आर्यभट्ट

आर्यभट्ट का जीवन परिचय:--

आर्यभटीय: आर्यभट का प्रमुख ग्रंथ:--

आर्यभट के गणितीय योगदान :--

संख्या प्रणाली (Number System):--

पाई (π) का मान:--

त्रिकोणमिति (Trigonometry):--

बीजगणित (Algebra):--

आर्यभट के खगोलीय योगदान :--

पृथ्वी की गति (Earth's Rotation):--

चंद्रमा की रोशनी (Moon's Light):--

ग्रहण (Eclipses):--

ग्रहों की गति (Planetary Motion):--

समय की गणना (Time Calculation):--

आर्यभट ने वर्ष की लंबाई को 365 दिन, 6 घंटे, 12 मिनट और 30 सेकंड के रूप में निर्धारित किया, जो आधुनिक गणना के बहुत करीब है।

आर्यभट का ज्योतिष में योगदान:--

आर्यभट्ट द्वारा प्रतिपादित अन्य सिद्धांत इस प्रकार हैं—

1. पृथ्वी, चंद्रमा व अन्य ग्रह सूर्य के प्रकाश से परावर्तित होकर चमकते।

2. ग्रहों का परिक्रमा कक्ष अंडाकार है।

3. एक वर्ष में 365 दिन 6 घंटे, 12 मिनट तथा 30 सेकंड होते हैं।

और उन्होंने विभिन्न अक्षरों को संख्यात्मक मान दिए थे— 

इसी प्रकार उन्होंने स्वरों को भी मान दिए थे—

आर्यभट का प्रभाव :--

आर्यभट का सम्मान :--

निष्कर्ष :--

Aryabhata was a great mathematician and astronomer of ancient India, who made unique contributions in the field of mathematics, astronomy and astrology. He was born in 476 AD and made revolutionary discoveries in the field of science and mathematics during his lifetime. Aryabhata compiled his knowledge through his famous treatise "Aryabhatiya", which is still a source of inspiration for scholars and researchers.

Biography of Aryabhata:--

Aryabhata was born in 476 AD. There is disagreement among scholars about his birthplace, but most scholars believe that he was born in the southern part of India, in present-day Kerala or Tamil Nadu. Some scholars also associate him with Kusumpur (present-day Patna, Bihar), as he has mentioned Kusumpur in his treatise "Aryabhatiya".

Aryabhata received his education at Nalanda University, which was a major center of education and knowledge at that time. He developed a keen interest in mathematics and astronomy and mastered these subjects.

Aryabhatiya: The Major Text of Aryabhata:-

The most famous text of Aryabhata is "Aryabhatiya", written in Sanskrit. This text is divided into four parts and contains 121 verses. This text was written to explain the principles of mathematics and astronomy. The four parts of Aryabhatiya are as follows:

Dasagitika: It contains 10 verses and explains the number system, astronomical constants, and the basic principles of the universe.

Ganitapada: It contains 33 verses and explains mathematical principles, such as arithmetic, algebra, and geometry.

Kalakriyapada: It contains 25 verses and deals with the calculation of time, calendar, and calculation of astronomical phenomena.

Golapada: It contains 50 verses and explains astronomy, planetary motion, and the structure of the universe.

Mathematical Contributions of Aryabhata:--

Aryabhata made many important contributions in the field of mathematics. Following are some of his major contributions:

Number System:--

Aryabhata developed a unique system for expressing numbers. He understood the importance of zero (0) and used it. His number system was based on the decimal system.

Value of Pi (π):--

Aryabhata determined the value of Pi (π) as 3.1416, which was very accurate for that time. He used a special formula to calculate this value.

Trigonometry:--

Aryabhata developed the concept of sine function and calculated its values. He tabulated the values ​​of sine and cosine.

Algebra:--

Aryabhata developed various methods to solve algebraic equations. He used a special formula to solve quadratic equations.

Arithmetic:--

Aryabhata explained arithmetic operations, such as addition, subtraction, multiplication, and division, in a simple and systematic way.

Astronomical contributions of Aryabhata:--

Aryabhata also made many important contributions in the field of astronomy. Some of his major contributions are as follows:

Earth's Rotation:--

Aryabhata proved that the Earth rotates on its axis and this is why there are days and nights. He also told that the position of celestial bodies changes due to the movement of the Earth.

Moon's Light:--

Aryabhata proved that the light of the moon is due to the reflection of sunlight. He also told that the moon has no light of its own.

Eclipses:--

Aryabhata explained the scientific reasons for eclipses (solar and lunar eclipses). He told that solar eclipse occurs when the Moon comes between the Sun and the Earth, and lunar eclipse occurs when the Earth comes between the Sun and the Moon.

Planetary Motion:--

Aryabhata studied the motion of planets and calculated their orbits. He also told that the motion of planets is elliptical.

Time Calculation:--

Aryabhata determined the length of the year as 365 days, 6 hours, 12 minutes and 30 seconds, which is very close to modern calculations.

Aryabhata's contribution to astrology:--

Aryabhata gave a scientific basis to astrology and used mathematical formulas for this. He studied the position of planets and their effects and linked it with astrology. His works gave astrology a scientific approach.

Other theories propounded by Aryabhata are as follows -

1. Earth, Moon and other planets shine by reflecting sunlight.

2. The orbit of the planets is elliptical.

3. There are 365 days, 6 hours, 12 minutes and 30 seconds in a year.

This is only slightly different from the actual value. At that time, people considered solar and lunar eclipses to be the effects of demon kings Rahu and Ketu, but Aryabhatta explained their real causes.

