A Geometer's Washington D.C. Notebook

A Frame-by-Frame Look at Geometric Aspects of the Design of Washington D.C.

Updated June 16 - Images open in new windows so that you can look at as many at once as you need to. This will be added to and revised as time permits.


Geometry

  • If you were new to the idea, and did a search for the term "sacred geometry", you might get the sense that the subject was a sub-set of geometry, restricted to figures like Metatron's Cube and the Flower of Life, and notions like pi and phi. The truth is that Philosophers have, for centuries, considered all of Geometry to be sacred; and some, like Plato and Pythagoras, consider it to be the 'corner stone' of their system of study.

    Plato wrote above the entrance to his academy, "Let none ignorant of geometry enter here", meaning that no one could understand his philosophy without knowing geometry, because geometry contained the fundamental secrets of all the ancient sciences. This viewpoint is shared by Masonry.

    You will please note that the notion of the sacredness of mathematics and geometry is inconsistent with the idea that some numbers and some geometric figure are inherently evil. Here is something from John Mitchell's "View Over Atlantis" that sums up this viewpoint:

    "It is inconsistent to relate moral principles to numbers, for numerical relationships are precise and unalterable while morals are neither, being simply mores, customs adapted by general consent in reponse to the circumstances at a particular time and place. No number, in itself is exclusively representative of a moral quality, whether negative or positive, for every natural principle has it's own rightful place in the Universe. A true cosmology must encompass every created element."

    . . .

  • Symmetry, the Triangle and the Rhombus

    see fig. 1 - The Washington DC map features two axes of symmetry - 16th Street runs north-south through the White House and Scott Circle, and East Capitol Street runs east-west through the Capitol Building and Lincoln Square. The central segment of Pennsylvania Avenue connects those two buildings to form a triangle. It is this triangle that David Ovason focuses on in Secret Architecture while ignoring the fact that Pennsylvania and Maryland Aves are symmetrical to one another. Ovason also focuses on the August sunset along Penn Ave without ever mentioning the May sunset there, or the sunsets along Maryland Ave in Feb and Nov.

    This is the pair of streets that people liken to the compass in the map. The Jefferson Memorial is symmetrical to the WH seen from the CB. (In the image above looking west the Wash Mmt is directly ahead, the WH is down Penn Ave to the right, and the Jeff Mm, is to the left down Maryland Avenue.)

    Maryland and New York Avenues help form similar triangles around the point intended for a monument to George Washington 1 2, located where those axes cross (marked 'A'). These three (Penn, NY and Maryland) provide all but one side of a rhombus around the monument location.

  • The rhombus, formed by pairs of crossing diagonal lines (or four triangles), turns out to be the central geometric figure in the plan rather than a triangle, and we see more than one there. Other rhombus are found east of the CB, between it and Lincoln Square, and north of the WH, between it and Scott Circle.

  • The Pentagram, the Rhombus and Scale

    see fig. 2 - Connecting the points of the pentagram in the map produces parallel diagonal lines that forms a rhombus grid that features 23.5 degree angles (just like the tropics). Note how short and wide the pentagram is.

    see fig. 2a The East-West Scale of the map is determined by the Wide Points of the Pentagram (the long axis of the rhombus). The east west distance between these is the same as the e-w distance between the WH and the CB. L'Enfant had described Pennsylvania Avenue as running from Georgetown to the East Branch of the Potomac, and as you can see the avenue was built with seven evenly spaced nodes. Compare to this image from the St Paul's Chapel in NYC 1 2 where Washington and L'Enfant attended church there. Note the hexagon at the center of the figure.

    see fig. 2b The Upper Points of the Pentagram further divide the East-West Scale of the map.

    Tres Rhombus

    see fig. 2c The book Canon recommends that the rhombus and the cross determine the layout of the Milan Cathedral, but in the DC map we see three rhombus, each with a different ratio of sides. The map consists of three sections, each with a different diagonal grid. I am calling the red section the 'correct section'.

    see fig. 2c2 - L'Enfant's Dotted Line Map from August 1791 confirms both the parallel lines and the different rhombus. In this image the only triangle that we see is only half there. New Hampshire connects two points of the pentagram and forms the left hand side of an isoceles triangle.

