So below you will find some interesting information. If you don't find it interesting and think the entry is boring well then, it speaks to your ignorance. Those who don't understand often get frustrated, bored and defensive when challenged with new and higher-intelligent based information.
I've taken information from my life-long studies and will be imparting it unto you. Please use it wisely.
The Grail Geometry used to compose paintings is explained:
This diagram comes from an ancient proof of Plato's Theorem:
STEP 2. A circle is inscribed within the smaller square so as to be tangent to all sides.
This diagram is the Templar Variation of Plato's Theorem:
The TILTED TRIANGLE:
STEP 3. The all-important equilateral triangle (all sides equal, all angles equaling 60 degrees) A—V1—V2 is drawn with all sides tangent to the circle. This is the so-called “Tilted Triangle” that one searches for among the painted features in a composition. The letters J and M identify the fact that this triangle is “tilted” downwards 15 degrees from the horizontal line AB. The point A is often called “The Northwest Point” when the Grail Geometry, hidden a painting, is transferred to the landscape at the proper scale and in registration with certain predetermined permanent landmarks on the map
The TILTED SQUARE:
STEP 4. Using the top side of the triangle A—V1--V2, the "Tilted Square" AMNO is drawn. This square is important, because in some cases, the artist includes a symbolic reference to a crypt, or burial chamber. The location of a symbolic burial site is indicated at the intersection of the diagonals of the tilted square. Note how diagonals AN and MO intersect at the point designated as PX – or “X marks the Spot”. This is the basic Grail Geometry that emerged in the 13th century in The Templar Map of Jerusalem (now in the Royal Library, The Hague)
Step 5. To the original tilted triangle A—V1—V2 is added a second equilateral triangle VH1—VH2—VH3. This makes a regular hexagram – an important feature of the Grail Geometry. This geometric pattern remained secret since the 13th century until it was divulged in the 20th.
Note that at “V1”, the lower vertex of the first tilted triangle, the angles 75, 60, and 45 degrees are shown. These angles, made with the horizontal base line of the pattern, are the sine qua non of the Grail Geometry. If these angles are discovered (as shown) in a painting, it is a sure sign that the artist knew and employed this secret geometry.
Vermeer was devoted to using the hexagram as a compositional guide. In some paintings he used two and even three hexagrams to achieve the effect he wished.
Step 6. A grid has been superimposed on the geometric pattern to show that J falls at a point such that the line segment B-J is equal to line segments A-E and E-B. This fact is very useful when trying to discover how the artist laid out his work – if, indeed, he employed the Grail Geometry, as did Vermeer in at least nine of his paintings.
In the painting “Lady Standing at the Virginals”, Vermeer employed the full 16 square grid and two hexagrams to achieve a harmonious composition. His work has been called “sphinx--like”, because its harmony derives from the riddle of a hidden geometric skeleton.
The question as to why Vermeer employed this complicated pattern is often asked. The short answer is that many artists believe that basing their compositions on geometric figures and patterns lends a harmony and structure to their work that is at once pleasing, but at the same time strangely captivating.
This writer is of the opinion that, since Vermeer knew and used a then secret geometric formula -- secret in the opinion of sources believed as reliable by this writer -- he must have been taught it in secret. Therefore, Vermeer must have been at least apprenticed to -- and possibly might even have been a member of -- the secret group or society that preserved this iconic pattern. Many such groups existed in the 17th century. Two important secret societies were “The Priory of Sion -- Prieure de Sion” and "The ILLUMINATI -- Los ALUMBRADOS". 20th and 21st century non-fiction and fictional writings ( for example, the best selling novels -- in 2003 -- "The Da Vinci Code"; and -- in 2000 -- "Angels and Demons" ) refer to the above-mentioned secret societies as historical fact. A search of the World Wide Web will yield some fascinating information about these and many other secret societies, in addition to their connection to The Knights Templar and the Freemasons among other well-known ancient and contemporary organizations.
Admittedly, there is a tinge of the sinister in all of this. Consider that Vermeer's wife is said to have lamented after his untimely death at age forty-three -- (1632-1675) -- only 43 years old at death! (Paraphrasing): "One day he was walking around healthy and happy -- the next day -- dead!" Make of this what you will . . . For my own part, I suspect foul play. Vermeer's haunting images presented a clear and present danger to many of his contemporaries in those perilous times.
