Sulbasutras: Indian Texts on Sacred Geometry,
Part Two

BY: SUN STAFF


Nov 07, 2013 — CANADA (SUN) — Vedic instruction on geometric design of sacred structures and spaces, by Parameswaran Murthiyedath.


A Few Sutras

An extract from the book
with Commentary by Parameswaran Murthiyedath

Sutra 12 (Kankaciti)

Sutra 12.1
Kankacita etenatma
Puccam ca vyakhyatam

(The Kankacita defined here will have a body and a tail)

The Kankacita is known to have the shape of a heron.

Sutra 12.2
sirasi pancopadadhyat
tasyakrtirvyakhyata
sirasi pancopadadhya
ttasyakrtirvyakhyata

(the head will be obtained as 5 by definition of its shape)

As per the definition the head will be obtained as 5.

This states that the length of the head along the east west is 5 aratni from the body. With the same words a meaning that the area of the head is 5 sq. aratni could also be derived. Both meanings are true and so meant.

Sutra 12.3
Saptapancasaddaksine paksa upadadhyat
tathottare
Saptapancasaddaksinepaksa upadadhya
ttathottare

(5 and 7 to south the wing will be obtained next the north)

The wing at south will be obtained as 5 and 7and likewise the north. Again, The wing tips are at a distance of 12aratni's to south (5+7) and at the same time it means that the area of the wings are 57 sq. aratni.

Sutra 12.4

Vyayamena sapradesna paksayorapanamah
pancamabhagiyardhyabhih sat sat patrani kuryat
adhyardhavasisyate vyayamena
sapradesnapaksayorapanamah
pancamabhagiyardhyabhih
sat sat
patrani kuryat
adhyardhavasisyate

(by vyayama measure with the pradesa the wings bent with the pancami and adhyardha six and six wing cuts as stated an adhyardha will be balanced)


Figure 2: Karika city layout (BSS-12.2-6)


(The wings will be set out at a measure of 1 vyayama added with 1 pradesa at an angle and the wings tips will have six notches of a measurement of 1 pancami by 1 pancami and a half. An adhyardha will be balanced)

The configuration of the wings are made by the diagonal of a square of 108A first taken forward and then retraced to give a mirrored bent. The sutra further categorically states that the wing tips configuration is with 6 nos of 1aratni by 1 adhyardha cuts. This adds to the area of 54 sq. aratni and additional 3aratni and the statement of 57 sq. aratni are now established. The statement 'adhyardhavasisyate' is about the excess area resulted amounting to 1½ aratni in the configuration which will be later adjusted by the leg trimming of the tail.

Fig. 12.1 given here shows the citi geometry. First a basic square 1-2-3-4 will be established with side as 144A, deriving from the statement of 'saratnipradesa'. The south end of the wings from which the wing tips take off is line 9-10, parallel to1-4 and at a distance of 12 aratni (288A). Line 4-8 is the diagonal of a square of 108A as side. Line 8-9 is mirrored from line 4-8. Thus the wing formation of 4-8-9-10-13-1 is established. The six wing tips are formed by the diagonals of boxes of an aratni by an adhyardha (1½ aratni) as sides, as shown within9-10-11-12.

Sutra 12.5

taya pucchasyavastat
padavaratnimatravaratnyantaralau
pradesavyasau bhavatah
tayoravastadabhito
dvaudvavastamabhagau pragbhedavupadadhyat
taya pucchasyavastat
padavaratnimatravaratnyantaralau
pradesavyasau bhavatah
tayoravastadabhito
dvaudvavastamabhagau
pragbhedavupadadhyat

(At the backside of the tail feet of an aratni length in an aratni gap with 1 pradesa as width at the back and near as 2 and 2, and 8 sided with a forward cut will be obtained)

The tail is having a forward cut of 1 aratni length and 1 pradesa as width of sides, in a gap of 1 aratni, and thus having 8 sides split into two as forward cut.

The tail portion of 15-14-16-17 contains the details mentioned above. Thus the tail have two cuts of 1 aratni square which is modified to form the root and two such feet are placed touching each other as stated forming an 8 sided cut in total.

A statement like 'pancadasa pucche' is judiciously left out for the reason of the cut in the tail, though the overall outline agreed to such a statement. Further in sutra 12.8 the placement of two astamsi bricks at the tail to obtain this configuration are mentioned, to which the presentation here corresponds.


Figure 2: Karika city layer 1


Sutra 12.6

evam saratnipradesah saptavidhah sampadyate
evam saratnipradesah
saptavidhah sampadyate

(With only the aratni and pradesa the saptavidhah concept will be achieved)

Thus with the aratni and pradesa measures alone, the saptavidhah concept will be achieved. Indeed, the altar shape graphically feeds back an area report of exactly 7.5 times the purusam square, as could also be seen from the calculation of area given here.


Table 1: Area of Kankacit

Sutra 12.7

athestakanam vikarah
pancamabhagiyah
savayavah
padestakam caturbhih
parigrhniyadardhapradesenadhyardhapradesena


Figure 4: Karika city, Layer 2

pradesena pradesasavises eneti
adhyardhestakam caturbhih parigrhniyadardhavyayamena
dvabhyamaratnibhyamaratnisavises eneti
tah sat


Figure 5: Karika city, Bricks

Athestakanam
Vikarah
pancamabhagiyah savayavah
padestakam caturbhih
parigrhniyadardhapradesenadhyardhapradesena
pradesena pradesasavises eneti
adhyardhestakam
caturbhih
parigrhniyadardhavyayamena
dvabhyamaratnibhyamaratnisavises eneti
tah sat

Now the bricks configuration with the pancami all over with the pada square brick with surrounded (sliced) ardha and pradesa and the adhyardha and pradesa and the adhyardha and pradesa with pradesa and a modified pradesa with the adhyardha brick from a square brick with the surrounded (sliced) half vyayama by two and by aratni and aratni modified like that six.

With pancami as the basic brick allover with the pada of a square brick, and the ardha, the adhyardhardha and pradesa sliced, the vyayama and the aratni sliced, the modified aratni consisting 6 bricks will be used.

However, some more bricks are found required and the lists of bricks are as given below:

Sutra 12.8

tasam
caturasrapadyah
sastamabhagah
padayorupadhaya
sesam yathayogam
yathasamkhyam yathaadharmam
copadadhyat

with these the caturasrapadyah and 8 divided part at the wings having placed balance as required in as many numbers as per rules be placed

The caturasrapadyah and the astamsi bricks having placed as the feet, the balance will be filled with the required numbers as per rules.


Table 2: Kanchita Bricks


Parameswaran Murthiyedath is a scholar of Vedic Mathematics. From "Kriti Rakshana", National Mission for Manuscripta.




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