Geometric Design Principles


One of my secondary theses is that the 'doubling the circle' exercise that uses the vesica piscis (seen below) represents the geometric scheme common to all geometers, artists and builders past and present. Doubling the circle just shows that a vesica locates 30 degrees on a sphere or a circle and cuts the radius in half and quarters the diameter. The first thing that we see is the yin/yang symbol (below), which requires two smaller circles.

The images below show that nested squares double in size, as do the circles that are associated with those squares. It also shows two different alignments of squares. The image on the right below indicates that the diagonal squares are half the size of the right squares, as one small square equals two triangles, and one large square equals four triangles. Nested squares alternate, right, oblique, right, oblique. What you see is the 'no word' solution to the pythagorean theorem using a 45 degree isoceles triangle (the Master's Square).

  

Overlapping equal circles touch at 30 and 60 degrees on each other, creating a 4x4 grid just like the squares do. We can continue to use overlapping circles to produce parallels lines that halfen the circle. Below we see the Star of David and Metatron's Cube and further reductions. As the sine function is determined by the percentage of a vertical radius, we know that the sine of 30 is .5. The full circle has a radius of 1, and the next one has a radius of .5 (diameter of 1).

This means that we can determine exactly where each of the next reductions occur; at .25, .125, .0625, etc. These would represent radii of 1/4, 1/8, and 1/16th, which is about 7 degrees.

Of special interest is the circle and triangle produced by the second reduction (below). As you can see by looking, it is very close to the cross section image of the Great Pyramid and the angle generated by two points of a heptagram (seven pointed star). You will remember that this (51+ degree) triangle is used in the DC map, with New Hampshire Avenue creating the angle. 360/7 = 51.4 degrees, the latitude of Greenwich, England. (London and the Stonehenge are close.) That triangle touches at three points of the heptagon.

  • I say very close, because it is not exact. While reducing the circle with the vesica produces a 7 degree inner circle, dividing the circumference by 7 or 14 yields an inner circle of just over 8 degrees. That means that the 12/6 system and the 14/7 systems are within a degree of each other at that level. The eight degree circle fits 1/2 degree on each side of the seven degree circle. If you use one or the other circles it doesn't much matter, as long as you don't use them to calculate other points and multiply the errors.

    I suggest that this scheme is used to design the Sri Yantra. As you can see, only the six points of these two triangles touch the outer circle (below). You can also recognize equilateral triangles in the design. Before we tackle the yanta I would like to take a look at the Aztec Calendar Stone where we see mainly circles, but the logic of the design is the same.

    Here you can see that the circles are associated with a variety of other geometric figures. Remember that every circle generates squares and equilateral triangles and visa versa. Once you study 'the pattern' for a little bit, you will be able to tell what figures are being implied. For instance, you can tell from the size of the central circle that it is tangent to the base of the 51.4 triangle. I begin with this blue outer circle. Note the arrows at the top.

    Note especially the rectangles formed at 30 and 60 degrees by the vesica. Look at the upright rectangle, and the arrow at the top. Lines from the center of the top line of the rectangle to the bottom corners are tangent to the central circle. As you can see, you can do more reductions toward the center.

    On page 164 of "Lost Symbol", Langdon/Brown speaks of requests for help deciphering some of history's gereat unresolved codes. One that he mentions is the Phaistos Disk, and although I had never examined it before, in less than five minutes I had seen 'the pattern'. I offer this interpretation of that.

      

    Now let's look again at the sri yantra where they do more reductions. Note especially the inscribed square (red) at 45 degrees and the rectangles at 30 and 60 degrees.

    Below we show that lines that bisect the angles of equilateral triangles also bisect the opposite sides. All three of the sides of the top triangle are equal to half the side of the larger triangle. 30 degree diagonals bisect equilateral triangles as well as circles. For now I want you to focus on the base of the smaller triangle. As the image above shows, this line is very close to be the same as the side of a regular heptagon inscribed in the circle. Note also that the base of the small triangle is the same distance from the center of the circle as the base of our 52 degree traiangle.

      

    We use a circle to project the sides of the small triangle onto the big circle. Notice how this circle touches the next smallest circle (above right). We use the same principle to divide the small triangle (below left), and reflecting lines back to the center we get a pentagram. Remember that the top points are half as far apart as the wide points are. In the DC map, this is eight blocks wide. It is 16 blocks from the White House to the Capitol and between the wide points there. You will recognize the Gates of Light version of the Tree of Life in this image. I call that the A-shaped tree which looks like a tree. I call the Kircher version of the tree (right below) the H-shaped tree.

      

  • Astronomical Lines

    You will recall that the Great Pyramid has 51+ degree base angles and is located just south of 30 degrees latitude, where a hexagon touches a circle. Interestingly, if we shorten an equilateral triangle with diagonals producing 30 degree angles to a ~52 degree cross section, the diagonals become 23+ degrees like the troipcs. This is exactly what we see in the DC map. An equilateral triangle (with diagonals and a pentagram) is shortened to ~52 degrees, producing a 23+ degree diagonal grid.

    While 23+ degrees represents the range of the sun's apparent position, both the moon and Mercury range beyond that. The moon moves more than 5 degrees beyond the sun's path, while Mercury, the most eccentric planet moves more than 7 degrees beyond that. In its orbit, Mercury can be as far as 31 degrees from the equator. This is why Mercury is associated with bounaries and limits, surveying etc. The 31 degree latitiude line is 6/7's of the equator.

    You will note that the zodiac belt marks the 'inhabited' part of the sky, within which the planets move. This is marked by the 14+ degree range of Mercury, 7 degrees on either side of the sun. The mesoamerican ball courts were built in the shaped of four squares end to end, making the 1:4 rectangle with 14 degree diagonals. This is what I am calling the second reduction. The first reduction produces a 30 degree diagonal which is just short of Mercury's range. The parallel lines in the hexagram mark Mercury's range from the equator.

    Remembering that a 'bark' was the sun's boat in Egypt, let's look at the dimensions of Noah's Ark, which are given as 300x50x30. If we divide by 5 and multiply by 6 we get 360x60x36. 360x60 can be seen as a rectangle that is 60 degrees wide around the globe, from 30 north to 30 south latitude.

    Continue to Stone Circles.


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