    Metatron's Cube

    see fig. 2d A hexagon inside another hexagon is Metatron's Cube. The double rhombus relates to the cube, the vesica etc. Recall the hexagon at the center of the St Paul's image.

    The Tree of Life

    see fig. 2e The Tree of Life, a pentagram overlapping a hexagram, is there too. Note that the tree requires the Wash Mmt and the Jeff Mml. The tree shares eight of the points of Metatron's Cube, but instead of using Scott Circle, the tree utilizes the top two points of the pentagram.

    The Dodecahedron

    see fig. 2f The Dodecahedron integrates Metatron's Cube and the Tree of Life images. Note that the cube is composed of three rhombus, and one of these results from a hexagon overlapping a pentagon. Note also that the Kircher version of the tree does not work here or in the map.


    Topography and the Capitol Building

    see fig. 3 If we measure the angle formed by New Hampshire Avenue we see that it is about 52 degrees, the same as the base angles of the Pyramid Cross-section. Connecting the dots on the right hand side of the pentagram does NOT point to the Capitol Building.

    see fig. 4 Topography - The CB appears to have been moved slightly north because the planned location fell on the steep side of Jenkins Heights. Had the CB been further south Penn Ave would have been straight from Georgetown to the East Branch.

    see fig. 5 19.5 Degrees - Moving the CB north also moved Maryland Ave and the Jeff Mml, East Capitol Street with Lincoln Square and the Washington Monument. This determined the bearing of Virginia Avenue which is sighted on the Wash Mmt.

  • Moving the CB south would re-align everything east and south of the WH.

    see fig. 5a Straightening Penn Ave - Moving the CB so that PA was straight would put the Jeff Mml the same distance from the WH as the top of the triangle is and would bring Maryland and New York into line with the red part of the map.

  • The giant rhombus shape suggests a monument opposite to the Capitol's location.

  • The McMillan Plan

    see fig. 6 The McMillan Plan misses the rhomboid nature of the event. Nothing in the early map hints at the location of the Lincoln Mmeorial.

    see fig. 6a The misaligned Licoln Memorial is linked with the 23.5 degree diagonal grid by running New Hampshire past the Capitol's location to Arlington, then reflective back via Memorial Drive through the memorial to the center of the Ellipse.

    see fig. 7 The Pentagon is also aligned with the 23.5 degree grid.

    see fig. 7a Moving the Capitol would move the Washington Monument and Virginia Ave.

    see fig. 7b Mass Ave can be straightened by moving Lincoln Square east after moving the CB south.

    I invite you to take a quick look at two different flags and compare them to Metatron's Cube, the Confederate flag, and the rhombus grid above; one is the personal flag of the Commander-In-Chief (GW) used during the Revolutionary War and the other is the first official United States flag.

        

    As you can see the same grid is used on the flags, and stars are placed where 'lines' cross in the map figure above. The grid provides the 'regulating lines' for the flags as well as for the map. The diagonals form 30 degree angles.

    See Washington DC's Isometric Map Grid.

    The Washington Monument and Pyramid Cross Section

    see fig. 8 The Mall as designed by the McMilan Commission does not form a 'perfect cross'.

    see fig. 8a The Washington Monument is offset just like the Queen's Chamber in the Great Pyramid. New Hampshire forms the same angle as the pyramid cross section. Overlaying the two on one another reveals a close match. Except for the Capitol which appears to be north of where it should be. Note that this does not work if the monument is not offset.

    see fig. 8b If the CB had been further south the match with the pyramid image would be better.


    The Milan Cathedral Plan, the Vesica and the Map

    see milan-cathedral.jpg In 1897 William Stirling published this image accomapnied by this quote: "By the scheme before us, the geometrical figure forming the basis of the plan of the Milan cathedral is the rhombus or vesica. It is here invisibly introduced into the plan as the mystical complement of the cross." You can easily see the upright rhombus made of two equilateral triangles.

    see vesica.jpg What he is saying is that the proportions of the cathedral plan were determined by the vesica piscis or the rhombus and cross that it generates. Two equal circles that overlap one radius automatically produce equilateral triangles, rhombus and hexagons. The ratio of the long axis to the short one in this rhombus is 26:15, or 52:30. The equilateral triangles are 13 tall with a base of 15.

