Eternal India Encyclopedia

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.

SELECTED REFERENCES

Datta, B.B. (1993)

Ancient Hindu Geometry

: The Science of the Sulba.

The standard reference on the Sulbas in English.

Seidenberg, A. (1978)

The Origin of Mathematics, in

Archive for History of Exact Sciences,

Vol. 18

A monumental and definitive study establishing the connections between the

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

Rajaram, N.S. (1994)

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

the

guru-sisya-parampara

(teacher-student

tradition).

Different

recensions

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.

Ancient Concepts, Sciences & Systems

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.

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.

(Dr. N.S.R)

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:

Perpetual Fire Altars

(Area coverage: 1 sq. purusha):

Ahava-

niya

(square),

Garhapatya

(circle/square),

Dakshinagni

(semi-

circle).

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.

Vedis:

Mahavedi

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

MEDIEVAL MATHEMATICS