Geometry and Construction of
Fire Altars in Ancient India
Shobha Bagai
ILLL
University of Delhi

1
GEOMETRY AND CONSTRUCTION OF FIRE ALTARS IN ANCIENT INDIA
Construct a square with the same area as a
given circle using only a compass and a straightedge.
From our school geometry knowledge we know that if
the radius of the circle is one unit then the side of the
square must be
√π
.
But imagine encountering this problem when people had
only a rope to serve as a straightedge and a compass. It
has now been established that this problem cannot be
solved. But the Aryans in the Vedic period had solution
to construct a square whose area is nearly equal to the area of the given circle.
INTRODUCTION
The basis and inspiration for the ancient Indian
mathematics
is
geometry.
The
first
use
of
mathematics was in the
Indus valley
and dates
back to 3000 B.C. Excavations at Mohenjodaro
and
Harappa
present
knowledge
of
basic
geometry.
In 2000 B.C. the Aryans invaded and destroyed
the Harappan culture. They founded the Vedic
religion. During this age (known as the
Vedic
period
), the Vedas, the oldest sacred texts of
Hinduism were composed. The four Vedas were
1.
Rigveda
, containing hymns to be recited by the chief priest
2.
Yajurveda
, containing formulas to be recited by an official priest
3.
Samaveda
, containing formulas to be sung by a chanting priest
4.
Atharveda
, collection of magic spells and healing charms
The only source of knowledge of Indian mathematics from the Vedic period are the
Shulba Sutras
. They are a part of a larger text
Shrauta Sutras
, appended to the
Vedas. The word '
shulba
' is derived from the Sanskrit root '
shulb'
meaning 'to
measure' and hence its etymological significance is 'measuring' or 'act of
measurement'. Geometry was also known as
ʻ
Rajju
ʼ
. The word '
Rajju
' literally means
a 'rope' or an instrument of measuring. Therefore the rules of geometry were known
as
'Shulba-Sutra'
, the Sanskrit word 'sutra' meaning an 'aphorism' or a short rule.
Excavated ruins of Mohenjo-daro, Pakistan [
link
]

2
The only instruments used for measurements were
chords with knots
and
bamboos with cuts
. With the help of these a wealth of mathematics was produced,
all required for the preparation of fire altars. The fact that these altars were
considered sacred might have led to great emphasis on the accuracy in
measurement right down to details of construction.
Eight of the
Shulba Sutras
have been traced which are as follows:
•
Baudhyayana
•
Vadhula
•
Apastamba
•
Hiranyakesin
•
Manava
•
Varaha
•
Laugaski
•
Katayana
All these are named after the authors belonging to different schools. Out of these,
Baudhyayana, Apastamba, Manava and Katayana
have been translated and an in
depth study of them conducted
.
SHULBA SUTRAS
Number of geometrical results is either explictly mentioned or clearly implied in
the construction of the altars of the prescribed shape and sizes in the
Shulba
Sutras
. Some of the important ones are
1.
The quadrilateral formed by joining the midpoints of the sides of the
rectangle is a rhombus whose area is half of that of the rectangle.

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- Fall '09
- Math, Geometry, Pythagorean Theorem, triangle, equal parts, Indian mathematics