a brief look at the measurement methods and measurement units in sulbasutras

8/13/2019 A Brief Look at the Measurement Methods and Measurement Units in Sulbasutras

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National Se

minar on Gemetrical Conceptsin Sulba Sutras

Sri Venkateswara Vedic UniversityTirupati

27-28 December 2013


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A brief look at the measurementmethods and units ofmeasurement in Sulbasutras

M Rajagopala Rao*;

Dr. RVSS Avadhanulu**


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About the Authors

M Rajagopala Rao, M.Sc.(Tech.)-GeophysicsExecutive Director-Chief Knowledge Officer(Retd.), ONGC

Principal Coach, Success With Self (SWIS),Hyderabad

ONGC Project Saraswati

Piligramage to Kailash-Mansarovar twice Conducting classes at DAV schools in

Hyderabad


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About the Authors

Dr. RVSS Avadhanulu, M.Sc.(Nuclear Physics),M.A.Ph.D.(Sanskrit), M.A.Ph.D.(Jyotisha),

Dy. Director (Computers)(Retd.), NIMS,Hyderabad,

Managing Trustee & Chief Executive, Shri VedaBharati, Hyderabad

PioneerIndian Languages on Computers

Introduction of computer technology to Vedas Golden Nandi award for Veda Ganitam on TV

Research on Science in Vedas


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Sulba

The meanings of ulva or ulba are string,code, rope, copper, sacrificial act andconduct.

basically means to mete or to create.

laying out of temple and the measurementand construction of altars took the form of a

body of knowledge known as theulvastras or rules of the cord.


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Sutra

One of the most famous definitions of a sutrain Indian literature is itself a sutra and comesfrom the Vayu Purana

Of minimal syllabary, unambiguous, pithy,comprehensive,continuous, and without flaw:who knows the sutra knows it to be thus.


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Sulbasutras - part of Vedic Literature

Vedga of six kindsKalpa (rituals), ik (phonetics),nirukti (etymology), vykaraa

(grammar), candas (prosody), jyotia(astrology).

Kalpa vedga - four groupsrautastra, ghyastra,dharmastra andulvastra.


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Sulbasutras - part of Vedic Literature

ulvastra: Mathematical theories and thearchitectural methods to build altars

Srautastra:Descriptions of great sacrifices

Ghyastra: Daily domestic sacrifices

Dharmastra: Instructions for the worldly life andsupra mundane life


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Subject matter of Sulbasutras

Sulbasutras are not books of geometry.

Information of geometry given in them islimited as a utilitarian material for theaccurate layout of Vedisetc.

They are finely crafted, integrated manualsfor the construction of citisor ceremonial

platforms

Certain key words, however, suggest thatthe applications go far beyond this.


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Number of Sulbasutras

According to tradition Nrada, Kapila, Lagadh,pastambha,

Katyyana, Baudhyanaetc. are ancient

mathematiciansTen ulvastras found KtyyanaShukla Yajurveda

Baudhyana,pastamba, Mnava, VarhaMaitrya,, VadhlaKrishna Yajurveda Maaka, Satyha, and Hirayake


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Dates for Sulbasutras

Earlier Researchers held that

Sulbasutra writtenby Vedic Hindus

starting before 600 B.C. suffix yana to the end indicates

editors or compilers

compilations of oral wisdom that maygo back to 2000 B.C.


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Dates for SulbasutrasNew research

Aryan invasion (1500 BCE)Not tenable theory

Extensive scientific exploration of Paleo- RiverSaraswati

Geological, Hydrological, Climatological, RemoteSensing, Genetic and Archeological studies arepointing at continuity in civilization

Eastward migration on drying up of Saraswatiaround 5000 years ago

May push back the dates for Vedas andthence Sulbasutras


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Some constructions in Sulbasutras

Square of side of given length

Square equal to sum of two unequalsquares

Square equal to difference of twosquares

Square equal to a Rectangle

Circle equal to a square

Square equal to a circle


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Baudhayana Verse I,50

Suppose the two given squares are ABCDand EFGH with AB > EF. Mark off points J, Kon AB and DC with AJ = DK = EF. Then the

line AK is the side of the required square.

To construct a square equal to the sum oftwo unequal squares.


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Use of the constructionsCreating equal area Vedis for

Garhapatyasquare

AvahaneeyaCircular

DakshinagniSemicircular

Fire altars

fromKalibangan2900 BC


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Geometric Theorems and Arithmatic values

Value of 2 (dwi-karani)

'square to circle, 'circle to square' and'square root of two' constructions fittogether with an accuracy of 0.0003%


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The Syena Citi

Layers 1, 3 and 5 Layers 2 and 4


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The Kurma Citi



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The Rathacakra Citi



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Standardised units

angulawas used as standard unit formeasuring lengths of different vedis,

mandapas etc.purusawas used as standard formeasuring lengths of citis.

All other units are derived from thesetwo.


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Units of measurement

agula length of the middle section of the middle finger

of the sacrificer Bodhayana: Length of fourteen grains ofAnu

(Panicum Milliaceum) or that of 34 grains ofSesamum when placed in contact with each otheralong their width.

