2. THE ANCIENT HINDU MATHEMATICS
• Oldest and most complex in the world
• Developed over centuries they contain many sophisticated concepts that are
still used today. Includes trigonometry, calculus, geometry and probability.
• The Hindu mathematics rooted back to the Indus Valley Civillization.
3. Origin and the earliest evidence of
Mathematical Application in daily Life
The Wheel of Bullock Cart
The Bullock carts of the Harappan civilization had
a metallic band wrapped around the rim of a
wheel. It clearly hints at the fact that people were
aware of the ratio of the circumference of the
circle to the diameter and the pi system. All this
facts help us conclude that Harappan people had
the basic knowledge of geometry. e
e
4. Standardize system of weights (O’
Cannor Robertson)
• Was used for measurement by the
inhabitants of the civilization. These
weights corresponded to the ratios of
1/20, 1/10, 1/5, ½, 1, 2, 5, 10, 20, 50, 100,
200 and 500. Their enhancement in
weights and measures led to the
development of trade and commerce.
Weights were produce in mass numbers
and were of different geometric shapes
like hexahedra, barrels, cones, cylinders etc.
5. Mohenjo-Daro Ruler
• Stands testimony to the accurate use of the
standardize measure of length it was divided
into ten equal parts or 3.4 cm (1.332 inches
each) the dimensions of the breaks used in
mohenjo-daro often were integral multiples of
this unit of length (3.4 cm or 1.32 inches). More
over the breaks used for construction were made
with the dimensions of 4:2:1 ratio.
6. Notable Ancient Mathematicians and their
Contributions to Mathematics
Aryabhatta (5th Century)
• Was a notable Indian Mathematician and
astronomer in the golden age.
• Books: Aryabhatiya and ARYA siddhanta
(Square and cuberoots mensuration, value
of pi, trigonometry and geometry).
• Concept of zero
7. Brahmagupta (6th Century)
• An Indian mathematician
• First person to lay down rules stating the
computation of zero.
• Book: Brahmasphutasiddhanta (c. 628 CE)
- Set of rules for making with negative and positive
numbers, calculating square roots, solving linear
and quadratic equations, summing series, the
author’s identity and theorem.
- - (a theoretical treatise on mathematical astronomy
with 26 chapters), text are present in the form of
elliptic Sanskrit verses.
: Khandakhadyaka (c. 665 CE).
(mathematics and astronomy).
8.
9. Brahmagupta dedicated a substantial portion of his
work geometry and trigonometry. He established
√10 (3.162277) as a good practical approximation
for 𝜋 (3.141593), and gave a formula, now known
as Brahmagupta’s Formula, for the area of a cyclic
quadrilateral, as well as a celebrated theorem on the
diagonals of a cyclic quadrilateral, usually referred
to as Brahmagupta's Theorem.
10. Bhaskara (7th Century)
• An Indian Maathematician and
astronomer
• Study of Fractions
• Representation of numbers in a
positional system.
• Set an example by writing numbers in
the Hindu decimal system placing a
circle for a zero.
• Aryabhatiyabhasya (unique rational
approximation of the sine function).
11. Archarya Hemachandra (12th Century)
• Prodigy in multiple fields
• A scholar of the excellent kind he
gained the title “kalikalasarvajṅa”
which roughly translates to
“omniscient one of the degenerate
age”.
• Made contributions to the Fibonacci
numbers half a century before
Fibonacci introduced them in his
book “Liber Abaci”
12. Oldest and Existing Manuscript of
Mathematics
Bakshali Manuscript
• Oldest Indian manuscript that exist today and
also the worlds oldest hand-written record on
mathematics.
• Consists of mathematical problems, their
prosaic solutions, the concept of zero and a
lot more.
13. • Was discovered in 1881 in Bakshali (in present day Pakistan). It is an
unfinished manuscript compiled in the 70 leaves of a birch bark. The script
closely resembles sharada script in the language is Sanskrit.
• The mathematics in the manuscript is broadly divided into 2 portions.
1. Poem that presents a problem economically
2. Prose commentary or a detailed solution of the problem.
• The Bakshali manuscript contains zero as a dot in the place value
calculation. The dots symbol came to be known as shunya-bindu which
literally means the dot of the empty place or dot of nothingness.
• Fractions were not separated by a line as is the usage in recent times the only
similarity was the dot they were written one over the other.
• The concepts of equalizations and square root are equally present in the
manuscript.
14. 3rd millennium BC
Earliest use of a decimal
scale measurement for
weight and lengths. Similarity
with contemporary
civilizations indicates
possible diffusion of ideas
1000-800BC
The Yajur Veda expounds
the earliest recorded concept
of infinity: “If you remove a
part from infinity or add a
part of infinity, still what
remains is infinity.
800BC
Baudhayana gives the first known formulation
of Pythagoras theorem, nearly three centuries
before Pythagoras who may have picked it up
during hhis travels in the East.
He also gives the first known procedure to
calculate square roots.
15. 500BC
Panini write his comprehensive
text on Sanskrit grammar, which
includes concepts of Boolean
logic, null functions and other
concepts used to described
modern programming
languages.
400BC
Sanskrit texts first mention the
word Shoonya, to refer to zero
or nothingness
300BC
The first recorded instance of
Brahmi numerals, the ancestors
of modern numerals.
16. 400-600AD
The Bakhshali manuscript is
written, which describes various
kinds of infinity, a theory of
logarithms and square roots of
numbers as large as a million,
accurate to eleven decimal
places.
500AD
Aryabhata writes the
Aryabhata Siddhanta, which
introduces trigonometry in a
form similar to that used
today.
820AD
Persian mathematician, Al-Khwarizmi,
having already written book explaining
the use of Indian numerals, writes Al-
jabr, which later becomes Algebra. Based
on several influences, the book also
includes concepts propounded by Indian
mathematicians, and is influential in the
development of Algebra.
17. 1150AD
Bhaskaracharya formulates
calculus and several theorems
that turn up in European
mathematics only five hundred
years later.
1202AD
Leonardo Fibonacci extols the
ease and facility offered by
Indian numerals, in his book
Liber Abaci (book of the
Abacus)
14000AD
Madhava of Sangamagramma develops
several important concepts in calculus
which are expanded upon in later
centuries by other mathematics of the
Kerala School of Astronomy and
Mathematics. This may have influenced
European development of calculus by
Pierre Fermat, Blaise Pascal and John
Wallis.
18. 1501AD
Nikantha Somayaji conceives of
a planetary model very similar to
the model adopted by the
Renaissance astronomer Tycho
Brahe, eighty years later.
1700AD
Kamalakara produces the only
Sanskrit treatise on geometrical
optics.
1887-1920AD
Srinivasa Ramanujam
independently compiles around
3900 results which have today
opened entirely new fields of
research in mathematics and
impacted subjects like physics
and computer science.
