The earliest material evidence of Indian mathematics is found
among the ruins of the Harappa civilization, dated at the start
of the third millennium B.C. An elaborate system of weights and
measures related to binary and decimal series' has been brought
to light. A notable feature of the Harappa culture was its use
of kiln-fired bricks. These provide a link between the "frozen"
geometry unearthed by archaeologists and the earliest written
geometry, a guide to constructing Vedic brick altars.
TheSulbasutras and theSathapatha Brahmana contain valuable
information about the geometry of ancient India, including
instructions for constructing sacrificial altars (vedi) and
locating sacred fires (agni). The altars used during Agnicayana,
a 12-day ceremony, are especially interesting in terms of
geometry. The procedures described for their construction
involve methods for approximating the values for the square roots of 2 and 5.
One of the most elaborate public altars was shaped like a giant
falcon poised for flight. Its shape and construction were
minutely prescribed, while its height could be varied for special
occasions. Mathematical problems of its construction involved
finding a square equal in area to two or more given squares, and
converting other geometrical shapes into a square of equal area,
or vice versa. Solutions were achieved through the principle of
dissection and reassembly and ingenious algorithms, including the
so-called Pythagorean theorem.
There is a view that Indian mathematics originated in the service
of religion, but the magicoİreligious beliefs surrounding the
Vedic rituals may be overly emphasized when considering the
origins of Indian mathematics. The rituals associated with the
construction of fire altars may be looked at from two
standpoints. The first is from the standpoint of the beliefs
connecting the shapes of altars with the specific desires to be
fulfilled by their use in the sacrifices. The second is that of
technology pure and simple: How exactly were the altars
constructed to conform to specifications for shapes, sizes and
number and types of bricks.
Where are the origins of geometry in India? One hypothesis
suggests that it must have come into being when there was already
an advanced form of brick technology with a long tradition behind
it. One may speculate that the geometry eventually codified in
the Sulbasutras could have come down from the Harappan period.
If this is so, the first and earliest discontinuity in the
chronology of Indian mathematics has been filled with the
assistance of bricks.
