viene dado por la solución a la ecuación de segundo grado x + x² = 1 x = 1+√5 /2 = 1,618033989 Propiedades 1/ 1,618 = 0,618 1,618... x 1,618... = 2,618... Dado una circunferencia de radio 1 el lado del decágono inscrito en él es 0,618... Dado un pentágono de lado 1, las diagonales de ese pentágono = 1,618... La técnica con la que opera la arquitectura es la de las concatenaciones. Una de ellas, la más usual, es la que presentamos en el dibujo. Si la circunferencia en color azul tiene R=1 el radio de la roja es R= 2,618, correspondiente a la que presentamos en “El vitruvio” deLeonardo da Vinci en la portada de este trabajo.
Se aplicará en la restitución de una tabla de F. Brunelleschi Nº 6.
NÚMERO DE PLATA - EL OCTÓGONO
Así como el número de oro está asociado a la √5 el número de plata está asociado a √2 y presenta una serie de propiedades similares a las del número de oro. √2 = 1,414213562 tg. 22,5º = 0,414213562 tg.67,5º = 2,414213562 1/2,4142... = 0,4142... 2,4142... x 1,4142... = 3,4142... Observa nuevamente la concatenación, esta vez con el octógono, de la circunferencia en color azul sobre la de color rojo. Si el radio de la circunferencia azul es 1 la de color rojo es 2,4142.... Si el radio de la circunferencia azul es 0,4142... la de rojo es 1. Aquí tenéis un ejemplo.
Se aplicará en la Rix House de J. Soane Nº 3.
NÚMERO DE PLATINO - EL HEXÁGONO
De igual forma que el número de oro está relacionado con la √5 y el de plata con la √2, el de platino lo va a estar con la √3 √3 = tg.60º = 1,732050808 1,732... x 2,732... = 4,732... Combinación, esta, muy utilizada por Andrea Palladio. Observa la concatenación de la circunferencia azul sobre la de rojo, a través del hexágono, directamente a la circunferencia azul. Si el radio de la circunferencia color azul es 1 el de la circunferencia en color rojo es 2 y el lado del triángulo inscrito es 2 x 1,732... Este polígono es el más prolífico en la historia de arquitectura como vamos a verlo en los ejercicios. Aquí tenéis un ejemplo.
Se aplicará al resto de los trabajos Nº 1 - 2 - 4 y 5.
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Primer 
"Geometry has two great treasures; one is the Theorem of
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t, or duat, is the ancient Egyptian symbol for the underworld or place of the soul's transformation. However, there are considerable differences of opinion amongst modern scholars as to the meaning assigned to the duat by the ancient Egyptians and the issue is by no means a settled one."
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