The Hindu News ( Nov.25th 1984 ) and Alexy Pavlovich Kulaichev Research Paper
Alexy Pavlovich Kulaichev’s Research Paper Moscow University, USSR - (1984)
Sri Yantra was found to be used in and by Buddhist religion, Vedic period, Pharaohs of Egypt and has been proved from various sources, which are collected from the past.
This ancient Geometry [Yantra] proves to be connected with the Government Ruling authority from the past till today. Information about this Ancient geometry will be continued in the next issue.
“ANCIENT GEOMETRY IS AN OCEAN AND GEOMETRY IS A PART OF IT”
Indian Journal of Science 19 (3:279-292 (1984)
SRI YANTRA AND ITS MATHEMATICAL PROPERTIES
Alexy Pavlovic kulaichev Biology Faculty of Moscow University, Moscow USSR
(Received 29 July 1983)
The SRIYANTRA (the great or supreme Yantra) is the ancient geometrical Portrayal and its belongs to the class of objects (Yantra) which are used for Meditation in various school of tantrism. The process of precise reproduction of the Sri Yantra central seal (14-angled polygon composed by intersection of 9 Triangles) is a highly difficult problem which is above the capacity of hand drawing because of requirement of precise super position of numerous points of intersection. On the other hand, the task of general analysis of the Sri Yantra seal is linked with such volume of calculations which is very far from the power of modern computers.
The paper includes data of structural and analytical investigation of the Yantra seal, the classification of available specimens and analysis of its frequency- and-time spreading. On this data is based the theory about the existence of ancient spherical origin of the Sri Yantra seal. In this case, the more simple and more contemporary specimens may have been produced by a century old accumulation of errors in successive reproduction of this prototype. In the conclusion it is emphasized that a deeper study of this complicated and relatively unknown phenomenon requires co-operation of specialists from different fields of knowledge.
INTRODUCTION
From the ancient world we can find out examples of some cultural achievements, which, at first sight, may appear to have used very high mathematical knowledge much above the capacities of the ancient culture. The investigation of such phenomenons may lead us to discover the cultural and historical alternatives of the mathematical knowledge and help us to understand more deeply the significance of the world's scientific-and-technological progress. One of such unique objects in the Sri Yantra (The great or the supreme Yantra) of Indian Tantric tradition. The mathematical properties of this Yantra is very Complicated and its Interpretation is linked with very deep Cosmogonic and psychophysiological concepts.
The Sriyantra belongs to the class of objects (yantra) which are used for meditation in various schools of Tantrism. One of the earliest known specimens is the portrait of the Sriyantra in the religious institutions. Sringari matha established by the famous philosopher Sankara in 18th century A.D . Therefore , the Sriyanta has already covered a long path of confirmation as an important object for rituals. Thus the hymn from Atharva Veda( ie. 12th century B.C) is dedicated to the Sriyantra- like figure composed of 9 Triangles.
Three Questions? From AP. Kulaichev, Moscow Univesity Of the Union Of Soviet Socialist Republic (USSR)
Alexy Pavlovich Kulaichev’s Research Paper Moscow University, USSR - (1984)
We apply the suitable limitations on the loose-parameters(on coordinates C,D), any required value of a ratio between the chosen sides of triangles would be achieved.
CONCLUSIONS
From our discussion we find that the precise construction of the hypothetical spherical prototype III of the Sriyantra Seal and the real plane II-type specimens,not to speak of their design would involve a very high level of the mathematical knowledge.
As we know, the Medieval and Ancient Indian Mathematicians did not possess knowledge of higher mathematics, even at its golden period (7to12 century A.D) of outstanding achievements. One of the possible ways to solve this Paradox is to suppose the possibility of existence of unknown cultural-and historical alternative of mathematical knowledge, e.g. The highly developed tradition of the special imagination.
The Sriyantra, as shown here, is a very complicated and many-sided object and for its deep study it is required to apply efforts by specialists from different fields of knowledge: Mathematics, History, Ethnography, Psychology, Philosophy, etc.
NOTES AND REFERENCES
A description of the Sriyantra may be found in different Tantric texts: Tantraraja Tantra.ed.J.Woodroffe, Madras 1954 ;Soundarya-lahari ed.Anantakrsna Sastri, Madras, 1957;Karmakala-Vilasa.ed.J.Woodroffe,Madras, 1953;Bhavanopanisad.tr.S.Mitra,Madras,1976;GanDharva Tantra .ed .R.C.Kak and H.Shastri, Shrinagar, 1934;Nitvas odaSikarnava.with com .Sivananda,Banaras,1968;Sakta Upanisads.tr.A.G.Krishna Warrier ,Madras , 1967;and others.
J.Casparic.selected inscriptions from 7th to 19th century.Bundung , 1956;p.30,34,41.
Atharva veda ,X , v. 31-4,tr.S.Shamasastry in :The Origin of the Devanagari Alphabets,Varanasi, 1973.
More deep notion about the ritual signification of the Sriyantra may be received from the excellent monograph by Madhu Khanna:Yantra :the tantric Symbol of cosmic unity.London 1975.
This classification does not include some portrayals with obvious errors,e.g.tops of triangles do not connect with horizontal lines.
Nicolas J. Bolten, D.Nicol Mac leon..The Geomentry of the Sriyantra ,Religion, London,v.7,N1,1977.P.H.Pott.Yoga and Yantra. .Nij Hoff ,1966.
Bolton and Macleod, op.cit., and Pott, op.cit.
The reproduction of Convex surface, see in:Madhu Khanna, op.cit.
Fig 8 is represented from the specimen of Philip Rawson. Tantra. the Indian Cult Ecstacy. London 1973.
These three portrayals are in:Madhu Khanna, op.cit., and Nic Douglas, Tantra yoga. New Delhi, 1971.
Similar attempts(In respect to golden proportion and number [pie] )have been undertaken in:Bolton and Mac leod, op.cit., which is the only, we know, research of the Sriyantra as a mathematical object.
The Letter From Vice-Consul of Consulate General of the USSR in Madras
The Hindu, Monday, January 11, 1999
