DRAWING THE “JESUS TOMB” SYMBOL, PART 14

Q:  The diameter of the royal blue circle seems to be one-third the diameter of the standard circle – is it?

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.  This post should be read in conjunction with the previous ones.  (Index.)

The royal blue line (royal blue in the following image) is by my definition a line through the bottommost point (A) of my standard circle (pink), and tangential to the tomb symbol circle (black-green and one-fourth the diameter of the standard circle), when the tomb symbol circle is in its original position with its center on the lower vertical radius of the standard circle and intersecting its center.  The royal blue circle (deep wedgewood) is centered on the center of the standard circle and is tangential to the royal blue line. 

Full-size image

The radius of each circle is perpendicular to the tangential royal blue line at the point where it intersects the circle.  I drew these perpendiculars for each circle creating right angles.  In the royal blue circle there is radius CF, from center C to point of tangentiality F.  In the tomb symbol circle there is radius ED, from center E to point of tangentiality D.  I then have two right triangles (both “similar”) with point A their common corner.

In the following set of calculations I show that the sine of angle EAD equals the sine of angle CAF, when I assume that the radius of the royal blue circle is one-sixth the diameter of the standard circle. 

The diameter of the standard circle is 1.  The radius of the standard circle is therefore 1/2.  Radius ED is 1/8.  Radius CF is assumed to be 1/6.

sin EAD = opposite / hypotenuse = ED / EA = (1/8) / (3/8) = 1/3

sin CAF = opposite / hypotenuse = CF / CA = (1/6) / (1/2) = 1/3

It works!  The royal blue circle is tangential to the royal blue line AND its diameter is indeed one-third the diameter of the standard circle!  Hooray!  (Chortle.)

At first it didn’t work out exactly when I used decimals and an electronic calculator (and got repeating decimals that didn’t quite match) so I am grateful someone suggested I use fractions instead.  Continued here.

-2008-

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This post was posted on September 30, 2008.