INDIAN ASTRONOMERS

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India´s Contributions Acknowledged

"We owe a lot to the Indians, who taught us how to count, without

which no worthwhile scientific discovery could have been made."

- Albert Einstein.

Astronomy, geography, constellation science and mathematics

India invented the Zero, without which there would be no binary

system. No computers! Counting would be clumsy and cumbersome! The

earliest recorded date, an inscription of Zero on Sankheda Copper

Plate was found in Gujarat, India (585-586 CE). In Brahma-Phuta-

Siddhanta of Brahmagupta (7th century CE), the Zero is lucidly

explained and was rendered into Arabic books around 770 CE. From

these it was carried to Europe in the 8th century. However, the

concept of Zero is referred to as Shunya in the early Sanskrit texts

of the 4th century BCE and clearly explained in Pingala´s Sutra of

the 2nd century.

Sage Aryabhatt (b. 476 CE) wrote texts on astronomy and mathematics.

He formulated the process of calculating the motion of planets and

the time of eclipses. Aryabhatt was the first to proclaim the earth

was round, rotating on an axis, orbiting the sun and suspended in

space. This was around 1,000 years before Copernicus. He was a

geometry genius credited with calculating pi to four decimal places,

developing the trigonomic sine table and the area of a triangle.

Perhaps his most important contribution was the concept of the zero.

Details are found in Shulva sutra. Other sages of mathematics include

Baudhayana, Katyayana, and Apastamba.

Varahamihr (499 - 587 CE) was another eminent astronomer. In his

book, Panschsiddhant, he noted that the moon and planets shine due to

the sun. Many of his other contributions captured in his books Bruhad

Samhita and Bruhad Jatak, were in the fields of geography,

constellation science, botany and animal science. For example he

presented cures for various diseases of plants and trees.

Knowledge of botany (Vrksh-Ayurveda) dates back more than 5,000

years, discussed in India's Rig Veda. Sage Parashara (100 BCE) is

called the "father of botany" because he classified flowering plants

into various families, nearly 2,000 years before Lannaeus (the modern

father of taxonomy). Parashara described plant cells - the outer and

inner walls, sap color-matter and something not visible to the eye -

anvasva. Nearly 2,000 years -later Robert Hooke, using a microscope

described the outer and inner wall and sap color-matter.

Algebra, arithmetic and geometry, planetary positions, eclipses,

cosmography, and mathematical techniques. force of gravity

In the field of mathematics, Bhaskaracharya II (1114 - 1183 CE)

contributed to the fields of algebra, arithmetic and geometry. Two of

his most well known books are Lilavati and Bijaganita, which are

translated in several languages of the world. In his book, Siddhant

Shiromani, he expounds on planetary positions, eclipses, cosmography,

and mathematical techniques. Another of his books, Surya Siddhant

discusses the force of gravity, 500 years before Sir Isaac Newton.

Sage Sridharacharya developed the quadratic equation around 991 CE.

The Decimal

Ancient India invented the decimal scale using base 10. They number-

names to denote numbers. In the 9th century CE, an Arab

mathematician, Al-Khwarizmi, learned Sanskrit and wrote a book

explaining the Hindu system of numeration. In the 12th century CE the

book was translated into Latin. The British used this numerical

system and credited the Arabs - mislabelling it 'Arabic

numerals'. "We owe a lot to the Indians, who taught us how to count,

without which no worthwhile scientific discovery could have been

made." - Albert Einstein.

Geometry

Invention of Geometry

The word Geometry seems to have emerged from the Indian

word 'Gyaamiti´ which means measuring the Earth. And the word

Trigonometry is similar to 'Trikonamiti´ meaning measuring triangular

forms. Euclid is credited with the invention of Geometry in 300 BCE

while the concept of Geometry in India emerged in 1000 BCE, from the

practice of making fire altars in square and rectangular shapes. The

treatise of Surya Siddhanta (4th century CE) describes amazing

details of Trigonometry, which were introduced to Europe 1200 years

later in the 16th century by Briggs.

The Value of PI in India

The ratio of the circumference and the diameter of a circle are known

as Pi, which gives its value as 3,1428571. The old Sanskrit text

Baudhayana Shulba Sutra of the 6th century BCE mentions this ratio as

approximately equal to 3. Aryabhatta in 499, CE worked the value of

Pi to the fourth decimal place as 3.1416. Centuries later, in 825 CE

Arab mathematician Mohammed Ibna Musa says that "This value has been

given by the Hindus (Indians)".

Pythagorean Theorem or Baudhayana Theorem?

