STEP 2. Tilted Triangle and Hexagram

STEP 2 of 3. Now the final Tilted Triangle may be built on the triangle 3-5-6 as exhibited above. The line from 6 to 5 to 4 is extended to 7 (again, not an arbitrary point -- it's in the proper position demanded by the geometry. The key to finding this point comes from the educated guess that Vermeer used point 2 as a central point in the geometry. Indeed, he painted the corner of the cover in registration with the center of the hexagram on his layout sheet -- my assumption). The equilateral Tilted Triangle may be constructed using the 6-7 line as the proper side.  Note that this new 6-7 side causes the top of the sought-after Tilted Triangle to extend beyond the confines of the painted canvas. This is typical of all of Vermeer’s Grail Geometry compositions identified thus far.

To construct a hexagram, a circle may be drawn around the Tilted Triangle so that another equilateral triangle may be added (according to the procedure of the Grail Geometry Section ). Having done so, we see that the line from 3 to 2 to 5, when extended downward and to the right, hits the Lady’s left eye. Surely this is no coincidence. The many confirming features in the painting show that Vermeer used this hexagram as a guide.

The Hexagram further confirmed: A remarkable confirmation is point 2, the corner of the cover – it is in the exact center of the Hexagram! This was not forced by the analysis; it faithfully represents the way Vermeer laid out this composition. Note that the lower right-hand corner of the music sheet, point 8, was positioned by the Hexagram. Note how Vermeer used the Hexagram to establish the left edge of his painting -- point 3.

We see that the artist began with a layout sheet larger than his canvas. To compose a painting so that the salient features of the composition fall on the lines, angles, and nodes of a pre-determined complex geometrical scheme is no simple exercise! No wonder that Vermeer only had time to produce a relatively small oeuvre of just thirty-five or so paintings in a span of about 25 years (about 1650 through 1675). Next Page 3, Step 3 >>>

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