Samhara and shrusti krama

July 13, 2005

Dear Srividyaganithas,

There are two kramas

by which Srichakra can be approached.

The samhara krama(used by vamacharins) and the shrusti krama(used by sadacharins).

The first can be rightly called CONSTRUCTION BY ORDER OF DESTRUCTION

The second can be called CONSTRUCTION BY ORDER OF CREATION.

The above two are historical methods of constructing(drawing) a srichakra.

Beneath the historical methods are two modern methods too which have been elucidiated.

They are

1. Construction by checkerboard

2.Construction by golden angle.

Hope all members find this posting interesting.

Below is an elaborate pattern of details regarding the four constructive models.

Samhara-krama

(From commentary on Saundarya Lahari written by Kaivalyasrmam.)

Attribute to the "Left Hand Path" of Tantrism, the inward approach to meditation, starting from a circle and moving towards the center.

This technique is rather involved, resulting in slight errors at the intersections (marma-sthana) and non-congruent large triangles. This method probably accounts for most of the examples in the literature.

Animation of the Construction Requires Netscape 2+

1. Draw a circle of the required size with a vertical line through the centre and divide this line into 48 equal units.

2. On this line make nine marks at a distance of 6, 12, 17, 20, 23, 27, 30, 36, and 42 units from the top, and draw nine horizontal lines (numbered 1-9) through these marks to meet with the circle.

3. At both ends of the 1st, 2nd, 4th, 5th, 6th, 8th, and 9th lines rub off 3, 5, 16, 18, 16, 4 and 3 units respectively.

4. Join the ends of the 1st line to the centre of the 6th, the ends of the 2nd to the centre of the 9th, the ends of the 3rd to the circle at the bottom of the axis, the ends of the 4th to the centre of the 8th, the ends of the 5th to the centre of the 7th, the ends of the 6th to the centre of the 2nd, the ends of the 7th to the circle at the top of the vertical axis, the ends of the 8th to the centre of the 1st, and the ends of the 9th to the centre of the 3rd.

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Srsti-krama

From commentary on Sudarya-lahari by Laksmidhara.

Attribute to the Tantric 'Right Hand Path'. The instructions are complicated and somewhat obscure, and it is not obvious that a yantra can be constructed in this fashion without a lot of luck or an example to work from.

This method potentially results in perfect intersections (marma-sthana)

Inner eight-pointed figure

A. Draw isosceles triangle A with apex pointing down and vertical line through the apex and centre of base. Place the bindu on this line near the apex of A.

B. Above the bindu, draw hiorizontal through the sides of A to form the base of triangle B also drawn with apex pointing down.

C. Draw horizontal through apex of A to form base of triangle C with apex pointing up and sides passing through the intersections of the sides of A and the base of B.

Inner ten-pointed figure (antar-dasara):

D. Produce base of A both ways to form base of triangle D with apex pointing down and sides passing through the ends of base of C.

E. Produce base of C both ways to form base of triangle E with apex pointing up and sides passing through the ends of base of A and B.

A1. Produce sides of A to meet horizontal through apex of C.

C1. Produce sides of C to meet horizontal through apex of B.

Outer ten-pointed figure (bahir-dasara):

F. Produce base of A1 both ways to form base of triangle F with apex pointing down and sides passing through the ends of base of E and C1.

G. Produce base of C1 both ways to form base of triangle G with apex pointing up and sides passing through the ends of base of D and A1

A2. Produce sides of A to meet horizontal through the apex of E.

C2. Produce sides of C to meet horizontal through the apex of D.

Fourteen-pointed figure (caturdasara)

H. Produce base of A1/F both ways to form base of triangle H with apex pointing down and sides passing through the ends of base of G and C2. (The circle is not mentioned.)

J. Produce base of C1/G both ways to form base of triangle J with apex pointing up and sides passing through the ends of base of F and A2.

F1. Produce sides of F to meet horizontal through apex of E.

G1. Produce sides of G to meet horizonal though apex of D.

A3. Produce sides of A to meet horizontal through apex of G.

C3. Produce sides of C to meet horizontal through apex of F

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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.

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Division in Mean and Extreme Ratio

The base angle of the largest trinalges of most representations of Sri Yantra are about 52 degrees, close to the base angle of the Great Pyrmaid of Cheops, which is 51deg50'. With such a base angle, the ratio of the hypotenuse to half the base is phi, the Golden Ratio.

The design was investigated with the largest two triangles having this base angle. The construction continues similar to the 7x7 grid method. The result is striking, for apart from the fact that the error (at Z and W) is not noticeable, the overall shape is very simlar to examples from the literature. The error is only .3616% of length of the diameter. A small change in base angle results in large error - a 53 degree angle has an error of 9.125%!

1. Draw a rectangle of 2 x 1 units (ABCD) for construction of the large pyramid- angled triangles on base DC. The centre of DC is E.

2. Draw the diaganol DB. It's length is sqr-root 5, by Pythagoras.

3. Draw a circle of radius one centered at point B. Extend the diagonal.

4. Bisect the extended diaganol, creating two line segments of length sqr-root 5 plus 1, divided by 2. This length is phi!

5. Mark off the top and bottom vertices of the yantra with compass point at D and length phi, intersecting at a vertical line through E.

6. Draw the circle through these vertices, with compass point at E.

7. Draw in the largest triangles to meet the circle at their vertices. Points F and G are thereby defined. Points H and L are defined by assuming that the dista nces HJ, JK and KL are all equal. Draw LF and extend (an unknown distance). Poin ts M and N are thereby defined.

8. Draw JM down to level with L and complete that triangle. Point P is thereby d efined, and hence point Q after the horizontal is drawn in to meet HNG.

9. The horizontal through H is extended to meet the circle at R. The yantra ther efore touches the circle at eight points. RN is drawn and extended to meet the m id-line, thereby defining S. Point T is also defined, and hence point U after th e horizontal is drawn in to meet LMF.

10. Draw the horizontal at S, meeting LMF at V, and cutting JM at W. Draw W, cutt ing SN at X.

11. Draw the horizontal through X, meeting NG at Y. Draw YQ, cutting SV at Z. The error is represented by the horizontal distance between points W and Z.

12. Draw in the smallest downward pointing triangle, horizontal first.

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I find the last model very interesting and powerful as it involves the golden ratio and closely resembles what the divine couple(shiva and parvathy) enunciated to their son Skanda. The first two though historical have been drawn only by commentators who claim to have got it from older sources. They were in fact hiding certain things and did not reveal fully the secrets of construction of srichakra.

Srichakra which is not drawn to the divine measurements will not yield any result. It then becomes useless tinsel or at the best an article for decoration.

The best things in life are kept secretive.

Bindutrikonamadhya nilaye' !!

Yours yogically,

Shreeram Balijepalli

Purity, Powers, Parabrahmam...

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