DRAWING THE “JESUS TOMB” SYMBOL, PART 5

Well, I just keep on tossing in circles and they keep on meshing.

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:  Part 1, Part 2, Part 3, and Part 4.

I took the drawing from Part 4, grayed most of it, and around the periphery, added 8 half green circles.  (Previously called the “dark green circle,” it is one-half the diameter of the standard circle and one-half the diameter of the “green circle.”)  Each half green circle (dark green) is tangential to two half tomb symbol circles (light green filled).  See following image.

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Around the periphery in the following image, I have 8 half green circles (one-half the diameter of the standard circle).  Around the periphery, I’ve added 8 royal circles (one-third the diameter of the standard circle).  Each royal circle (royal blue) is tangential to three half green circles (dark green).

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Around the periphery in the following image, I’ve added 8 “yellow circles” (75 percent of the diameter of the standard circle).  Each yellow circle (deep yellow) intersects two points where two half green circles (dark green) intersect.  The yellow circles converge towards an inner circle the diameter of a half green circle.

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Around the periphery in the following image, I’ve added 8 tomb symbol circles (one-fourth the diameter of the standard circle).  Each tomb symbol circle is tangential to a yellow circle.  Then I added 8 green circles (same diameter as the standard circle) through the center of the standard circle.  Each green circle (deep turquoise) is tangential to two tomb symbol circles.

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Well, I’ve finished up here where I started in Part 4, with 8 tomb symbol circles and the standard circle.  I’ve come full circle.  And I suppose I could go ‘round again.  Continued here.

Slide show and music on my main page.

-2008-

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This post was updated on May 12, 2008.

MARVELS IN THE “JESUS TOMB” SYMBOL

More marvels abound in the “Jesus Tomb” symbol.

I am continuing here with my three previous posts (January 28, February 3, and February 11) on the geometry of 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 will continue to use some terms I have defined in these earlier posts without re-stating definitions here.  Once again, let me say that I am going by what I observe in my drawings; I am not attempting mathematical proofs.

The following image is based on an arrangement of 8 circles around a central circle in a stained glass window that I saw in an ad for a university in Illinois.  I arranged 8 tomb symbol circles (black-green) around a central tomb symbol circle – each of the 8 tangential to the perimeter of my standard circle.  This arrangement of 8 is a departure from hexagonal geometry, but I’m still using the tomb symbol circle which is derived from a hexagon and which is one-fourth the diameter of the standard circle.  After I got the 9 circles arranged, I improvised.  I added a rosette of 8 tomb symbol circles by rotating the tomb symbol circle based on its original position in the tomb symbol (intersecting the center of the standard circle).  Then I added 8 circles which are 60 percent of the standard circle – each tangential to the perimeter of the standard circle.  In the following image, each 60 percent circle (turquoise) is tangential to three tomb symbol circles.  The 60 percent circles crisscross at the central tomb symbol circle.

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Then I added 8 circles which are 30 percent of the standard circle – each tangential to the perimeter of the standard circle.  In the following image, each 30 percent circle (red) is tangential to five tomb symbol circles.

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Then I added 8 royal circles (one-third the diameter of the standard circle).  Each royal circle (royal blue in the following image) intersects two points where tomb symbol circles of the inner rosette of 8 meet each other.  Also, each royal circle intersects two points where the 60 percent circles meet each other.

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Then I added 8 half royal circles (one-sixth the diameter of the standard circle).  Each half royal circle (pink in the following image) is tangential to four tomb symbol circles.

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Then I added 8 half tomb symbol circles (one-eighth the diameter of the standard circle).  Each half tomb symbol circle (green filled in the following image) is tangential to three tomb symbol circles and one half royal circle.  The following image has 58 interrelated circles.  Can you find them all?

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How on Earth can these forms mesh the way they do?  The tomb symbol just keeps on creating marvels. 

What more marvelous symbol could there be to honor the memory of Jesus than the Talpiot symbol?  Continued here.

Slide show and music on my main page.

-2008-

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This post was updated on July 25, 2008.

OMEGA IN THE “JESUS TOMB” SYMBOL

Here’s another surprise from the large symbol on the “Jesus Tomb” at Talpiot, 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.)  

This post is a continuation of two previous posts, my January 28, 2008 post and my February 3, 2008 post.  So I won’t be re-explaining some terms that I have already explained.