From the book "VERMEER'S RIDDLE REVEALED" by Robert A diCurcio, 2001 ISBN 0917358139
Note -- Many other artists, some before Vermeer (1632-1675) and some after him, employed exactly the same Grail Geometry (GG) in some of their paintings. At this writing I have personally (and uniquely -- as far as I am aware) discovered the GG in "St. Peter" by El Greco (1541-1614); "Las Meninas" by Velazquez (1599-1660); "Bullfight" by Goya (1746-1828); "Virgin of the Rocks" (Paris 1483-86 and London 1503-06 versions) and "The Mona Lisa" by Leonardo da Vinci (1452-1519); "Sposalizio" by Raphael (1483-1520) . . .
These, and my latest Vermeer analyses, may be found at the "Spider Web" button on the left of these website pages. What other conclusion can possibly be drawn, but that this GG -- then secret and forbidden by "the powers that existed then" -- was passed down from master to apprentice from its inception with the Templar Map of Jerusalem of the 13th Century (The Royal Library, The Hague)?
Several original investigators, other than myself, have identified this type of tilted hexagram, tilted square geometry in the work of many other artists: e.g. Rene I, Duke of Anjou -- King of Naples, Sicily and Jerusalem [!] (1409-1480, "La Fontaine de Fortune"); Sir Anthony Van Dyck (1599-1641, "Lord George Stuart"); Nicolas Poussin (1594-1665, "Et In Arcadia Ego I & II"); David Teniers The Younger (1610-1690, "St. Antony and St. Paul") -- and in other works, some recently discovered -- some yet to be discovered. RAdiC 12/15/2003.
The Grail Geometry is a hexagonal geometry -- involving the hexagram (6--pointed star -- "Seal of Solomon" -- "Star of David") and the equilateral triangle and the multiples and divisors of the associated hexagram angle of sixty (60) degrees; -- as opposed to the pentagonal geometry -- involving the pentagram (the 5--pointed star of, for example, "Vitruvian Man") and it involves the "divine proportion" (other names include "golden section" and "golden ratio" and the Greek letter PHI for the ratio 1.618 to 1) and the multiples and the divisors of the associated pentagram angle of seventy-two (72) degrees. The paintings I have investigated are composed according to the hexagram (two equilateral triangles superimposed), and I find no evidence of the use of pentagonal geometry or the "golden section" in those paintings.
But, of course, some artists have used the PHI ratio and its proportions in their compositions. N. Poussin, (French, 1594-1665) may have used it in his famous painting "Et In Arcadia Ego, II" -- in addition to his obvious emphasis of the Grail Geometry. I will recommend to the interested viewer Chapter 7 of the recent (2002) book "The Golden Ratio" by Mario Livio. Livio seems to know nothing of the Grail Geometry -- but his seventh chapter does make the argument that serious artists have often attempted to perfect their compositions by basing them on geometric proportions, and a few have used the "golden ratio". But he is quite blunt in his debunking the contention that the use of the "golden ratio" is as widespread in art and esthetics as commonly imagined, however. RAdiC 01/21/2004.
Congrats - my faithful followers for trudging through that bit of information: if you made it through, please post an insight and incorporate the secret word "Flemmish"
So - you may be thinking to yourself: How is this relevant? Well - here is the answer:
J. Vermeer "The Artist In His Studio"
or "The Allegory of Painting"
This is one of the most beloved of Vermeer’s paintings. During his lifetime he kept it close to himself, using it to exhibit his prodigious capabilities. This painting, like others, is full of evidence of his use of the Grail Geometry to guide the composition. On a limited platform such as a website only a few of the features coinciding with the Grail Geometry can be exhibited. The interested Vermeer enthusiast is referred to Robert A. diCurcio’s book “Vermeer’s Riddle Revealed”, AETERNIUM Publishing, 2001, ISBN 0917358139 for an in-depth treatment.
The artist represented here is held to be Vermeer himself. Look at the trumpet or trombone in the hand of “Clio”, the Muse of History. The trumpet is symbolic of fame – fame for the artist who brings fame to his birthplace of Delft, Holland.
Look at the "maul stick" used by the painter to steady his hand. The orange tip of the maul stick and the ferrule on the trumpet (just to the right of her finger tips) play an important role in establishing the geometry upon which this masterpiece is based. See below.
Vermeer divided this painting into quarters:
A line drawn from the orange tip of the artist's maul stick through the ferrule on Clio's trumpet divides the image exactly in half horizontally. A vertical line drawn from the corner of the chair divides the image exactly in half vertically. Note how the figure of the female model is positioned with respect to these two lines. At this juncture we are encouraged to look for more geometric guidelines -- perhaps to find once more the Grail Geometry. See STEP 1 below. (But let's not forget the artist's brilliant orange stockings -- might this favorite color of Vermeer's have something to do with the House of Orange that ruled Holland in Vermeer's day?)
STEP 1. TROMBONE LINE.