Manava:(in case height of sacrificer shorter thanstandard purusha)6 lotus stalks equal hair ofthree year old heifer. 3 such hairs equal a mustardseed. 2 mustard seeds equal a grain of barley. 6

such barley grains put together sideways is angula


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Units of measurement

Purusha:

The length from tip of the toe to the tip of

the middle finger of the palm of sacrificerstanding on his toes, arms up stretchedover the head

120 angula = 5 aratnis = 1 vyama


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Other unitsPadam:

Toe to heel = 15 angulaPrakrama:

toe of front foot to heel of back foot when

two feet joined together =2 padams= 30angula

Samya(bahu):

36 angula

Vyayama :

Length from tip of middle finger to tip ofmiddle finger of out-streached hands = 96

angula


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Wh l ti t


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Why measure relative toSacrificer?

May be to facilitate performance ofritualistic acts on the vediby sacrificer

How the relative measures and thestandard measures reconciled?

Could be referring to some other realm

within the sacrificer

Wh t i th i ifi f


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What is the significane ofshapes chosen for citi

Why hawk, tortoise, wheel?

Why accurate sizes and relative

proportions emphasized?Why constant area irrespective ofshape?


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Is it only the physical ritual?

etymology and phonetics of terminologysuggest deeper significance

Citiclose to cit(conciousness)Vedi - one who knows (from vidtoknow)

Purushathe uninvolved witnessingquality of intelligence


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ReferencesGeometry According to Sulbasutras, 1983, Dr. R P

Kulakarni, Vadika Sansodhana Mandala, Pune

Square Roots in the Sulbasutra, David W.Henderson, Department of Mathematics, Cornell

University, Ithaca, NY, 14853-7901, USA (e-mail:[email protected])

Visualizing Time and Constructing Temples --Two Projects in Ethnomathematics, Jennifer

Wilson, Department of Natural Sciences andMathematics, Eugene Lang College the NewSchool for Liberal Arts
mailto:[email protected]:[email protected]


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ReferencesThe Lost River, MICHEL DANINO

http://www.dailypioneer.com/Sundayedition/sundayagenda/cover-story-agenda/103111-the-lost-river.html , SATURDAY, 20 OCTOBER 2012

GEOMETRICAL STRUCTURES IN BAUDHAYANA &APASTAMBA SULBASUTRASppt - Dr. P.Venkatachalapathi, Rashtriya SanskritVidyapeetham, TirupatiA.P.

Katyayana Sulba Sutra, 1974, Ed. S D Khadilkar,Vaidika Sansodhana Mandala, Poona
http://www.dailypioneer.com/sunday-edition/sundayagenda/cover-story-agenda/103111-the-lost-river.htmlhttp://www.dailypioneer.com/Sundayedition/sundayagenda/cover-story-agenda/103111-the-lost-river.html%C2%A0%E2%80%A6http://www.dailypioneer.com/Sundayedition/sundayagenda/cover-story-agenda/103111-the-lost-river.html%C2%A0%E2%80%A6http://www.dailypioneer.com/Sundayedition/sundayagenda/cover-story-agenda/103111-the-lost-river.html%C2%A0%E2%80%A6http://www.dailypioneer.com/Sundayedition/sundayagenda/cover-story-agenda/103111-the-lost-river.html%C2%A0%E2%80%A6http://www.dailypioneer.com/Sundayedition/sundayagenda/cover-story-agenda/103111-the-lost-river.html%C2%A0%E2%80%A6http://www.dailypioneer.com/Sundayedition/sundayagenda/cover-story-agenda/103111-the-lost-river.html%C2%A0%E2%80%A6http://www.dailypioneer.com/Sundayedition/sundayagenda/cover-story-agenda/103111-the-lost-river.html%C2%A0%E2%80%A6http://www.dailypioneer.com/Sundayedition/sundayagenda/cover-story-agenda/103111-the-lost-river.html%C2%A0%E2%80%A6http://www.dailypioneer.com/Sundayedition/sundayagenda/cover-story-agenda/103111-the-lost-river.html%C2%A0%E2%80%A6http://www.dailypioneer.com/Sundayedition/sundayagenda/cover-story-agenda/103111-the-lost-river.html%C2%A0%E2%80%A6http://www.dailypioneer.com/Sundayedition/sundayagenda/cover-story-agenda/103111-the-lost-river.html%C2%A0%E2%80%A6http://www.dailypioneer.com/Sundayedition/sundayagenda/cover-story-agenda/103111-the-lost-river.html%C2%A0%E2%80%A6http://www.dailypioneer.com/Sundayedition/sundayagenda/cover-story-agenda/103111-the-lost-river.html%C2%A0%E2%80%A6http://www.dailypioneer.com/Sundayedition/sundayagenda/cover-story-agenda/103111-the-lost-river.html%C2%A0%E2%80%A6http://www.dailypioneer.com/Sundayedition/sundayagenda/cover-story-agenda/103111-the-lost-river.html%C2%A0%E2%80%A6http://www.dailypioneer.com/Sundayedition/sundayagenda/cover-story-agenda/103111-the-lost-river.html%C2%A0%E2%80%A6http://www.dailypioneer.com/Sundayedition/sundayagenda/cover-story-agenda/103111-the-lost-river.html%C2%A0%E2%80%A6http://www.dailypioneer.com/Sundayedition/sundayagenda/cover-story-agenda/103111-the-lost-river.html%C2%A0%E2%80%A6http://www.dailypioneer.com/sunday-edition/sundayagenda/cover-story-agenda/103111-the-lost-river.html


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If the chair permits

any questions andcomments


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Thank you :

a brief look at the measurement methods and measurement units in sulbasutras

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