(Let me interject here that in this post, I am going by what I have observed in my drawings; I am not attempting mathematical proofs.)

I drew the “royal blue line” and its mirror image, both intersecting the bottom-most point of my standard circle, and tangential to the tomb symbol circle, and copied, rotated, and pasted the “royals” into each of the 20 pentagram points present in the 60-point design to make a “royal design,” as shown in the following image:

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The lines converge to form an inner circle I will call a “royal circle.”  The following image is made up of six royal circles placed around a seventh royal circle.  It turns out that the diameter of my royal circle is approximately one-third the diameter of my standard circle, and maybe would be that exactly if it were possible to split a pixel.  It’s one-third as best I can tell without re-designing my standard circle.  I got the idea for arranging the circles like this from a picture of a stained glass window in a cathedral in northern Europe.  Isn’t it neat the way all these circles fit together so snugly?

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By rotating a wreath of six royal circles 90 degrees, I get a wreath of 12, as shown in the following image.  Each royal circle intersects with its neighbor, at an interval equaling the width of the horizontal line of a pentagram inscribed in a tomb symbol circle.  Thus 12 stars can be inserted point to point all around, using the foundation of a tomb symbol circle.  I decided to have the pentagrams point inward – that way the tomb symbol circles are tangential to each other and don’t overlap, and the pentagram can interact with the underlying 12-point star.  This Queen of Heaven diadem of 12 stars is one of my favorites.

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Of course, the cathedral’s window of six circles around a seventh could have been instead an arrangement of tomb symbol circles confined by a hexagram, as shown by the yellow circles in the following image.  This drawing also contains 12 royal circles which make up the 12-pointed rosette in the center, many circles which are half the diameter of a royal circle, and six additional tomb symbol circles that are not fully colored.    In the image these circles mesh very neatly with the geometry of a 12-point star (two interlocking hexagrams) – the red lines.  Notice for instance, how the half royal circles fit exactly into the equilateral triangle corners of the star.

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Some measurements I’ve observed: 

###  The diameter of the tomb symbol circle is one-fourth the diameter of a standard circle and four tomb symbol circles fit precisely in a row across a standard circle.  Three tomb symbol circles fit in a row across a hexagram. 

###  The diameter of the royal circle is one-third the diameter of a standard circle and three royal circles fit precisely in a row across a standard circle.  Two royal circles fit in a row across a hexagram. 

###  The diameter of the half royal circle is one-sixth the diameter of a standard circle and six half royal circles fit precisely in a row across a standard circle.  Five half royal circles fit in a row across a hexagram.

The tomb symbol can catalyze the transformation of a hexagram into a pentagram, or so it would seem (see my January 28, 2008 post).  Can it do the reverse?  Change a pentagram into a hexagram? 

Can I go full circle in my wanderings?  From hexagram to pentagram, through many transformations, and then back to a hexagram?  The short answer is “yes.”

I got out my royal design.  Next I overlaid the 40 points of “pink latticework.”  After that I overlaid a 12-point star.  I found there are 8 points where there is a three-way intersection among the three forms of 12-point star, “royal design,” and inner circle of “pink latticework.”  Therefore, a hexagram can be derived if you have the two forms of royal design and pink latticework (both derived from the tomb symbol).  By the way, each of the 8 three-way intersections lie at or about a midpoint, between a midpoint and the end point of a side of the equilateral triangle (four of which comprise the 12-point star).  See next image.

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The Talpiot tomb symbol would seem to be a handy device for converting a hexagram into a pentagram, and also for converting a pentagram into a hexagram.

If you have followed my wanderings in these posts, you have seen how the tomb symbol effected many transformations through time, yet now it has gone full circle back to its hexagonal beginnings.  Just as in our journey through time we return to the One who is our Source.  The tomb symbol holds a reassuring message for us – we are on a spiritual journey in this life, and all of us will eventually find our way safely back home.  Alpha and Omega are One.

From my point of view, my mathematical meanderings have been mainly an exercise in drawing pretty pictures.  The most interesting part of the process has been watching ideas pop into my head.  I’ve made a lot of guesses here.  I’ve had a lot of fun with this.  And learned a lot.  Continued here.

Slide show and music on my main page.

-2008-

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This post was updated on May 5, 2008.

