Construction of Shrichakra

[Guest guest]

My friend and I had a discussion on this topic sometime ago. He

summarized the same in the below discussion, which I am attaching.

Unfortunately I cannot append the figures.

 

Much has been said about this topic and it has been technically

discussed by a variety of authors. The shrI chakra is one of most

intricate and geometrically complex (that is in terms of precise

construction) in the entire tantric parlance and stands apart from

most other yantra-s in the tantric sphere. In popular discourse we

often hear of the methods of the famous shrIvidyA adepts namely that

of kaivalyAshrama and that of lakShmIdhara to construct the shrI

chakra. Of these, kaivalyAshrama’s is an approximation that results in

inaccuracies of the marma-sthAna-s. Thus, it is not a real

construction method, but probably an attempt to copy a real perfect

yantra resulting in an approximation. Either, the otherwise learned

kaivalyAshrama was unaware of the genuine method of construction, or

mere wanted to provide a rough and ready means of drawing it. On the

other hand, lakShmIdhara’s method is too vague to successfully

reproduce even an approximate version of the yantra. lakShmIdhara’s

explanation of the marman-s suggests that his knowledge of the

construction of the yantra was perhaps tentative. This observation

might imply that by the medieval period the actual method of accurate

construction of the yantra might not have been common knowledge

amongst certain tantric authorities. I was puzzled by this issue

because: 1) errors in the marman-s are not tolerated in tantric

practice †" more erroneous the yantra less or negative are the results,

just like inappropriate application of the pa~nchadashi can have

disastrous effects on the practitioner. 2) Throughout the medieval

period very accurate shrI chakra-s were produced in both North and

South India, suggesting that the knowledge of accurate production of

the yantra had survived over large parts of India, inherited from a

single ancestral source. For example, very accurate samples can be

seen in several South Indian temples and maTha-s (like Shringeri).

 

I noticed that some well-versed sthApati-s as well as women

well-versed with production of ranga-rekhA-s had means of producing

this yantra from reasonable to high degree-s of accuracy. From the

time of my introduction to the shrI chakra I was keen on being able to

construct it with 100% accuracy. It became apparent that, as pointed

by certain researchers like G. Huet and CS. Rao, there are multiple

solutions that meet the defining constraints of the shrI chakra in

terms of the contacts of the triangles and the intersections of 3

lines. There of course remained the question if there was one ideal

form of the yantra. From the view point of aesthetics, as well as the

viewpoint of some pristine versions possessed by smArta-s from the

drAviDa country, it became clear to me that the version incorporating

the Golden ratio (phi) triangle and the 3-4-5 triangle is the ideal

one. Thus, the largest shiva triangle (the shrIkaNTha-1) has the

isosceles sides = phi and base = 2 units. The largest shakti triangle

(the shiva-yuvati-1) is a combination of two 3-4-5 right triangles

which are welded along the 4 side to produce a triangle with the

isosceles sides being the 5 sides of the parent 3-4-5 triangles. The

radius of the circle that encloses the 9 triangles (a circumcircle of

both the Golden ratio triangle and the 3-4-5 derived triangle) is

((phi)^3/2)/2. The distance from the bindu (circumcenter of the Golden

ratio triangle) to its base is ((phi)^-3/2)/2. The height of this

shrIkaNTha-1= (phi)^1/2. Thus the shrI chakra encodes not only the

value of phi but also its multiple fractional powers.

 

R had asked me more than once whether the yantra could be constructed

using just a compass and a straight edge. Seeing how the women draw

their ranga-rekhA it became clear that a topologically accurate shrI

chakra could be constructed using just a compass and straight edge by

inscribing a dodecagon in a starting circle and then connecting

specific points to get the base of the shiva-yuvati-1 and then

shrI-kaNTha-1. This method yields the secant of the isosceles angle of

shiva-yuvati-1 to be 1.62, which is the Golden ratio rounded off to 2

decimal places. In this method the ratio of the height to the base of

½ of the shiva-yuvati-1 is 1.3. This is the ratio 4/3 of the ideal

3-4-5 triangle correct to 1 decimal place. It is interesting to note

that this dodecagon method not only produces a topologically perfect

exact version of the yantra but also so closely approximates the ideal

angular constraints. I realized that a construction method based on

dodecagon inscription was published on the web by a certain Michael

Pudney.

 

The version with the ideal angular constraints that is (Golden ratio

and the 3-4-5 triangle) can also be easily drawn with a compass and

straight-edge. I attempted this construction with the free geometry

construction simulator program C.a.R (seen below) and compared it with

a similar construction of the dodecagon method. A comparable

construction, albeit assuming several steps, has been published nearly

2 decades ago by Patrick Flanagan. Both produce very similar perfect

yantra-s that resemble the pristine samples from different parts of

India. The net conclusion of this exercise is that even in the

medieval period, we did have methods of shrI-chakra construction that

were far more accurate than that provided by kaivalyAshrama. They

appear to have been most possibly based on the dodecagon method.

 

Another aspect of all this is that the Hindus have been said to

possess a lower level of geometric awareness relative to their Greek

cousins by many scholars. But the encoding of the phi and its

properties as well as the 3-4-5 triangle in the shrI chakra suggests

that founders of the shrI kula stream were actually holders of that

“missing†tradition of constructional geometry comparable to that of

the yavana-s amongst the Hindus. It should be noted that the same type

of Golden ratio triangle has been incorporated into the yantras of

bAlA and kurukullA, who are major deities of shrI-vidyA practice.

Likewise, phi appears again in certain other yantras like those of

mAtangI or uchChiShTa chANDAlinI.

 

The Golden ratio and the 3-4-5 triangle amongst the Hindus might

actually have earlier antecedents. The 3-4-5 triangle is already

provided by baudhAyana in his sulba sUtra. The golden ratio appears to

emerge in a trapezoidal brick used in the vedi contruction. Thus, the

original construction of the shrI chakra might primarily draw upon the

ancient aspects of Hindu practical geometry.

[Guest guest]

Please read the book - " SRICHAKRA-A LINEAR APPROXIMATION TO A NON LINEAR

REALITY " by my brother PROF.Venkata GKM Pisipati to understand SRI CHAKRA from

both spiritual & architecture angles.

 

dr.p.r.k.prasad

 

 

 

 

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