Vedic
Mathematics
Sulba
Sutras
The Sulba Sutras or Sulva Sutras are texts
of the Hindu canon dealing with the geometry
of altar construction. They are parts of
larger works called Dharma Sutras which
are appendices to the Vedas elaborating
sacrificial rituals, the conduct of marriage,
the sacred law and such. The Sulba Sutras
are our only source of knowledge of Indian
mathematics of the Vedic period.
The name "Sulba Sutra" means rule
of chords, which is another name for geometry.
Of the Sulvas so far 'uncovered', the four
major and most mathematically significant
are those composed by Baudhayana, Manava,
Apastamba and Katyayana. These Sulba Sutras
have been dated from around 800500 BC and
include first 'use' of irrational numbers,
quadratic equations of the form ax2 = c
and ax2 + bx = c, unarguable evidence of
the use of the Pythagorean theorem and Pythagorean
triples, predating Pythagoras (c 572  497
BC), and evidence of a number of geometrical
proofs.
Pythagoras's theorem is first found in the
Baudhayana sutra—so was hence known
from around 800 BC. It is also implied in
the later work of Apastamba, and Pythagorean
triples are found in his rules for altar
construction. One of the Sulba Sutras estimates
the value of pi as 3.16049. Altar construction
also led to the discovery of irrational
numbers—a remarkable estimation of
the square root of 2 is found in three of
the sutras. The method for approximating
the value of this number gives the following
result:
The result is correct to 5 decimal places.
Elsewhere in Indian works however it is
stated that various square root values cannot
be exactly determined, which strongly suggests
an initial knowledge of irrationality.
Indeed an early method for calculating square
roots can be found in some Sutras, the method
involves repeated application of the formula:
Before the period of the Sulbasutras was
at an end, the Brahmi numerals had definitely
begun to appear (c. 300BC) and the similarity
with modern day numerals is clear to see.
More importantly even still was the development
of the concept of decimal place value. Certain
rules given by the famous Indian grammarian
Panini (c. 500 BC) imply the concept of
the mathematical zero.
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Vedic mathematics is a system of mental
calculation developed by Shri Bharati Krishna
Tirthaji in the middle 20th century which
he claimed he had based on a lost appendix
of Atharvaveda, an ancient text of the Indian
teachings called Veda. It has some similarities
to the Trachtenberg system in that it speeds
up some arithmetic calculations. It claims
to have applications to more advanced mathematics,
such as calculus and linear algebra. The
system was first published in the book Vedic
Mathematics ISBN 8120801644 in 1965. The
system has since been developed further
and there have been several other books
released.
