India
has to its credit one of the oldest civilization in the world. There
are a lot of significant contributions that India has made to the world
in the field of art, science, mathematics and so on. A lot of modern day
inventions are based on the principals that were created in India right
from the mythological age. Take a look at the amazing ancient Indian
inventions that changed the world today.
Aryabhatta
The number system was invented in India. Aryabhatta invented Zero.There is some argument over the claim of Aryabhatta being the inventor
of place value system that made use of zero. Georges Ifrah, in his work
‘Universal history of numbers: From prehistory to the invention of the
computer (London, 1998)’ writes in work, “..it is extremely likely that
Aryabhatta knew the sign for zero and the numerals of the place value
system”. Georges Ifrah has studied the works of Aryabhatta and found
that the counting and mathematical work carried out by him would have
been not possible without zero or place value system. Aryabhatta
I or Aryabhata (476-550?), was a famous Indian mathematician and
astronomer, born in a place called Taregana, in Bihar (though some
people do not agree with the evidence). Taregana (also spelled as
Taragna) which literally means songs of stars in Bihari, is a small
place situated nearly 30 km from Patna, which was then known as
Kusumpura later Pataliputra, the capital of the Gupta Empire. This is
the very empire that has been dubbed as the “golden period in Indian
history”. The best introduction to the genius of past is seen in the
words of Bhaskara I who said, “Aryabhatta is the master who, after
reaching the furthest shores and plumbing the inmost depths of the sea
of ultimate knowledge of mathematics, kinematics and spherics, handed
over the three sciences to the learned world”.
Aryabhatta on science and mathematics
Aryabhatta is
considered to be one of the mathematicians who changed the course of
mathematics and astronomy to a great extent. He is known to have
considerable influence on Arabic science world too, where he is referred
to as Arjehir. His notable contributions to the world of science and
mathematics includes the theory that the earth rotates on its axis,
explanations of the solar and lunar eclipses, solving of quadratic
equations, place value system with zero, and approximation of pie (π).
Aryabhatta approximatted pi
Aryabhatta exerted
influence on the Indian astronomical tradition to such an extent that
his presence was felt in neighboring countries and cultures also. There
have been various translations of his work among which the Arabic
translation during the 820CE is very significant.
When mathematical students are confused with trigonometry even today, Aryabhatta had
defined sine, cosine, versine and inverse sine back in his era,
influencing the birth of trigonometry. The signs were originally known
as jya, kojya, utkrama-jya and otkram jya. In Arabic they were
translated as jiba and kojiba, which later when being translated into
Latin was misunderstood to be ‘fold in a garment’ by Gerard of Cremona,
who stated it as sinus, which meant fold in Latin. Aryabhatta was the
first mathematician to detail both
Aryabhatiya
It is known that Aryabhatta has authored
at least three astronomical books, in addition he also wrote some free
stanzas. Among them “Aryabhatiya” is the only text that
has survived to this day, whereas unfortunately his other works have
been extinct. It is a small treatise written is 118 verses, which
summarizes the Hindu mathematics of that time. This great mathematical
masterpiece of the past starts with 10 verse introduction, which is then
followed by mathematical section which is written in 33 verses that
gives out 66 mathematical rules, but there is no proof to go with it.
The mathematical part of the Aryabhatiya is about
algebra, arithmetic, plane trigonometry and spherical trigonometry in
addition to advanced mathematics on continued fractions, quadratic
equations, sums of power series and a table of sines.
Quadratic equation by Aryabhatta
The next section consists of 25 verses
which gives us glimpse into the planetary models. The final section of
the book is dedicated to sphere and eclipses which runs into 50 verses.
He states that the moon and planets shine by reflected sunlight. Instead
of the prevailing cosmogony where eclipses were believed to be caused
by pseudo-planetary nodes Rahu and Ketu, he explains eclipses in terms
of shadows cast by earth or those shadows that fall on earth. It is
amazing how Aryabhatta could explain both lunar and solar eclipse so
accurately.
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sine and versine (1 − cos x) tables, in 3.75° intervals from 0° to 90°, to 4 decimal places.
Aryabhatta’s
astronomical calculations influenced the Arabians, who used the
trigonometric tables to compute many astronomical tables. His calendared
calculation has been in continuous use in India, on which the present
day Panchangam is based. His studies are also base for the national
calendars of Iran and Afghanistan today.
Aryabhatiya
It is known that Aryabhatta has
authored at least three astronomical books, in addition he also wrote
some free stanzas. Among them “Aryabhatiya” is the only
text that has survived to this day, whereas unfortunately his other
works have been extinct. It is a small treatise written is 118 verses,
which summarizes the Hindu mathematics of that time. This great
mathematical masterpiece of the past starts with 10 verse introduction,
which is then followed by mathematical section which is written in 33
verses that gives out 66 mathematical rules, but there is no proof to go
with it. The mathematical part of the Aryabhatiya is
about algebra, arithmetic, plane trigonometry and spherical trigonometry
in addition to advanced mathematics on continued fractions, quadratic
equations, sums of power series and a table of sines.
Quadratic equation by AryabhattaThe
next section consists of 25 verses which gives us glimpse into the
planetary models. The final section of the book is dedicated to sphere
and eclipses which runs into 50 verses. He states that the moon and
planets shine by reflected sunlight. Instead of the prevailing cosmogony
where eclipses were believed to be caused by pseudo-planetary nodes
Rahu and Ketu, he explains eclipses in terms of shadows cast by earth or
those shadows that fall on earth. It is amazing how Aryabhatta could
explain both lunar and solar eclipse so accurately.
Honouring Aryabhatta
The Indian ISRO (Indian Space Research
Organization) named its first satellite after the genius mathematician
and astronomer. A research establishment has been set up in Nainital,
called the Aryabhatta Research Institute of Observational Sciences
(ARIOS) to honor his contribution to the field of science. There is also
a lunar crater and a species of bacteria discovered by ISRO named after
Aryabhatta.
Some of the works of Aryabhatta include
Aryabhatta worked out the value of pi.
He worked out the area of a triangle. His exact words were, “ribhujasya phalashariram samadalakoti bhujardhasamvargah” which translates “for a triangle, the result of a perpendicular with the half side is the area”.
He discussed the idea of sin.
He worked on the summation of series of squares and cubes (square-root and cube-root).
He talks about the “rule of three” which is to find the value of x when three numbers a, b and c is given.
Aryabhatta calculates the volume of a sphere.
Aryabhatta described the model of the solar system, where the sun
and moon are each carried by epicycles that in turn revolve around the
Earth. He also talks about the number of rotations of the earth,
describes that the earth rotating on its axis, the order of the planets
in terms of distance from earth.
Aryabhatta describes the solar and lunar eclipses scientifically.
Aryabhatta describes that the moon and planets shine by light reflected from the sun.
Aryabhatta calculated the sidereal rotation which is the rotation of
the earth with respect to the stars as 23 hours, 56 minutes and 4.1
seconds.
He calculated the length of the sidereal year as 365 days, 6 hours,
12 minutes and 30 seconds. The actual value shows that his calculations
was an error of 3 minutes and 20 seconds over a year.
Mention of rotation of the earth on its axis by Aryabhatta
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