Construction by Checkerboard

# Seven by Seven Grid

By Bolton and Macleod

When the Sri-yantra is first examined it soon becomes clear that a number of parameters must be fixed before it can be constructed. The design was first investigated with the assumption that it could fit into a square which it touched at six points with the vertices of the two largest triangles. These triangles, which are assumed to be equal in size, must be drawn first, and it then remains to fix three other points, viz. E, F and L (Figure 2).

The simple technique within a 7x7 square, a common motif in Indian Art, results in an error of only .2229 % of the length of side of the construction square. The error is a points U and P, not visible due to the pixelization.

Animation of the Construction Requires Netscape 2+ Nomenclature shown on one side only.

1. Define the square. (The vertices are indicated.)

2. Draw in the two largest triangles such that points A and B are one unit from the centre of the side of the square. Points C and D are thereby defined. Define points E and F; mid-line, one unit inwards. Draw FC and ED and extend about one unit. Points G and H are thereby defined.

4. Draw J H to level with F. Point K thereby defined. Draw horizontal through po ints K to meet E G D.

5. Define point L: mid-line, half a unit down from the centre. Draw L G to level with E; thereby defining Draw horizontal through points M to meet F H C.

6. Draw horizontal through L to meet F H C at N. Note that N L and J H K cross a t P. Define point Q and draw QN. Point R is thereby defined.

7. Draw horizontal through points R, meeting E G D and S. Define point T and dra w S T, cutting N L at U. The error of the diagram is represented by the horizont al difference between points P and U on the line N L.

8. Draw in the smallest triangle, horizontal first.