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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
Layers 1, 3 and 5 Layers 2 and 4
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The Rathacakra Citi
Layers 1, 3 and 5 Layers 2 and 4
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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]8/13/2019 A Brief Look at the Measurement Methods and Measurement Units in Sulbasutras
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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.html8/13/2019 A Brief Look at the Measurement Methods and Measurement Units in Sulbasutras
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If the chair permits
any questions andcomments
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Thank you :