    The cathedral image had originally been published in 1521 by Caesarino as an example of the 'German method' of fixing the measures of a cathedral. This image shows architect Hughes Libergier holding an architectural model. He died in 1263 and the image comes from his burial crypt. Note the upright rhombus on the model.

    In the image below we can see that the cathedral plan is analogous to the DC map image, including the overlapping pentagram and hexagram inside the triangle, with the big difference being that the cathedral plan does not depict the top points of the pentagram as the map does. Daath is located in the dome, at the roof line. Note the horizontal rhombus in these images (generated by the overlapping pentagram and hexagram) and how extending the top sides of the hexagon locates the top points of the pentagon.

    This is the first published image of the Kabbalistic Tree of Life which fits both the map and the cathedral plan. Note the three columns, the cape, the cap, the model in the right hand, and compare the shape of his chair to the calipers that appear on the Libergier tomb. The tree conceptually fits inside the upright rhombus on his model. [Note that the Kircher version of the tree does not work here due to the large triangle and the pentagram. see Kircher.gif]

    Another Architect with His Model

  • see penthex.jpg The second difference between the two is that the pentagram and hexagram in the map are short and wide, and the big triangle has 52 degree base angles, not 60 as in the equilateral triangle used for the cathedral plan. In general the template for the map was shortened (from 60 to 52 degrees), so that the figure below the White House is an ellipse, not the circle that is depicted in the McMillan Plan.

    see sco_cir.jpg Scott Circle is a point in a circle in a hexagram that has been shortened. Shortening the equilateral triangle produces 23.5 degree diagonals and Scott Circle lies at the junction of Mass and Rhode Island Aves, at the top of the hexagon.

  • The Stonehenge and Cross Quarter Days

    see shng2_2.jpg The shortened hexagram from the DC map looks like this on the Stonehenge. The corners of the rectangle match the Station Stones. One of the diagonals of this rectangle at the Stonehenge aligns with the cross-quarter sunset just like the northwest segment of Penn Ave.

    Norman Lockyer, a naturalist, suggests that ancient astronomical monuments like the Stonehenge were originally sighted according to what he called the May-November year instead of to the solstices and equinoxes. The May and November dates correspond to what are known as cross quarter days that are half way between the solstices and equinoxes; the other two are in February and August. Since the sun moves more quickly through the solar arc near the equinoxes, it moves 71% of 23.5 degrees (16.6 degrees) between the equinoxes and cross quarter days at the equator.

    At the equator the cross quarter sunrises and sunsets occur 16.6 degrees north and south of due east and west. At the latitude of DC they occur at 23+ degrees. At the Stonehenge it's 28+ degrees. The pyramid of the sun in Mexico is aligned to the Aug 13 sunset which is very close. see sunpyr.gif

    . . .

    52 Degrees

    These next images show how the vesica piscis can be used to generate both the equilateral and the 52 degree triangles. Here both triangles are equal in height but if we were to scale the 52 degree triangle so that it had the same base as the equilateral triangle it would be shorter than that.

    The 60 degree triangle represents the cathedral
    while the 52 degree triangle represents the map.

    see Animation2.gif The derivation of the Tree of Life, Metatron's Cube and the cathedral plan from the original vesica shows that while the cross centers on the rhombus, the center of the triangle (where the diagonals cross) lies at Daath's location. A static version of that looks like this: see 60.jpg.

    This image shows just the upright rhombus plus the 52 degree triangle that we see above. see rhombus52.jpg The diagonals of the equilateral triangle form 30 degree angles, in the 52 degree triangle they are 23+ degrees. see vesica52b.jpg

  • see Animation3.gif The derivation of the grid upon which DC is based looks like this . All the elements are the same height as in the 60 degree model, they are just wider. Here is a simplified version of that: see grid52a.jpg

  • Ad Quadratum and Ad Triangulum

    The center circle of the cathedral plan shows an inscribed triangle, hexagon and square. The triangle and hexagon represent the ad triangulum while the square represent the ad quadratum. The DC boundary is shaped like this oblique square and represents the quadratum.

