Vermeer's Riddle Revealed - Geometric Analysis of Lady Seated at the Virginals

J. Vermeer Lady Seated at the Virginals

STEP 1 of 3. Tilted Triangle search. Note how the bow of the viola (lower left) is strangely (and unrealistically) enmeshed in the strings and the bridge of the instrument. This is the artist’s way of calling our attention to it – and his way of challenging us to look for his geometric guidelines.

STEP 1. (continued) The line of the viola bow is extended upwards (from 6 -- not an arbitrary point -- explained below) to point 3, the edge of the image. Note how the left edge of the open virginal cover is parallel to the viola bow line – that is, because Vermeer made it so. It is a simple matter to check and see that the top of the virginal's cover (from 2 to 3) forms a 60 degree angle with the extended viola bow line (from 6 to 1 to 3) – a likely sign that we have the potential for an equilateral triangle. The top cover line is extended from 3, the top left corner of the virginal's cover (hidden behind the drapery), to 2, the corner of the cover; and extended further downward to the right. Note that, by extension, this line hits the corner of the picture frame, 5! – a welcome confirmation that we are on the right track. The dashed line drawn diagonally from the cover's top corner, 2, to the cover's bottom corner, 1, makes a neat equilateral triangle 1-2-3. This was obviously planned by the artist and cannot be a coincidence – Vermeer was devoted to equilateral triangles to guide his compositions.

STEP 1. (continued) Triangle 1-2-3 is not the Tilted Equilateral Triangle of the completed Grail Geometry -- but it is an excellent step in the right direction. Searching for another line to complete a larger equilateral triangle, we draw a line from 5 to 6 so that it is parallel to line 1—2. (This is how point 6 -- not at all arbitrary -- was established.) By extension, this line is confirmed by hitting point 4, the inside corner of the frame!

Now another equilateral triangle may be identified: It is triangle 3-5-6. It was obviously used by Vermeer to position the picture frame (among other uses just described). And yet it is not the final Tilted Equilateral Triangle demanded by The Grail Geometry. That triangle will emerge in STEP 2 on the next page.

At this juncture, we have now identified six features painted by Vermeer that convincingly appear to be guided by two equilateral triangles and the expected Tilted Equilateral Triangle of the Grail Geometry. These features were obviously painted to conform to this pattern. Next Page and STEP 2 >>

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