Aryabhata (476–550 CE) was the first in the line of greatmathematician-astronomers from the classical age of Indian mathematics and Indian astronomy. His most famous works are the Aryabhatiya (499 CE, when he was 23 years old) and the Arya-siddhanta. Name While there is a tendency to misspell his name as "Aryabhatta" by analogy with other names having the "bhatta" suffix, his name is properly spelled Aryabhata: every astronomical text spells his name thus,[1] including Brahmagupta's references to him "in more than a hundred places by name".[2] Furthermore, in most instances "Aryabhatta" does not fit the metre either.[1] Birth Aryabhata mentions in the Aryabhatiya that it was composed 3,600 years into the Kali Yuga, when he was 23 years old. This corresponds to 499 CE, and implies that he was born in 476 CE.[1] Aryabhata provides no information about his place of birth. The only information comes from Bhāskara I, who describes Aryabhata as āśmakīya, "one belonging to the aśmaka country." While aśmaka was originally situated in the northwest of India, it is widely attested that, during the Buddha's time, a branch of the Aśmaka people settled in the region between the Narmada and Godavari rivers, in the South Gujarat–North Maharashtra region of central India. Aryabhata is believed to have been born there.[1][3] However, early Buddhist texts describe Ashmaka as being further south, in dakshinapath or the Deccan, while other texts describe the Ashmakas as having fought Alexander, which would put them further north.[3] Mathematics Place value system and zero The place-value system, first seen in the 3rd century Bakhshali Manuscript, was clearly in place in his work. While he did not use a symbol for zero, the French mathematician Georges Ifrah argues that knowledge of zero was implicit in Aryabhata's place-value system as a place holder for the powers of ten with null coefficients[10] However, Aryabhata did not use the brahmi numerals. Continuing the Sanskritic tradition from Vedic times, he used letters of the alphabet to denote numbers, expressing quantities, such as the table of sines in a mnemonic form.[11] ]Pi as irrational Aryabhata worked on the approximation for Pi (π), and may have come to the conclusion that π is irrational. In the second part of the Aryabhatiyam (gaṇitapāda10), he writes: caturadhikam śatamaṣṭaguṇam dvāṣaṣṭistathā sahasrāṇām ayutadvayaviṣkambhasyāsanno vṛttapariṇāhaḥ. "Add four to 100, multiply by eight, and then add 62,000. By this rule the circumference of a circle with a diameter of 20,000 can be approached."[12] This implies that the ratio of the circumference to the diameter is ((4+100)×8+62000)/20000 = 62832/20000 = 3.1416, which is accurate to five significant figures. It is speculated that Aryabhata used the word āsanna (approaching), to mean that not only is this an approximation but that the value is incommensurable (orirrational). If this is correct, it is quite a sophisticated insight, because the irrationality of pi was proved in Europe only in 1761 by Lambert).[13] After Aryabhatiya was translated into Arabic (ca. 820 CE) this approximation was mentioned in Al-Khwarizmi's book on algebra.[3] Mensuration and trigonometry In Ganitapada 6, Aryabhata gives the area of a triangle as tribhujasya phalashariram samadalakoti bhujardhasamvargah that translates to: "for a triangle, the result of a perpendicular with the half-side is the area Aryabhata discussed the concept of sine in his work by the name of ardha-jya. Literally, it means "half-chord". For simplicity, people started calling it jya. When Arabic writers translated his works from Sanskrit into Arabic, they referred it as jiba. However, in Arabic writings, vowels are omitted, and it was abbreviated as jb. Later writers substituted it with jiab, meaning "cove" or "bay." (In Arabic, jiba is a meaningless word.) Later in the 12th century, when Gherardo of Cremonatranslated these writings from Arabic into Latin, he replaced the...

...build extremely complex theorems and prove old ones. For example, starting with only axioms, he was able to prove the fundamental theorem of arithmetic. By using deductive reasoning, he was able to create nearly perfect theorems. Many later mathematicians, especially Girolama Saccheri, tried to out do the work of Euclid but all eventually gave up when they realized that his theories were flawless due to his extensive proofs.
He even adventured into new branches of...

...
Born: 1601 in Beaumont-de-Lomagne, France
Died: Jan 12, 1665 (at age 60 or 61), in Castres, France
Nationality: French
Famous For: Fermat’s Last Theorem
Pierre de Fermat (1601-1665)
Fermat’s contributions to mathematics
Fermat mathematician made significant contributions to number theory, probability theory, analytic geometry and the early development of infinitesimal calculus. He ventured into the areas of mathematics which included pre-evolved calculus and...

...Mathematicians of the 17th Century
Jacob Bernoulli (also known as James or Jacques) (27 December 1654/6 January 1655 – 16 August 1705) was one of the many prominent mathematicians in the Bernoulli family.
He became familiar with calculus through a correspondence with Gottfried Leibniz, then collaborated with his brother Johann on various applications, notably publishing papers ontranscendental curves (1696) and isoperimetry(1700, 1701). In 1690, Jacob Bernoulli...

...defeats on three ministries. The Calcutta Municipal Act of 1923 was a major landmark in the history of local self-government in India. The Swarajists were elected to the Calcutta Corporation in a majority in 1924. Deshbandhu was elected mayor and Subash Chandra Bose was appointedChief Executive Officer. The leaders of Swaraj Party began to advocate fordominion status to India. Many of the elected deputies soon forgot about obstruction and began cooperating with the...

...Indian Mathematicians
RAMANUJAN
He was born on 22na of December 1887 in a small village of Tanjore district, Madras. He failed in English in Intermediate, so his formal studies were stopped but his self-study of mathematics continued.
He sent a set of 120 theorems to Professor Hardy of Cambridge. As a result he invited Ramanujan to England.
Ramanujan showed that any big number can be written as sum of not more than four prime numbers.
He showed that how to divide the number...

...आर्यभट) (476–550 CE) was the first in the line of great mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy. His most famous works are the Āryabhaṭīya (499 CE, when he was 23 years old) and the Arya-siddhanta. Place value system and zero
The place-value system, first seen in the 3rd century Bakhshali Manuscript, was clearly in place in his work. While he did not use a symbol for zero, the French mathematician Georges Ifrah...

...What about rest 70%?
7. The large supermarket will import rest 70% which will increase current account deficit of the India. It will demotivate the small and medium scale industries. Hence it will increase unemployment.
In a developing country like India allowing FDI may help in booming the economy. But, this will only be up to a certain period of time only. Initially, India will get employment but that may also affect the middle class people who...

...Self-Realisatiotl
13.3 Emphasis on Human Reason
13.4 Critique of Nationalism
13.5 Differences with Gandlii
'13.6 A ~ ~ a l y sof Bolshevism is 13.7 Summary
13.8 Exercises
Rabindranath 'Tagorc (1861-1941) was an outstanding litcrnry figure of India who exerted consiclerable inf uence on human thinking in the contcml>oraryworld. T l ~ i s influence extcnded to the political arena as well by his lilcid elucidation of inlpartant conccpts like nationalis~m, freedom,...

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