ROYAL BLUE LINES AND THE SYMBOL

I had some drawings that I had made earlier with royal blue lines and decided to continue that train of thought for a while.  I got some inspiration from viewing the Buddhist Dharma Wheel, but I actually don’t have a clue as to its geometry.

I am continuing here with my series about the large symbol found on the Talpiot tomb in Israel (aka “The Lost Tomb of Jesus”).  The symbol is a stone relief sculpture of a small circle within an upside-down Y-shape.  (More on the tomb here.)  

I have been making designs derived from the tomb symbol.  I am going by what I observe in my drawings; I am not attempting mathematical proofs.  As I go along I define whatever terms I need to, but might not repeat definitions in each post.  So this post should be read in conjunction with the previous ones.  (Index.)

The following image is further development of the last drawing shown in Part 4.  I’ve added royal blue lines radiating from the center, mirrored pairs rotated in increments of 45 degrees.  The royal blue lines are colored red, so they will be more visible.  A royal blue line is by my definition a line through the bottommost point of the standard circle and tangential to the tomb symbol circle in its original position intersecting both the center of the standard circle and the mid-point of the circle’s lower vertical radius.  In this drawing, the royal blue line has been moved so it radiates from the center instead.  Of course, the tomb symbol circle (pink-filled) hanging from the topmost point of the standard circle (regular blue) is tangential to the royal blue lines radiating from its center, because the tomb symbol circle is still the same distance from the angle apex as before.  It was nice to learn that the half tomb symbol circle (pale green-filled) is also tangential to the royal blue lines when end to end with the topmost tomb symbol circle and below it, although this can be ascertained intuitively, once you think about it.

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I should mention here that some of my images are very wide and when shrunk down to fit in this column, they lose a lot of detail.  To view a full-size image in this series, click on “Full-size image” under the image, then click on the image to open or click “open.”  Then hover your cursor over the image to get a pop-up button in the lower right corner (or other feature depending on your browser – this will take a few moments), and click on that to get the actual full-size.

In the following image, several forms are rotated in increments of 45 degrees:  a 12-point star (navy) inscribed within the standard circle (regular blue), a half green circle (pale green and half the diameter of the standard circle) hanging from the topmost point of the standard circle, a mirrored pair of royal blue lines (red) radiating from the center of the standard circle, and a tomb symbol angle (dark green) anchored in its original position with apex at the midpoint of a hexagram’s upper horizontal line (also within the 12-point star).  I was pleased to see the rotated half green circles intersect other rotated half green circles at points where the horizontal and vertical lines of the 12-point star meet (see pair of red arrows marking this).  Red arrows also show where rotated royal blue lines pass through the intersections of rotated tomb symbol angle lines and rotated lines of 12-point stars.  Red arrows also show where rotated royal blue lines pass through the intersections of rotated tomb symbol angle lines and rotated half green circles.  Tomb symbol angle lines also pass through intersections of vertical/horizontal star lines and other star lines (16 points unmarked).

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There are no royal blue lines in the following drawing, but in setting up a design for the next two drawings after that, I decided to tarry a bit and experiment some more with the orange grid I developed in Part 7.  In the following drawing, the standard circle is pink-rimmed and pale blue-filled as is the 200 percent circle.  An equilateral triangle is inscribed in the standard circle, inscribed in the 200 percent circle, and inscribed in what would be (if shown) a 400 percent circle, all three concentric. 

I extended the orange grid (lines 45 degrees off the vertical forming a pattern of diamond shaped squares) so that it would fit the larger size image I am working with here.  Then I did a copy/invert/paste.  (In this case as in most of my drawings, the center of the design is the exact center of the image and so when I pasted in this instance, the center stayed at the center.)  I pasted this “original-orange-grid-with-invert” on the three triangle design, center on center.  I pasted it on again, not on the center this time, but with orange lines intersections (those above the smaller interval of orange lines) anchored on the topmost point of the standard circle, the same position the orange lines hold in “circle 2” in Part 7.  This created yet a smaller interval of orange lines.  Using that smaller distance as a benchmark, I pasted the “original-orange-grid-with-invert” both above and below existing intersections.  Again, the orange line intersections above the smaller interval of orange lines are what I anchored at the benchmarked distance. 

So what did I get?  In this new pattern of orange lines, each corner of each of the three triangles now bears the intersection of orange lines!  I don’t know if this could have been anticipated – I certainly didn’t know it would happen, and after just a few manipulations.  Wow!

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This next drawing is a bit more fun to look at and is derived from my musings about the Buddhist Dharma Wheel, yet maybe totally unrelated to it for all I know. 

Again, I have a mirrored pair of royal blue lines (this time in royal blue), rotated at intervals of 45 degrees to make 8 pairs.  The center of the design is not at the center of the image any more, but centered in the standard circle (regular blue and pink-filled). 

All the circles here are ones I have used before. In their order of ascent from the center, tangentially held within the royal blue lines (opening upward and partly chocolate brown-filled), these circles are:  

>>half tomb symbol circle (deep pink and one-eighth the diameter of the standard circle),

>>half royal blue circle (deep wedgewood and one-sixth the diameter of the standard circle),

>>tomb symbol circle (black-green and one-fourth the diameter of the standard circle),

>>royal blue circle (indigo and one-third the diameter of the standard circle),

>>half green circle (dark green and one-half the diameter of the standard circle),

>>yellow circle (gold and three-fourths the diameter of the standard circle), and

>>green circle (regular green and same diameter as the standard circle). 

As noted above for the first drawing in this post, the half tomb symbol circle and the tomb symbol circle fit end to end, both tangential to the royal blue lines.  It is just intuitive that other circles fit end to end likewise, those circles which are in succession each a factor of 2 larger than the previous, thus the progression: half tomb symbol circle – tomb symbol circle – half green circle – green circle.  The royal blue circle and its half also fit end to end.  The royal blue circle was developed using the royal blue lines in a previous post and it is just marvelous that this circle is also one-third the diameter of the standard circle.  It is positioned here (centered on the topmost point of the standard circle) at a distance from the apex of royal blue lines same as in its development, so its tangentiality at that point is anticipated.

The drawing also shows a variety of these circles tangential within the peaks of the three equilateral triangles (partly marked with red fill).

All the circles are linked one to another somehow, passing through a top, bottom, or center point of another, as best I can recall, and so there are repeating intervals within the column, for instance, that of the tomb symbol circle.  Two circles in this design are tangential to different sets of royal blue lines, those rotated by 45 degrees.

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The next drawing takes a segment of the previous and builds on it, adding more circles.  The royal circles (regular blue-filled) fit tangentially among the half green circles (lavender-filled) and the green circle (partly deep pink-filled).  This relationship is not new as it can be seen in my second drawing in Part 5, but has greater emphasis here.  It pleases me somehow.  And this is not the first time I’ve drawn five half royal circles in a row (yellow-filled) with centers on what would be the horizontal line of a hexagram (if shown).  Something interesting in this drawing is that each end half royal blue circle is tangential to three other circles:  the green circle, a half green circle, and a royal blue circle. 

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It is enormously difficult to write the text for these drawing posts, far more difficult than making the actual drawings, but if it helps my readers who take delight in drawing as I do, then it is worth it.  Continued here.

-2008-

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This post was posted on September 4, 2008.