STEP 1. The obvious place to draw an exploratory line is along the trombone, which we do from 1 (the arrow pointing to the beginning) slanting up to 2, an inside corner of the easel. Along the way, this line hits 3, where Vermeer painted the corner of Clio's collar, and 4, where he placed the intersection of the artist's beret with his hair. This could be coincidence -- but after observing how Vermeer placed certain features to divide this painting in exactly equal quarters (see above) it's likely we'll find a Tilted Triangle, so we'll proceed to search for that in the next steps below.
STEP 2. The TILTED TRIANGLE.
STEP 2. Building on STEP 1, we try an exploratory line (2--5--A) from 2 up to the left to point A -- so as to be tangent to the cartouche at 5 on the map. (If you're wondering how I know to do this right away -- let me say right away -- that I spent weeks doing trial-and-error lines before arriving at STEP 2 as I shall present it -- sparing you from going through all that!) Note that Vermeer has painted a bright area at A -- bright where there's no reason for brightness -- except that it's where his layout sheet called for it. Look closely and you'll see a faint, elongated, and anomalous "V" on the drapery at the apex marked A. (What did he do that for?) Now another line starting at A and drawn down through 1 (where we began this -- see above) turns out to make an exact 60 degree angle with line 2--5--A ! We have the makings of our equilateral Tilted Triangle -- lacking now just one more line to complete it. See below.
STEP 2 (continued). The line that completes our triangle is drawn from 2 at the required angle of 60 degrees to line 2--5--A. We hope that this line will be confirmed -- and we are not disappointed. This third side of the triangle goes through 6 on the edge of the artist's sleeve. And the significance of 6? It's exactly half way -- a line from A to 6 splits the triangle exactly in half! So we label our Tilted Triangle A--V1--V2 as has been done in the Grail Geometry Section. (Please go to this section to refresh your memory, if need be.)
As a check, we draw another bisecting line from 5 down through vertex V1 and are gratified to see it hit a decorative upholstery tack on the chair at 7! Note the exact center of the Tilted Triangle -- Clio's chin was painted just vertically above it! Look at the highlights on the blue garment under Clio's book -- the pattern is precisely guided by the 5--V1 line! All doubt is removed by now -- Vermeer used the Grail Geometry on his greatest masterpiece!
STEP 3. The TILTED SQUARE.
STEP 3. Having established the equilateral Tilted Triangle in this painting, we may follow the rules (see the Grail Geometry section) to readily draw the associated Tilted Square to see whether Vermeer has placed any features according to that figure. Yes, we note that the corner M falls on the right edge of the map -- or more properly: Vermeer painted the right edge of the map to coincide with the top right-hand corner of the Tilted Squareof his layout. (more below . . .)
STEP 3 (continued). The artist's right knee is guided by the side M--N. But the diagonals A--N and M--O tell the story: their intersection PX is exactly on the gutter of the open book on the table! The orange tip of the maul stick has been painted at Q -- right on Diagonal M--O! A line of black tiles has been painted along the line of diagonal A--N -- and the last of those tiles exits the bottom edge of the image at R, where the diagonal A--N intersects that bottom edge.
The intersection point of the diagonals A--N and M--O is the objective of the whole exercise. It is hard to say exactly what symbolism Vermeer had in mind for the 'X Marks the Spot' , which falls on the open book on the table. Since experts contend that the female model represents Clio, the Muse of History, and since Vermeer painted Clio looking down at that open book, we may speculate that his message is that the artist was making history by painting masterpieces that would bring credit to his native land -- and fame for himself. Note that he is shown at work on the crown of laurel leaves, symbolic of victory and fame. Holland at the time had emerged victorious in a struggle with Spain. This could well have been in Vermeer's mind -- and satisfactory it must have been to him, even though this and many other of his riddles would have to wait for centuries to be revealed.
STEP 4. The HEXAGRAM.
STEP 4. Going back to STEP 2 and the Tilted Triangle A--V1--V2, we add a second equilateral triangle VH1--VH2--VH3 to form a regular hexagram. The obvious question -- did Vermeer lay out this hexagram on his canvas first and then paint features to fall on it and be guided by it? Our answer -- yes -- we have already confirmed triangle A--V1--V2. But what about the rest of the Hexagram -- triangle VH1--VH2--VH3? Yes, again -- consider confirmations 1, 2, 3, and 4 to begin with -- see below.
