Eternal India Encyclopedia

Ancient Concepts, Sciences & Systems

Eternal India encyclopedia

anything is likely to prove to be an underestimate by a thousand years or so. The last word has not been said.

Language, mathematics and astronomy: a chronological synthesis for the Vedic Age, in the International Journal of Indian Studies, Special Issue on the Indo-Aryan Problem. January-June 1994. A systematic study of the mathematics of the ancient world, with special emphasis on the history and chronology of Vedic mathematics. Supplies several missing details in Seidenberg’s study and corrects some errors. It also shows some possible connections between Egyptian pyramids and Vedic altars going back to 2700 BCE. 4. Swami Bharati Krishna Tirthaji (1965, 1992) Vedic mathematics. Revised edition. Motilal Banarasidass, Delhi. A fascinating and controversial book with a somewhat misleading title. This famous monograph contains many interesting resiilts that its author claims are contained in secret form in the Vedas.

SELECTED REFERENCES

1. Datta, B.B. (1993) Ancient Hindu Geometry : The Science of the Sulba. The standard reference on the Sulbas in English. 2. Seidenberg, A. (1978)

Archive for History of Exact Sciences, Vol. 18

The Origin of Mathematics, in

A monumental and definitive study establishing the connections between the

Sulbas, Pythagorean Greek, Old-Babylonian and Egyptian mathematics.

3. Rajaram, N.S. (1994)

(Dr. N.S.R)

MEDIEVAL MATHEMATICS

INTRODUCTION The Indians in ancient time recognised two types of knowledge: Aparavidya (Inferior knowledge) and Paravidya (Superior or Spiri- tual knowledge). An act of worship done with a specific worldly desire was considered an inferior form of worship and was popular with the kings. Aparavidya enables man to attain material prog- ress, enrichment and fulfillment of life and Paravidya ensures at- tainment of self-realization or salvation in life (Chand. Up.7.1.7; Munda. Up. 1.2.4-5). The Vedic people, in general, made interest- ing synthesis by adopting nitya (perpetual or daily) and kamya (optional for wish-fulfillment) sacrifices or offerings. The first was supposed to bring happiness to the family and second was to give material progress. The perpetual daily sacred fires and the optional fires were placed on altars of various shapes. As to the reasons which might have induced the ancient Indians to devise all these strange shapes, the Rigveda (1.15.12) says, “He who desires heaven, may construct falcon shaped altar, for falcon is the best flyer among the birds”. These may appear to be. superstitious fancies but led to important contributions in geometry and mathe- matics because of their conviction in social value systems. The findings for the right time for religious, agricultural, New Year and other social festivals gave the motivations for recording of repeated events from seasons, stars, movement of planets, moon etc. This helped to develop many a framework for mapping of movements of heavenly bodies with reference to East, West, North and South points, nakshatras, calendar, yuga, mahayuga and movements of planets for mean and true positions of planets. Various mathematical and trigonometrical tables were also formu- lated for better and better results. The Vedanga Jyotisa mentions as under: "Having saluted Time with bent head, as also Goddess Saraswati, I shall explain the lore of Time, as enunciated by sage Lagadha. 'As the crests on the head of the peacocks, the jewels on the serpents, so is the (jyotisa ganitam ) held at the head of all lores among all vedanga sastras'Ganita is a variant reading for Jyotisa meaning computation which is the essence of this science. Another tradition which has enriched specialized activities in mathematics and astronomy is the guru-sisya-parampara (teacher-student tradition). Different recensions of Vedic schools, Sulbakaras, Jyotiskaras ( Varahamihira gives names of 20 scholars before him), Kusumpura school, schools of Ujjain and As- makadesa, Jain and Buddhist schools also are well known in this connection.

Beside these, there were commercial and other problems which were tackled for Lokavyavaharartha, used for common people. The restriction and emphasis were also assured on social use and value systems which helped people to take up different activities for commerce, education and other areas. These helped undoubtedly to concretize knowledge resulting in original contributions to mathe- matics and astronomy.

CONSTRUCTION OF ALTARS, AND NATURE OF KNOWLEDGE

The ritual connection of Indian geometry, as elaborated by Thi- baut and Burk, has been intensively discussed by Datta, Seiden- berg, Sen and Bag, and others. The ceremonies were performed on the top of altars built either in sacrificer’s house or on a nearby plot of ground. The altar is a specified raised area, generally made of bricks for keeping the fire. The fire altars were of two types. The perpetual fires ( nitya agnis) were constructed on a smaller area of one sq. purusha and optional fires ( kamya agnis ) were constructed on a bigger area of 7-1/2 sq purushas or more, each having mini- mum of five layers of bricks. The perpetual fires had 21 bricks and optional fires had 200 bricks in each layer in the first construction and the number of bricks became more in the subsequent construc- tion with other restrictions. For optional fire altars, the whole family of the organiser had to reside by the construction site of optional fire altars, for which another class of structure known as mahavedi and other related vedis were made. However, a sum- mary of these types of altars with ground shapes are grouped below: a) Perpetual Fire Altars (Area coverage: 1 sq. purusha): Ahava- niya (square), Garhapatya (circle/square), Dakshinagni (semi- circle). b) Optional Fire Altars (Area coverage: 7-1/2 sq. purusha): Catu- rasrasyenacit (hawk bird with sq. body, sq. wings, sq. tail), Kankacit and Alajacit (bird with curbed wings and tail) Prauga (triangle), Ubhayata Prauga (rhombus), • Ratha-Cakracit (circle), Dranacit (trough), Smasanacit, (Isosceles trapezium), Kurmacit (tortoise) etc. c) Vedis: Mahavedi or Saumiki vedi (isosceles trapezium) Sautramani vedi (isosceles trapezium, and also one-third of the mahavedi), Paitriki vedi (isos., trapezium or a square, area one- third of Sautramani vedi), Pragvamsha (rectangle). One can guess the nature of knowledge which could originate from such altar constructions. However, the sulbasutras of