What a wonder the symbol is!
I’ve found this symbol is easy to draw exactly and is easily reproduced to make proportional copies.
In the following image of the Talpiot tomb symbol, my turquoise overlay is derived from a hexagon, and has certain proportions which are consistently reproducible when using a hexagon as a template.
In the image, the tomb symbol appears to share three points (the top of the Y stem and the two ends of the arms of the Y) with the corners of a hexagon, with other relationships as follows: The diameter of the rim of the small circle is one-half the radius of the circle enclosing the hexagon. The rim of the smaller circle intersects both the center of the larger circle and the midpoint of the radius of the larger circle. My turquoise overlay defines this rim and also the angle under the arms of the upside-down Y. The lines forming this angle intersect at the midpoint of the horizontal line connecting two remaining corners of the hexagon. That intersection point is also a midpoint of the radius. The sixth and bottom-most corner of the hexagon would be barely above the center of the top of the entryway to the tomb.
My hexagonal design is easy to construct with simple tools. You need only a string and piece of chalk. This is how:
First attach your chalk to one end of your string. Anchor the other end of the string or have someone hold it in place at your designated center. Move your chalk-on-string to draw a circle with every part of the circle equidistant from the center. In a hexagon, each side of the hexagon is equal to the radius of the circle enclosing the hexagon. Therefore, you can mark off the corners, where the hexagon meets its enclosing circle, by using the same length of string you used for the radius of your circle. To find the point where the two arms of the upside-down “Y” intersect, draw lines as indicated in the image (or in the text above). Draw straight lines using a taunt string as a guide. To make the radius of the smaller circle fold your string in half twice (to make it one-fourth the length of the radius of the larger circle).
Is this the way the sculptor made the original tomb symbol? With chalk, string, chisel, and a hexagon? Who knows? It’s possible.
While my hexagon overlay fits the photo well, the fit could be better. One explanation – distortion could have been introduced in a number of ways: during my pencil/compass drawing of the hexagon, by my scanner, or by my drawing software while working with the hexagon or sizing the photo of the tomb symbol. Distortion might be inherent in the original photograph of the tomb symbol or the sculpture itself may lack absolute symmetry.
A hexagon yields other very pleasing designs, formed within it by making connecting lines. For example, the three hexagonal corners, where the “Y” shape meets the hexagon, correspond to the three points of an equilateral triangle. Also, two equal interlocking equilateral triangles form a six-pointed star (called a “hexagram”) within a hexagon.
Here is something that occurred to me as I played with my hexagon: The Talpiot tomb symbol shares at least 5 points (the 3 ends of the Y and the 2 midpoints of radii discussed above) with a six-pointed star (hexagram); 6 points, if the placement of the top of the entryway quite near the bottom-most point of the hexagon is not mere coincidence but is actually part of the design of the facade. The hexagram is often called the sign of King David. If the tomb symbol means “birth” as I hypothesized in an earlier post, and if it is linked conceptually to the hexagram by its shared points and its hexagonal derivation, then perhaps the tomb symbol means “of the lineage of David” or Son of David. I definitely was intrigued and pleased to discover hexagonal geometry in the symbol carved on what might be the Tomb of Jesus.
Of course, maybe I’m reading too much into this. Maybe the hexagon is just a ubiquitous artist’s tool, or maybe there is no hexagon at all – maybe the sculptor just drew freehand.
Drawing hint: To draw a hexagram onscreen, begin by dividing the vertical diameter of a circle into four equal quarters. This yields the two points where the horizontal lines of the hexagram cross. Onscreen, a perfect circle begins with a perfect square.
I took another look at the Talpiot tomb symbol in the context of a hexagon and hexagram. I discovered five amazing phenomena – see the next image. (Now these are merely my observations based on my drawings, and I have not attempted mathematical proofs. There are significant changes in this update, as I improve my drawing techniques.) As you read the following, think about the relationships that are defined, and how these tie together the forms of circle-under-angle, that angle, and the hexagram.
(1) Red line: I was wondering how far the tomb symbol’s small circle was from its overarching angle. So I made a line from the circle’s center perpendicular to the side of the angle (the shortest distance between them). That line is approximately the same as the diameter of the circle. A pleasing design. On a whim I extended the line and found that it intersects one peripheral point of the hexagram and also intersects a point where the interlocking equilateral triangles of the hexagram intersect. Why do all these points line up? I don’t know!