Contrary to mythological beliefs, he stated that the earth rotates on its axis. Aryabhatta gave revolutionary ideas in many matters. Due to this, his contemporary and immediate later scholars like Brahmagupta, Varahamihir etc. did not accept his concepts.

An example of this is that according to mythological beliefs, the division of time was like this—

One Kalpa = 14 Manvantars

+ 6 Mahayugas = One thousand Yugas

One Manvantar = 71 Mahayugas

One Mahayuga = 43,20,000 years

Aryabhatta simplified it and presented it like this—

One Kalpa = 14 Manvantars = 1008 Mahayugas

One Manvantar = 72 Mahayugas

One Mahayuga = 43,20,000 years.

Contrary to mythological beliefs, Aryabhatta said that all the Yugas of Mahayuga will be equal, that is, Satyayuga, Tretayuga, Dwapara and Kaliyuga will have 10,80,000 years each. Later, ‘Aryabhatiya’ started being taught in Gurukuls. According to estimates, he died in 520 AD.

Aryabhatta also gave a systematic knowledge about the position of celestial bodies in the sky. He gave the circumference of the earth as 24,835 miles, which is the best possible value as compared to the modern value of 24,902 miles.

Aryabhata believed that the apparent rotation of celestial bodies is possible due to the axial rotation of the earth. This is an important concept of the nature or character of the solar system. But this idea was considered erroneous and was abandoned by later thinkers.

Aryabhata gives the radius of celestial planets in relation to the radius of the earth-sun. He is of the opinion that the moon and other planets shine by the light reflected from the sun.

Surprisingly, he believes that the orbits of the planets are elliptical. Aryabhata has explained the correct causes of solar and lunar eclipses, whereas before him people considered the demons Rahu and Ketu to be the cause of these eclipses. Aryabhata also presented many revolutionary ideas for the first time in the field of astrology. He was the first Indian scientist who clearly stated that the earth rotates on its axis and the globe of stars is stationary.

The mythological belief was contrary to this, therefore later astrologers like Varahamihir, Brahmagupta etc. did not accept his correct belief. Aryabhata did not believe in the creation of the world and its destruction cycle. He considered time to be eternal and infinite. He was definitely a revolutionary thinker.

By presenting correct ideas against the tradition of Shruti, Smriti and Puranas, he showed great courage and established a healthy tradition of scientific research in India. Aryabhata did not describe any astrologer, mathematician or ruler in his book.

His book named 'Aryabhatiya' is a purely scientific book of Indian mathematics and astrology. In his honor, India named its first artificial satellite 'Aryabhata'.

Similarly, he had written in one of his books that when Aryabhatta was 23 years old, 3,600 years of Kali Yuga had passed. On this basis, his date of birth was calculated. That period was the Gupta period, i.e. the golden age of India. It is believed that Aryabhatta had written at least three books.

But only one of these, i.e. ‘Aryabhatiya’ is available, but that is enough to prove him a great mathematician. In this book of 121 verses, various introductions have been given in the first 16 verses. There are 33 verses related to mathematics, which

are called ‘Ganit Pada’. In this, square root, cube root, triangle area, sine difference, questions related to light and shadow, unspecified equations etc. are described. In this, 1,100, 10,000 etc. have been considered as square places and 10,1000, 1,00,000 have been considered as non-square; Because their square root is not an integer. Aryabhatta was skilled in expressing his mathematics in a concise manner

and he gave numerical values ​​to different letters—

Ka=1

Kha=2

Ga=3

Gha=4

Nga=5

Cha=6

Chha=7

Ja=8

Zha=9

Na=0

Ta=11

Ta=2

Da=13

Dha14

Na=15

Ta=6

Tha=17

Da=8

Dha=19

Na=20

Pa=21

Pha=22

Ba=23

Bha=24

Ma=25

Ya=30

Ra=40

La=50

Va=60

Sha=70

Sha=80

Sa=90

Ha=100 

Similarly, he had given values ​​to vowels as well-

A=1

I=100

U=10000

Ri=10000000

Lri=1000000000

E=100000000000

Ai=10000000000000

O=1000000000000000

Au=100000000000000000

Au=100000000000000000

U=10000000000000000

U=10000000000000000

U=10000000000000000

U=1000000000000000

U=1000000000000000

U=1000000000000000

U=1000000000000000

U=1000000000000000

U=1000 According to him, it was 3.1416.

But later he did not use this value and used 10, which comes to 3.1622. Thus he was very close to the value of (pi) and he considered it an irrational number. His contribution to trigonometry was also amazing. He presented a table of sine. In this, he showed the possible values ​​at an interval of 900/24=3045’. Aryabhatta discussed in detail about the position of celestial bodies in the sky. He told the circumference of the earth to be 4,967 yojanas and the diameter to be 1581 yojanas. One yojana = 5 miles and thus the circumference was measured to be 24,835 miles, which is very close to the modern actual value of 24,902 miles.

Influence of Aryabhatta :--

The works of Aryabhatta influenced mathematics and astronomy not only in India but the whole world. His theories were studied and further developed by later scholars such as Brahmagupta and Bhaskaracharya. Aryabhata's works also influenced Arab and European scholars.

Honor to Aryabhata:--

India named its first satellite "Aryabhata" in honor of Aryabhata, which was launched on 19 April 1975. The satellite was launched by the Indian Space Research Organization (ISRO) and brought a new consciousness to India's space program.

Conclusion:--

Aryabhata was a great mathematician and astronomer who made invaluable contributions to the field of science and mathematics through his knowledge and research. His works are still a source of inspiration for scholars and researchers. Aryabhata is considered a lighthouse of Indian science, and his contributions will always be remembered.