This was originally presented by Sachin Motwani (the creator of the PPT) in Goodley Public School (his Alma mater) on the occasion of the Indian Mathematics Day in 2016 in an audience of 12th Class Students.

1. What would be the sixth rung of the following
pyramid?
1
11
21
1211
111221
--------------
-

3. What’s MATHEMATICS for You?

4. It’s ‘Magic’ until you
understand it;
It’s ‘MATHS’
thereafter..!
- B.K.Tirthaji

5. Maths Then…
Addition, Counting, Division,
Shapes, Tables, etc.

6. Calculus, Geometry,
Trigonometry, etc.

7. Fair is Foul and Foul is Fair!

8. Neither trigonometry/calculus nor any other
mathematical concept appeared suddenly. Years of
observations, analysis & dedication resulted in the
way we know mathematics today.
So, let us see how & up to what extent India
contributed in it’s nurturing. The Purpose of this
PPT, is also to encourage & excite the youth to get
into the infinity of Mathematics!

9. (1879-1955), One of the greatest
scientists, philosopher, receiver of
Nobel Prize for his ‘Theory of
Relativity’
-Albert Einstein
“We owe a lot to
who taught us
how to count, without
which no worthwhile
scientific discovery
could have been
made.”

10. -By Sachin Motwani

11. The Prehistoric Mathematics
 General sensibility
 Drawings : Way of expression.

12. Tally marks on cave walls…
Tally marks
Prehistoric mathematics

13. Symmetry
Prehistoric mathematics
Vittala temple in Hampi

14. THE EVOLUTION
OF HINDU-ARABIC
NUMBERS
Present accepted
numerical
 First generated in Indian subcontinent
 Shared with the Arabs
 Arabs took it to Europe
This way the Hindu-numbers got Arab notation.
(Muḥammad ibn Mūsā al-
Khwārizmī)
Brahmi
script

15. The Vedic Contribution
 ARITHMETIC OPERATIONS, FRACTIONS,
SQUARES, CUBES & ROOTS.
 VEDIC MATHEMATICS
 1911-1918
 “Rediscovered" system of calculation
 Difficult arithmetic problems & huge sums solved
immediately
(A gift from Indian sages)
Sri B.K.Tirthaji Maharaj
(1884-1960)

16. Pythagoras Theorem before Pythagoras
• 8th century BC, long before Pythagoras(around 5th
century BC)
• “Sulba Sutras” (or "Sulva Sutras")
• Listed several Pythagorean triplets
The Sulba form of Pythagoras theorem
Indeed, It is believed that quite likely
Pythagoras learned his basic geometry from the
"Sulba Sutras".
Vedic Contribution

17. More from The Sulva Sutras
What’s the
value of √2?

18. REMARKABLY ACCURATE FIGURE
CORRECT TO 5 DECIMAL PLACES
OBTAINED AS FOLLOWS:
1 +
1
3
+
1
3 ∗ 4
−
1
3 ∗ 4 ∗ 34
= 1.4142156 = √2
More from The Sulva Sutras
SQUARE ROOT OF 2

19. THE INFINITY FACTOR
Ancient Buddhist literature
demonstrates the numbers deemed to be
of three types:
Countable
Uncountable
Infinite.
Gautama Buddha

20. Understanding INFINITY
0 2
∞0,1
∞0,2
∞0,1 < ∞ 0,2

21. ‘ ’: The Superhero
• Aryabhata : Founder of Zero
• Established the basic mathematical rules for
dealing with zero:
• 0 + # = #
• 0 - # = -#
• 0 x # = 0
* # ∈ N
Bhaskara II (12th Century) is credited with explaining the
previously misunderstood operation of division by zero.
Bhaskara II

22. Bhaskara 2 noticed
1 ÷ 1⁄2 = 2
Similarly,
1 ÷ 1⁄3 = 3
So, dividing 1 by smaller
and smaller factions yields
a larger and larger number
of pieces.
Ultimately,
1 ÷ 0 = ∞
Illustration of infinity as the reciprocal of zero

23. Downside
Why?
2 ÷ 0 = ∞
7 ÷ 0 = ∞

24. The Modern View
A number divided by zero is actually ‘undefined’
(i.e. it doesn't make sense)

25. •The “Surya Siddhanta”, indicates the first
real use of sines, cosines, inverse sines,
tangents and secants.
•Trigonometric properties were further
documented by the 5th century (AD) Indian
mathematician and astronomer Aryabhata.
(Golden Age of Indian mathematicians)

26. Madhavan of
Sangamagrama
(14th century)
described the
way to calculate
the approximate
value of pi.

27. Srinivasa Ramanujan: A True Motivation
 Self-taught
 Had managed to prove many results (theorems
today) with almost no knowledge of
developments in the Western world
 And with No formal Education
 He claimed that most of his ideas came to him in
dreams.
 Proved over 3,000 theorems, identities and
equations.

28. WHAT’S SO SPECIAL WITH
THIS?
8 1 6
3 5 7
4 9 2

29. INTERESTING!
8 1 6
3 5 7
4 9 2
=15
=15=1
=15
=15
=1 =15

30. CAN YOU THINK
OF SUCH A
GRID…

32. Ramanujan’s Magic Square
Sum of the numbers of any diagonal
or row/column is 139
Ramanujan

33. Can you appreciate something of mathematical significance in the picture?

34. Ramanujan’s taxicab numbers
 The smallest number
expressible as the sum
of two positive cubes in
‘n’ distinct ways.
Ramanujan

36. CONCLUSION
This PPT was to bring into limelight the contribution of our
ancestors towards mathematics & to inculcate your slightest
interest in the world of mathematics.
Hope the purpose was fulfilled!

37. Thank you for being patient listeners!