    Taking the bottom of the square and the top of the triangle gives us the Masonic Compass and Square, representing the triangulum and quadratum. The compass indicates the rhombus and the square the cross.

    This is the ideal (triangulum) template for the map which was shortened. It is basically Metatron's Cube, although you can also see the yin/yang symbol there among others. Letters and numbers as well. 1, 2, 3, 4 ...

    [Note that the sides of the triangle form the upright rhombus and the diagonals form the horizontal rhombus and the cube. Extending the top sides of the hexagon locate the top points of the pentagram.]

    The Upright Rhombus and Tree of Life
    Can Be Found Within Metatron's Cube

    John Mitchell readers will recognize this image as the source of his St. Mary's Chapel at Glastonbury and Stonehenge images. It is also the source of David Fideler's 'Three Worlds' image. Metatron's Cube is probably the source for the story in Rev 21 about the cubic city with twelve gates. Neither Mitchell or Fideler mention Metatron's Cube. The geometry on the 1935 version of the Great Seal that we find on the dollar bill relates to this template as well.

        

    In an equilateral triangle lines that bisect the corner angles also bisect the opposite sides. These three lines cross at the 'center' of the triangle. Reducing the height of the triangle so that the base angles are 52 degrees produces diagonals of 23 degrees like we see in the map. see sixpoints.jpg

    Close enough to mimic the passages in the pyramid (which are at 26+ degrees).

    Note the pentagonal fractals


    Coincidently

  • If we inscribe a hexagram in a circle, the points touch the circle at 30 degrees north and south; the same angles of the lines that bisect the corners and sides of the equilateral triangle. The Great Pyramid is located just south of 30 degrees north latitude. In Washington DC, the solar arc is just over 30 degrees north and south, so that a hexagram could be used to lay out a sun wheel there. At the equator (or a lodge) the hexagram can serve to determine the arc of all of the planets, including Mercury the most eratic. That is to say, at the equator none of the planetary bodies strays outside of a 62 degree arc, while at DC this is the arc of the sun itself.

    At the equator the solar arc is 23.5 degrees and the sun moves from 23+ degrees north of the eqiuator to 23+ degrees south of there. At the equator you need 47 degrees of free space in order to watch the sun rise or set each day. Since the moon's orbit varies 5 degrees beyond that of the sun as seen from the earth, we would need 57 degrees to see it too there.

    Mercury varies 7.5 degrees above and below the sun, so to see it we need 62 degrees of space on the horizon. This means that no planet is overhead further north than 31 degrees. Bromwell points out that we can depict this 60+ degree band 360 degrees wide as a rectangle that is 1:6 without much distortion to the map.

  • The Pyramid lies just below 30 degrees north latitude but neither it's faces nor it's cross-section is an equilateral triangle. The faces are 58 degrees and the cross section is ~52 degrees. The map illustrates that if we ruduce the equilateral traingle to 52 degrees, the 30 degree diagonals become 23.5 degrees like the tropics. The passages in the pyramid run at 26.5 degrees (about half of 52).

    The upright rhombus image above has a ratio of 26:15 for the long to the short axis (52:30), and as was pointed out, this ratio was altered three times in the map. It was also pointed out that the triangle base angles were altered from 60 to 52 degrees.

  • If the triangle in the vesica images above is 481+ feet tall, the diameter of the circle is 555+ feet (or 6660+ inches); that is, 555+ foot diameter circles produce a vesica 481+ feet tall. The Great Pyramid is 481+ feet tall and the Washington Monument is 555+ feet tall. In Greek leters were also numbers and the word 'rhombus' totals to 482


  • More about Geometry

  • Geometric Design Principles , or how the templates were applied to the DC map, ties esoteric geometry to design theory

  • DC's Isometric Map Grid , the ideal template for the map confirms the straight-line hypothesis that the Capitol was displaced

  • Doubling the Circle A drawing exercise that uses vesicas was used to design the Great Seal and much more

  • The Map and the Milan Cathedral Plan both derive from the doubling the circle images

  • Contemplating the Hexagon

  • Occult Symbolism: As American as Baseball Nine men per side, nine innings, three strikes, three outs, four balls, four bases (including home) 90 feet etc