STEP 4 (continued). Confirmations: 1 -- the corner of the book painted at line VH1--VH2; 2 -- the left edge of the artist's long hair painted on line VH2--VH3; 3 -- the rectangular cartouche on the map painted on line VH3--VH1; 4 -- the edge of the hanging drapery painted to coincide with the intersection of lines A--VH2 and VH3--VH1. Note how the top edge of the map is painted to fall precisely on the apex VH3! Note also how the extension of line A--VH2 arrives exactly at the lower right corner of the image, suggesting strongly that Vermeer established this corner of his canvas on the line! No coincidence could explain all of this -- Vermeer used the Tilted Triangle, The Tilted Square, and this Hexagram -- and yet another hexagram! See below.
STEP 5. Another HEXAGRAM!
STEP 5. This hexagram A-B-C--D-E-F is bigger than the previous one (A-V1-V2--VH1-VH2-VH3) identified in STEP 4. This one (see below) is governed by the slant of the maul stick, line C-1-4-B.
(It is one thing to draw lines on Vermeer's work -- but yet another to contemplate the preparation and planning that must have gone into Vermeer's achievement of this geometric tour de force.)
STEP 5 (continued). As for confirmations, four of several are circled above: Vermeer painted 1, the orange tip of the maul stick on line B--C, the bottom side of the large tilted triangle A-B-C; he painted 2, a strong confirmation, the vertical line on the map on the intersection of lines A-C and D-E; he painted 3, the corner of the table, on line B-E, a diagonal of the hexagram. Note that 4 is also a comparatively strong confirmation, being the edge the model's gown, painted on the intersection of the two lines B--C and D--F.
The edified observer can probably identify a few more features whose positioning was guided by the lines, nodes, and angles of this larger hexagram. For example, look at E, the apex of the hexagram. Does it not appear that Vermeer positioned the center of the chandelier precisely there? Look at line A-B. Does it not appear that the artist positioned on that line the edge where the drapery covers the trombone or trumpet? Follow the lines and the circle -- and you'll be struck by how strictly this composition is adjusted to this geometric pattern (as well as to all the other ones discussed above).
STEP 6. MORE EXPLORATORY ANALYSIS.
STEP 6. Vermeer went beyond the Grail Geometry in this painting, but first let's refer back to STEP 4 and the first hexagram. I have exhibited it in dashed lines (below) and labeled the relevant diagonal V1--VH3 as was done in STEP 4. I have extended this diagonal upwards, and I find that Vermeer painted 2, the top part of the chandelier, exactly on the diagonal! (STEP 6 continued below...)
STEP 6 (continued). Extending diagonal V1--VH3 downward, I find that Vermeer painted 3, a corner of the chair, on that line. The back of the chair is emphasized by line 3--5; while the seat of the chair is emphasized by line 3--4 , which I've terminated exactly at the corner of the black tile -- where Vermeer painted that feature.
Beyond the usual Grail Geometry, Vermeer arranged the position and angle of the artist's easel supports along the lines X--Y and Y--Z (above). The lower two of the four small white arrows (above) pointing to the easel lines X--Y and Y--Z call attention to more confirming intersections -- one at the top of the beret and the other at the top of the artist's canvas. (I have used the top two small white arrows above to emphasize the slant of both the easel supports.) Both points X and Z call attention to the fact that the artist positioned the easel according to the tile pattern (or vice-versa) on the floor.
Note that Y, the apex of the angle X-Y-Z falls almost exactly on the top of the map. I have no doublt that Vermeer intended it that way. After about 350 years, this canvas, like all the others, must have distorted at least slightly. Moreover, we have the distortions of photography and the scanning of the image into the computer. Consequently, we must be judicious and allow a bit of leeway with these confirmations, accepting "very close" in some cases where it is obvious that this is justified.
Vermeer did not need to use geometry to compose a masterpiece. In some of his paintings, I find no evidence of a geometric basis. But in this one, only a die-hard skeptic would question the use of a geometric pattern here -- the Grail Geometry is without question in evidence in this masterpiece of masterpieces.
Since this Grail Geometry was not only still secret in Vermeer's time (being divulged by publications only in the latter half of the 20th century) -- it was also considered heretical at that time by the Church. For Vermeer to have known it and used it is a significant revelation concerning his hitherto murky apprenticeship. He was clearly instructed by a secret society -- most probably The Priory of Sion.
Furthermore this sheds some light on, and raises questions about his supposed adherence to the Catholicism that he, a Protestant, embraced on marrying a wealthy Catholc girl. They did raise their many children as Catholics. Vermeer's Delft, Holland, was a 17th century community very much riven by relgious differences -- yet it was a progressive city whose shining lights were on the cutting edge of the technologies of the times: cartography, optics, instrument-making, and tile-making to name a few famous specialties -- not to mention marvelous masterpieces of Dutch genre painting by Delft's most famous denizen -- Johannis Reynierszoon Vermeer.