THE SURPRISE IN THE “JESUS TOMB” SYMBOL

The tomb symbol yields a stunning surprise!

I am continuing here with my January 28 post on 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 was able to draw the following image by manipulating the tomb symbol and its associated hexagram (6-point star) and its associated pentagram (5-point star).  Oh, and I should mention, I did this using clues in the words of Jesus and Ezekiel in the Bible.  More on that later.

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In this image you can see an “Eye of God,” a bulging, protruding EYE BALL, not flat like so many other similar designs.  Click here and then click on the image to make it full size, and then step back.  It leaps off the screen at you!

I drew this after considering the mathematical relationships among the tomb symbol, a hexagram and a pentagram.  See my January 28, 2008 post, “Drawing the ‘Jesus Tomb’ Symbol,” for an explanation of these relationships.

To make the “Eye,” I arranged five hexagrams within a pentagram as follows:  On the pentagram, I overlaid a hexagram with its companion tomb symbol, so that the top point of the hexagram coincided with the top point of the pentagram.  I repeated for each point of the pentagram.  This makes a flowery design with 30 peripheral points and a central rosette of five petals (see next image).  Notice that the pentagram lines (red) seem to intersect where some hexagram lines (gray) crisscross.

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Next I copied the design, rotated it 90 degrees, and pasted it back on the original.  I pasted again at 180 degrees and again at 270 degrees.  This makes the “Eye” design with 60 peripheral points and a central rosette of 20 petals.

What is the importance of the tomb symbol in all this?  Without the circle-under-angle of the tomb symbol (shown in turquoise and black-green), there would be no bulging “Eye.”  The tomb symbol creates the Eye.

The tomb symbol is a powerful agent of transformation.  In my January 28 post, I explain how the tomb symbol, apparently derived from a hexagon, seemingly transforms a hexagram into pentagram (click here for my graphic).  The tomb symbol also transforms hexagrams-within-a-pentagram into an “Eye.”  This transforming power must have seemed quite magical to the ancients who first discovered this.

During my voyage of discovery, I had the words of Jesus, “thirty, sixty, or even a hundred times” (Mark 4:8 and 20, NIV) tumbling about in my head.  I had been wondering about his mathematical riddle for many months, and this week, I decided to see if I could solve the riddle in the context of the “Jesus tomb” symbol.  Thinking of “thirty,” and realizing it was the product of 5 and 6, I began to experiment by combining a pentagram and a hexagram in various ways.

Well, I found a thirty point design and I found a sixty point design (as shown above), but I would not have found these without big help from the Book of Ezekiel in the Old Testament written long before the time of Jesus. 

I consulted Ezekiel, chapters 1 and 10 (NIV).  Ezekiel gave me the clues I needed to construct the “Eye.”  Doing a careful reading, I guessed that his “cherubim” is a pentagram, with a “head” and four “wings.”  I guessed that the circle “on the ground” is the circle of the tomb symbol that is low on its associated pentagram.  I guessed that the “hand” under the “wings” is the five-pointed, finger-like rosette I’d get if I rotated the forms.  (Without this clue of the “hand,” I would have proceeded with my initial attempt, in which I had overlaid a pentagram-with-tomb-symbol on each peripheral point of a hexagram, making a 6-fingered rosette). 

But how far to rotate my five-fingered rosette with 30 outer points to get 60 points?  Ezekiel gives an indispensable clue.  He says the “south side” and the “east gate” (aka “threshold”?).  Now if I assume that his “south side” is a point coincident with the point of a pentagram, and I assume his “east gate” is a blank space between two of the 30 peripheral points, just like a gate; then it appears that he rotates the design 90 degrees counter-clockwise, south to east.  However, my design was just the reverse of his with the “north side” coincident with a pentagram point, and the particular software I used can rotate only clockwise, so I rotated from north to east.  But it all works out.

I believe this process of copying, rotating, pasting, and then pasting two more times, is what Ezekiel calls “whirling wheels.”  I did the whirling with my computer software, and I cannot imagine how the ancients had the incredible patience to do all this with only feather pen, ink pot, and parchment!  I do plan to get more sophisticated software someday that will allow me to draw and “whirl” with greater precision (any suggestions on what I should buy?).

