the evaluation of pi in Bharat presentation.pdf

the evaluation of pi in Bharat presentation.pdf

1. "यथा �शखा मयूराणां नागानां मणयो यथा।
त????????????ेदांगशा??????ाणां ग�णतं मूध??????�न ????????????तम्॥"
(??? ????,?? ? ?????,:)

2. The Evolution of
π
in Bharatvarsh

3. What is π ?

4. Evolution of π in Bharatvarsh
ππ π π
Vedic Period 6th Century CE 14th Century CE 20th Century CE
Approximation of π in Veda

5. Classification of Vedic Knowledge System
Vedic Scriptures

6. Kalpsutra (Sulba Sutra)
Fire rituals in Vedic period involved very
specific requirements for the altars
including the shapes, areas etc.
Tretagni - 3 Altars for Fire worship in every
household – had to be of equal area!
The World’s Oldest Applied Geometry still in
practice!

7. चतुर
स◌??????ं म??????लं �चक�ष??????????????????ादासे �नपा?????? पा????????????तः प??????र�ल- ?????? त?????? यद�त??????र??????ं भव�त, त?????? तृतीयेन सह म??????लं प??????र�लखे� समा�धः ।। १३ ।।
म??????लं
चतुर
स◌??????ं �चक�ष??????न् ??????व????????????ं प??????दशभागा??????ृ�ा ??????ावु-दरे??????ेषः करणी ॥ १४ ॥
(Squaring a Circle)
...A rope when stretched across the circle, also goes 3 times around the circle…
Once across Diameter = 3 times around the Circle
Circumference
Diameter
3
1
π
Katyayana Sulba Sutra 3.14
Katyayana Sulba Sutra 3.13
= =

8. Vedic Period
6th Century CE
14th Century CE 20th Century CE
ππ π π
Evolution of π in Bharatvarsh
Approximation of π in by Aryabhatta
& Brahmagupta

9. Approximation of π in by Aryabhatta
चतुरा�धकं शतम??????गुणं ??????ाष??????????????????था सह??????ाणाम् ।
??????युत??????य??????व??????????????????ास??????ो वृ??????प??????रणाहः ॥ १० ॥

- 10th Slokam, Ganita Pada, Aryabhatiya
"Add 4 to 100 , multiplied by 8 and add 62,000,
this is the circumference of a circle whose
diameter is 20,000".

10. π
62,832
20,000
3.1416= =
He used this to estimate the circumference of the Earth, arriving
at a figure of 24,835 miles, only 70 miles off its true value.

11. समप??????रणाह??????ाध� ??????व????????????ाध??????हतमेव वृ??????फलम् ।

- 7th Slokam, Ganita Pada, Aryabhatiya
Calculating Area of Circle without π
" Half of the Circumference when
multiplied by Half of Diameter exactly
gives area of the circle "
Area of Circle = ½ Circumference X Radius
r

12. ●Established approximate value for π as √10
(3.162277)

●First mathematician to treat zero as a
number!
Brahmagupta (598-668CE)

13. Vedic Period
6th Century CE
14th Century CE
20th Century CE
ππ π π
Evolution of π in Bharatvarsh
Infinite Series of π in by Madhvacharya

14. Infinite Series of π
व्यासे वा?र?ध?नहते रूपहृते व्याससागरा?भहते।
ित्रिशरा?द?वषमसङ्ख्याभक्तमृणं स्वं पृथक् क्रमात् कुयर्यात् ॥

-Mahajyanayana Prakara

15. Came up with an infinite series to approximate the value of Pi. The value
he arrived at was correct up to 11 places - 3.14159265359!
This was later discovered after another 2 centuries in Europe by Leibniz.

16. Vedic Period
6th Century CE 14th Century CE 20th Century CE
ππ π π
Evolution of π in Bharatvarsh
Fastest Calculation of π by Ramanujan

17. Fastest Calculation of π by Ramanujan
●Self taught Mathematical genius!

●His rapidly converging formula for
discovered in 1914 was improved upon by
the Chudnovsky brothers in 1988.

●This algorithm was the one used to
calculate the value upto 50 Trillion digits.

18. ●Check out 2014 Kollywood movie
Ramanujan & 2016 Hollywood movie,
The Man who knew Infinity!

19. Evolution of π in Bharatvarsh
ππ π π
Vedic Period 6th Century CE 14th Century CE 20th Century CE
Approximation of π in Veda

20. Thought Process of Archimedes & Madhava for π
The method of exhaustion for approximation of л was invented by
Archimedes and was implemented geometrically by him. Madhava
incorporated the same thought arithmetically…