(2) Green circle: I wanted to discover more about the tomb symbol’s angle, and about the point where the “red line” perpendicularly intersects the symbol’s angle and also, the corresponding mirror-image point on the other side of the angle. I’ll call these points the “A points.” I got out my compass and it told me that each “A point” is at a distance from the topmost point of the hexagram equal to the radius of the circle enclosing the hexagram. Cool! A circle passing through the two “A points” also passes through the circumference of the symbol’s small circle and two peripheral points of the hexagram. This “green circle” is the same diameter as the hexagram’s enclosing circle.
(3) Yellow circle: What next? Well, I couldn’t resist making a test circle with the center at the top of the tomb symbol’s angle and with the circumference passing through the center of the tomb symbol’s circle. It appears to be tangential to two sides of the hexagram. Amazing!
(4) Turquoise circle: Is there more? Oh help, I found another circle. This one centered where the “red line” intersects the side of the upright equilateral triangle within the hexagram. The circumference of the circle passes through a peripheral point of the hexagram and also passes through the center of the circle enclosing the hexagram (and that latter center is also the top point on the circumference of the tomb symbol’s small circle). Gasp!
(5) Dark green circle:
This “dark green circle” is half the diameter of the hexagram’s enclosing circle, has its center at a midpoint of the side of the upright equilateral triangle within the hexagram, and passes through the center of the enclosing circle and a lateral point of the hexagram. The “dark green circle” intersects many other interesting points, but most importantly, it intersects the top point of the tomb symbol angle. Far out! Maybe that’s enough for now.
The enigmatic Mason symbol with its compass and square base had inspired me to get out my compass, and when I looked for a “square,” I found that there are many lines that are 45 degrees off the vertical, which intersect two or more interesting points, and which could form diamond-shaped squares. Just which one is the most important? This is something I am contemplating. (Other than the clues in the Mason symbol, I have no idea what Masons think about geometry.)
So the tomb symbol with circle and angle appears to be linked to a hexagram in many different ways. These relationships seem almost magical. I can well understand the pleasure and excitement that the first person who discovered this must have felt.
Long before the time of Jesus, Ezekiel reported he saw four “wheels” in a vision of angels. Could these “wheels” be my green, yellow, turquoise, and dark green circles? In Ezekiel 1:15-18, he says “Each appeared to be made like a wheel intersecting a wheel,” (New International Version). Did each of his four wheels intersect the same wheel just like my four colored circles intersect the tomb symbol’s small circle? “Their rims were high and awesome,” he says. Yeah, some of my rims are very high. Fascinating. Perhaps this math is very ancient; and perhaps it was mystical, even sacred, to those who first discovered it.
And where the New Living Translation says in Ezekiel 10:10, that “each wheel had a second wheel turning crosswise within it,” and the NIV renders that as “each was like a wheel intersecting a wheel,” could the original really mean that each wheel intersected “two” others, as is the case with my circles? (Each colored circle intersects at least two other colored circles.) Where the NIV says in Ezekiel 1:16, that “. . . . all four looked alike. Each appeared to be made like a wheel intersecting a wheel,” could the original really mean that all four were alike in that each wheel intersected the same wheel? But maybe Ezekiel was just writing about angels, not angles.
And while we’re visiting the Bible, let me ask you – in John 8:6-8, what was Jesus writing in the dirt? He could have conveyed words orally – so was he drawing? Was he drawing circles? Was he into sacred geometry?
One more image: I had to ask myself if a five-pointed star (pentagram) can be derived from the tomb symbol and its companion hexagram. It would seem that the lines of the pentagram intersect or are very close to the points where the “yellow circle” meets the “green circle,” and where the “yellow circle” meets the “dark green circle.” Using these points, you can draw a fairly decent pentagram.
My conclusion is that the relative proportions and relative arrangement of the circle and angle in the tomb symbol may be a shorthand way of signifying a broad array of geometrical wonders.
Maybe the symbol on the Talpiot tomb is there to remind us of the Eternal One who is the Great Designer of all those wonderful, and sometimes inexplicable, geometrical relationships; and to remind us that if there is such geometric beauty and order inherent in the Universe, then maybe, despite everything, there is hope. Continued here.
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This post was updated on May 19, 2009.