Now back to the words of Jesus.  I got the thirty point design.  I got the sixty point design.  But where is the one hundred?  How do I get forty additional points into my circle to make 100 points?  I pondered this for a long while, getting nowhere, and finally decided that I would simply add in forty points.  It would not be a circle with points equidistant from one another (at intervals of 3.6 degrees), but then again, the ancients weren’t into working with decimals.

But where to put the forty points?  I flipped through Ezekiel and found a passage where he describes a decorative pattern in a temple (41:17-20 NIV).  He says that each “cherubim” is flanked by a “palm tree” on each side, and this pattern goes “all around.”  He also says there are palm trees alternating with cherubim.  (Keep in mind the word “cherubim” is both singular and plural).  Well, I asked myself if the tomb symbol of circle-under-angle looks like leaves of a palm tree hanging down over a coconut, and I decided, yes, it does.  And still assuming that a “cherubim” was a pentagram, I looked at my 60-point design to see where the “trees” should go among the “cherubim.”  There are 20 pentagram points, 60 points total, and 60 spaces between points.  After much fussing, I decided that the 20 spaces holding the mid-points between pentagram points should remain blank, and that the “trees” should go evenly within all remaining spaces. 

But how to fashion the “trees”?  I found no clues in Ezekiel for this, but intuitively I did what I needed to do.  I anchored the tomb symbol so the top of the angle coincided with the top-most point of my standard circle.  I copied this ensemble, rotated it, pasted at 18 degrees, and repeated at 18 degree intervals (pentagram points), then rotated the entire design 3 degrees off, then copied, reversed left to right, and pasted.  Well, I know you are saying, “So what? – you just stuck in 40 points to get your one hundred – that’s cheating.”  But wait!  Something happened when I made those points!  This is what happens:  the tips of the tomb symbol angles all join up, each angle nicely linked to its inverse, to form a latticework (pink lines in the image below).  Rather pretty.  After a while, I noticed that the latticework appears to curve backwards into the screen, and the lines converge to give the appearance of a solid circle.

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Do I think that I have a clear understanding of Ezekiel?  Of course not.  Who would?  But I am thinking that maybe I’ve guessed it right, just because the results of “Eye” and “latticework” are so astonishing to me.  By the way, in this post I am just going by what I observe in my drawings – I am not attempting mathematical proofs.

Is it possible to tie the tomb symbol to Jesus through his words, “thirty, sixty, one hundred”?  Was Jesus intrigued by math?  Maybe.  But maybe the term “thirty, sixty, one hundred” was just a common everyday saying at that time.  Then again, if Jesus or his close followers were into “sacred geometry,” then finding Ezekiel’s math (if such it is) displayed so very prominently on the tomb of Jesus (if such it is) would not be entirely unexpected.

Not only does the Talpiot tomb symbol seem able to transform a hexagram into a pentagram, and able to create a mystical Eye from hexagrams-within-a-pentagram, but the tomb symbol can produce a latticework from the Eye design, a latticework that interconnects and bends inward to produce a seeming circle.  Quite a powerful symbol of transformation and creativity!  Reminding us of the Creator, that creator’s transformation of our daily lives, the interconnectedness of all created things, and our transformation when we transition into Eternal Life.

One more line.  I found another line that I will call the “royal blue line,” that ties together the forms present in the four-colored-wheels exercise in my January 28 post.  Apparently, this “royal blue line” is tangential to the tomb symbol circle (black-green in the following image), and intersects:  (1) the bottom-most point of the hexagram (navy), (2) a point where the pentagram (brown) meets a line (gray) which bisects the hexagram, and (3) a point where the pentagram meets a line of the 12-point star (gray).  After I completed the 100-point design, I asked myself if this “royal” line also intersects one of the 40 points of pink latticework that had completed the 100 points.  Well, it seems to intersect at 39 degrees (an arc of 39 degrees centered on the center of the design); however, a little high school math tells me it misses that point by a few hundredths of a degree.  The "royal blue line" has other uses (see Part 3, Part 13, Part 14 (Index)).  Interesting also that the connecting ends of pink latticework seem to meet at pentagram lines.  (See the following image – drawn with an application that rotates images more precisely than above, but also makes the rotated lines less distinct.)

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 Does the “Jesus Tomb” symbol hold even greater surprises?  Continued here.

Slide show and music on my main page.

-2008-

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This post was updated on September 30, 2008.