GRAVITATION - Indian tradition

GRAVITATION -
Indian tradition
V C Kuriakose
CUSAT, Kochi

►Gravity Gravity is one of those things we take
completely for granted.
► it is always there,
► it never changes

►Chronology Chronology of developments of
physics and astronomy
►Greek Greek’s s thoughts (Aristotle)
►Nicholas Nicholas Copernicus((AD
Copernicus( (AD 1473 – 1543,
Poland) Poland
►John John Kepler
(AD 1571- 1571 1630,Germany)
►Galileo Galileo (AD1564-1642, (AD1564 1642, Italy)
►Isaac Isaac Newton (1642-1727, (1642 1727, UK)

►Kanada Kanada (Kanad)
►
Kanad) - around BC 600
- Father of atomic theory:
- In his text, the Vaisheshik Darshana, Darshana he describes an
atomic theory
more than a century before Democritus
- All objects were composed of nine elements:
earth water light wind
ether time space mind soul.
- Gurutva (gravitation
( gravitation) ) was responsible for the falling
of objects on the Earth.

Aryabhatta born in (AD 476 –
►
550) .

Statue of
Aryabhata
on the grounds
of
IUCAA, Pune.

► Aryabhata
is the father of the Hindu-Arabic
Hindu Arabic or
the Decimal number system
- the Earth to spin on its axis, the planets move with
respect to the Sun.
- the Earth's circumference and diameter,
- explained the lunar eclipse and solar eclipse
- measured radius of the planetary orbits in terms of
the radius of the Earth/Sun orbit
- their periods of rotation around the Sun.
- orbits of the planets around the Sun are ellipses.
Aryabhatta's master piece, the Aryabhattiya,
Aryabhattiya,
was translated into Latin in the 13th century

►Varahamihira (AD AD 505 –
587) 587
Existence of force which might be keeping
bodies stuck to the Earth, and also keeping
heavenly bodies in their determined places. places.
The school of mathematics at Ujjain
►sin sin xx = cos(π/2 cos( /2 - xx), ),
►Sin^2( Sin^2(x) x) + cos^2( cos^2(xx )= 1, and
►(1 (1 -
cos
2xx)/2 )/2 = sin^2( sin^2(x) x). .

►Brahmagupta
Brahmagupta, (7th century)
He was the head of the astronomical observatory at
Ujjain
"Bodies fall towards the Earth as it is in the
nature of the Earth to attract bodies, just as it is
in the nature of water to flow".
Gurutvakarshan : amalgam of Guru-tva Guru tvaakarshan
- Gurutvakarshan
-
law of gravitations, sine tables and the
concept of trigonometry

►describes describes Zero as one of the numerals
which stood for meaning nothing.
► elaborates as to how integers positive
and negative consequence when played
with zero.

►Bh Bhāskara skara
I
(AD600 -
680 )
►first first to write numbers in the Hindu-Arabic
Hindu Arabic
decimal system
with a circle for the zero, zero,
and who gave a unique and remarkable
rational approximation
of the sine
function
in his commentary on Aryabhata's
Aryabhata's
work
►born born in Kerala
as a Nambudiri
Brahmin
►He He and Brahmagupta
are the most
renowed
Indian mathematicians who
made considerable contributions to the
study of fractions

►BHASKARA BHASKARA II (Bhaskaracharya
( Bhaskaracharya)
►Born: Born: 1114 in Vijayapura, Vijayapura,
India
Died: 1185 in Ujjain, Ujjain,
India
►Bhaskaracharya
Bhaskaracharya became head of the
astronomical observatory at Ujjain
►built built up a strong school of mathematical
astronomy.

►he he knew that x^2 x^2
= 9 had two solutions.
He also gave the formula

Kerala
school of astronomy
and mathematics :
►Madhava Madhava of Sangamagrama
►Parameshvara
Parameshvara, ,
►Neelakanta Neelakanta Somayaji, Somayaji,
►Jyeshtadeva
Jyeshtadeva, ,
►Achyuta Achyuta
►Melpathur Melpathur
►Achyuta Achyuta
Pisharati, Pisharati,
Narayana
Panikkar. Panikkar.
Bhattathiri
and

►The The school flourished between the 14th
and 16th centuries and the original
discoveries of the school seems to have
ended with Narayana
Bhattathiri
(1559- (1559
1632)
►Their Their most important results—series
results series
expansion for trigonometric functions— functions
were described in Sanskrit
verse in a book
by Neelakanta
called Tantrasangraha, Tantrasangraha,
and
again in a commentary on this work,
called Tantrasangraha--vakhya
Tantrasangraha vakhya, , of
unknown authorship

►The The theorems were stated without proof,
but proofs for the series for sine, cosine,
and inverse tangent were provided a
century later in the work Yuktibhasa Yuktibhasa
(c.1500-c.1610), (c.1500 c.1610), written in Malayalam, Malayalam,
by
Jyesthadeva, Jyesthadeva,
and also in a commentary on
Tantrasangraha.
Tantrasangraha.

►Their Their work, completed two centuries
before the invention of calculus
in Europe,
provided what is now considered the first
example of a power series
(apart from
geometric series). However, they did not
formulate a systematic theory of
differentiation
and integration, integration,
nor is there
any direct evidence of their results being
transmitted outside Kerala

►Madhava Madhava of Sangamagrama
(c. 1340- 1340
1425) lived at Irinjalakuda:
Irinjalakuda:
►Madhava Madhava’s discoveries include
Nilkantha
attributes the series for sine sine to
Madhava. Madhava.
►the the Taylor series for the sine, cosine,
tangent and arctangent functions;
►the the second-order second order Taylor series
approximations of the sine and cosine
functions and the third-order third order Taylor series
approximation of the sine function;

► the power series of π, , usually attributed to
Leibniz
but now known as the Madhava-Leibniz
Madhava Leibniz
series; series
► the solution of transcendental equations
by
iteration; iteration
► the approximation of transcendental numbers
by
continued fractions. fractions
► Madhava
correctly computed the value of π to 9
decimal places and 13 decimal places,
► produced sine and cosine tables to 9 decimal
places of accuracy
► extended some results found in earlier works,
including those of Bhaskara. Bhaskara.

►Jyesthadeva
Jyesthadeva
(c. 1500-1600)
1500 1600)
►Yuktibhasa Yuktibhasa (in Malayalam)
Malayalam)
- the world's
first Calculus
text
►contains contains proofs of theorems, derivations
of rules and series, a derivation and proof
of the Madhava-Gregory Madhava Gregory series of the
arctangent function, proofs of most
mathematical theorems and infinite series
earlier discovered by Madhava
and other
mathematicians of the Kerala

NP-2005-8-711-GSFC
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