The so-called Pythagoras Theorem - the square of the hypotenuse of a

right-angled triangle equals the sum of the square of the two sides -

was worked out earlier in India by Baudhayana in Baudhayana Sulba

Sutra. He describes: "The area produced by the diagonal of a

rectangle is equal to the sum of the area produced by it on two

sides." Note: Greek writers attributed the theorem of Euclid to

Pythagoras.

Indian astronomers have been mapping the skies for 3500 years.

1000 Years Before Copernicus

Copernicus published his theory of the revolution of the Earth in

1543. A thousand years before him, Aryabhatta in 5th century (400-500

CE) stated that the Earth revolves around the sun, "just as a person

travelling in a boat feels that the trees on the bank are moving,

people on earth feel that the sun is moving". In his treatise

Aryabhatteeam, he clearly states that our earth is round, it rotates

on its axis, orbits the sun and is suspended in space and explains

that lunar and solar eclipses occur by the interplay of the sun, the

moon and the earth.

The Law of Gravity - 1200 Years Before Newton

The Law of Gravity was known to the ancient Indian astronomer

Bhaskaracharya. In his Surya Siddhanta, he notes:

"Objects fall on earth due to a force of attraction by the earth.

therefore, the earth, the planets, constellations, the moon and the

sun are held in orbit due to this attraction".

It was not until the late 17th century in 1687, 1200 years later,

that Sir Isaac Newton rediscovered the Law of Gravity.

Measurement of Time

In Surya Siddhanta, Bhaskaracharya calculates the time taken for the

earth to orbit the sun to 9 decimal places.

Bhaskaracharya = 365.258756484 days.

Modern accepted measurement = 365.2596 days.

Between Bhaskaracharya´s ancient measurement 1500 years ago and the

modern measurement the difference is only 0.00085 days, only 0.0002%.

34000TH of a Second to 4.32 Billion Years

India has given the idea of the smallest and the largest measure of

time.

Krati Krati = 34,000th of a second

1 Truti = 300th of a second

2 Truti = 1 Luv

2 Luv = 1 Kshana

30 Kshana = 1 Vipal

60 Vipal = 1 Pal

60 Pal = 1 Ghadi (24 minutes)

2.5 Gadhi = 1 Hora (1 hour)

24 Hora = 1 Divas (1 day)

7 Divas = 1 saptaah (1 week)

4 Saptaah = 1 Maas (1 month)

2 Maas = 1 Rutu (1 season)

6 Rutu = 1 Varsh (1 year)

100 Varsh = 1 Shataabda (1 century)

10 Shataabda = 1 sahasraabda

432 Sahasraabda = 1 Yug (Kaliyug)

2 Yug = 1 Dwaaparyug

3 Yug = 1 Tretaayug

4 Yug = 1 Krutayug

10 Yug = 1 Mahaayug (4,320,000 years)

1000 Mahaayug = 1 Kalpa

1 Kalpa = 4.32 billion years

Mathematics

The Decimal

100BCE the Decimal system flourished in India

"It was India that gave us the ingenious method of expressing all

numbers by means of ten symbols (Decimal System)….a profound and

important idea which escaped the genius of Archimedes and Apollonius,

two of the greatest men produced by antiquity."

-La Place

Raising 10 to the Power of 53

The highest prefix used for raising 10 to a power in today´s maths

is 'D´ for 10 to a power of 30 (from Greek Deca). While, as early as

100 BCE Indian Mathematicians had exact names for figures upto 10 to

the power of 53.

ekam =1

dashakam =10

shatam =100 (10 to the power of 10)

sahasram =1000 (10 power of 3)

dashasahasram =10000 (10 power of 4)

lakshaha =100000 (10 power of 5)

dashalakshaha =1000000 (10 power of 6)

kotihi =10000000 (10 power of 7)

ayutam =1000000000 (10 power of 9)

niyutam = (10 power of 11)

kankaram = (10 power of 13)

vivaram = (10 power of 15)

paraardhaha = (10 power of 17)

nivahaaha = (10 power of 19)

utsangaha = (10 power of 21)

vyavasthaana bahulam = (10 power of 23)

naagbaalaha = (10 power of 25)

titilambam = (10 power of 27)

pragnaptihi = (10 power of 29)

hetuheelam = (10 power of 31)

karahuhu = (10 power of 33)

hetvindreeyam = (10 power of 35)

samaapta lambhaha = (10 power of 37)

gananaagatihi) = (10 power of 39)

niravadyam = (10 power of 41)

mudraabaalam = (10 power of 43)

sarvabaalam = (10 power of 45)

vishamagnagatihi = (10 power of 47)

sarvagnaha = (10 power of 49)

vibhutangamaa = (10 power of 51)

tallaakshanam = (10 power of 53)

(In Anuyogdwaar Sutra written in 100 BCE one

numeral is raised as high as 10 to the power of 140).