Washington DC's Isometric Map Grid
A Circle and a Square The images below illustrate how a different version of the above glyph is derived from the square and circle rather than from the vesica. The angles featured here are 45 and 26.5 degrees. [Note that the length of the diagonals of the rhombus in the figure below are in the 2:1 ratio to one another; those in the rhombus derived from the vesica are 15:26.] A circle inscribed in a square touches at four points generating an equal armed cross; here we emphasize the square and cross. Intersecting diagonals of the rectangles quarter the arms of the cross in two planes allowing us to complete the orthogonal grid in blue. (Compare to the last page.) Here we add more diagonals (left). Where these cross on vertical axes mark the seven points of a hexagon/cube. Note the five nodes on the middle pillar where the red lines cross where blue lines meet. Next we line up from the mid point at the top, across the corner of the hexagon/cube to where the second blue line up on the right marks the Capitol's location. This and the line on the left side form a triangle and help locate the top corners of the pentagram. Note how the pentagon and hexagon overlap producing a rhombus. Remember that the vesica features 30-60-90 triangles where the sine is .5. The triangles in the square have a 26.5 degree acute angle, the tangent of which is also .5. The aspect ratio is different in the two meaning that the square version above does not fit the map exactly, although it looks very much the same. Continue

Washington DC's Isometric Map Grid

A Circle and a Square
The images below illustrate how a different version of the above glyph is derived from the square and circle rather than from the vesica. The angles featured here are 45 and 26.5 degrees. [Note that the length of the diagonals of the rhombus in the figure below are in the 2:1 ratio to one another; those in the rhombus derived from the vesica are 15:26.]

A circle inscribed in a square touches at four points generating an equal armed cross; here we emphasize the square and cross. Intersecting diagonals of the rectangles quarter the arms of the cross in two planes allowing us to complete the orthogonal grid in blue. (Compare to the last page.)

Here we add more diagonals (left). Where these cross on vertical axes mark the seven points of a hexagon/cube. Note the five nodes on the middle pillar where the red lines cross where blue lines meet.
Next we line up from the mid point at the top, across the corner of the hexagon/cube to where the second blue line up on the right marks the Capitol's location. This and the line on the left side form a triangle and help locate the top corners of the pentagram. Note how the pentagon and hexagon overlap producing a rhombus.

Remember that the vesica features 30-60-90 triangles where the sine is .5. The triangles in the square have a 26.5 degree acute angle, the tangent of which is also .5. The aspect ratio is different in the two meaning that the square version above does not fit the map exactly, although it looks very much the same.

Continue