| A Brief History of MathematicsPeople seem compelled to organize. They also have a practical need to count certain things: cattle, cornstalks, and so on. There is the need to deal with simple geometrical situations in providing shelter and dealing with land. Once some form of writing is added into the mix, mathematics cannot be far behind. It might even be said that the symbolic approach precedes and leads to the invention of writing.Archaeologists, anthropologists, linguists and others studying early societies have found that number ideas evolve slowly. There will typically be a different word or symbol for two people, two birds, or two stones. Only slowly does the idea of 'two'become independent from the things that there are two of. Similarly, of course, for other numbers. In fact, specific numbers beyond three are unknown in some lesser developed languages. A bit of this usage hangs on in our modern English when we speak, for example, of a flock of geese, but a school of fish.The Maya, the Chinese, the Civilization of the Indus Valley, the Egyptians, and the region of Mesopotamia between the Tigris and Euphrates rivers -- all had developed impressive bodies of mathematical knowledge by the dawn of their written histories. In each case, what we know of their mathematics comes from a combination of archaeology, the references of later writers, and their own written record.Mathematical documents from Ancient Egypt date back to 1900 B.C. The practical need to redraw field boundaries after the annual flooding of the Nile, and the fact that there was a small leisure class with time to think, helped to create a problem oriented, practical mathematics. A base-ten numeration system was able to handle positive whole numbers and some fractions. Algebra was developed only far enough to solve linear equations and, of course, calculate the volume of a pyramid. It is thought that only special cases of The Pythagorean Theorem were known; ropes knotted in the ratio 3:4:5 may have been used to construct right angles.What we know of the mathematics of Mesopotamia comes from cuneiform writing on clay tablets which date back as far as 2100 B.C. Sixty was the number system base -- a system that we have inherited and preserve to this day in our measurement of time and angles. Among the clay tablets are found multiplication tables, tables of reciprocals, squares and square roots. A general method for solving quadratic equations was available, and a few equations of higher degree could be handled. From what we can see today, both the Egyptians and the Mesopotamians (or Babylonians) stuck to specific practical problems; the idea of stating and proving general theorems did not seem to arise in either civilization.Chinese mathematics -- a vast and powerful body of knowledge --, although mainly practical and problem oriented, did contain general statements and proofs. A method similar to Gaussian Reduction with back-substitution for solving systems of linear equations was known two thousand years earlier in China than in the West. The value of was known to seven decimal places by 500 A.D., far in advance of the West.In India mathematics was also mainly practical. Methods of solving equations were largely centered around problems in astronomy. Negative and irrational numbers were used. Of course, India is noted for developing the concept of zero, that was passed into Western mathematics via the Arabic tradition, and is so important as a place holder in our modern decimal number system.The Classic Maya civilization (250 BC to 900 AD) also developed the zero and used it as a place holder in a base-twenty numeration system. Again, astronomy played a central role in their religion and motivated them to develop mathematics. It is noteworthy that the Maya calendar was more accurate than the European at the time the Spanish landed in The Yukatan Peninsula.Ancient GreeceThe axiomatic method came into full force in Ancient Greek times; it has...

...Thrissur, Kerala. Available evidence suggest that he went to Kusumapura for higher studies. He lived in Kusumapura, which his commentator Bhāskara I (AD 629) identifies as Pataliputra (modern Patna). K. Chandra Hari, a senior geoscientist at the Institute of Reservoir Studies of Oil and Natural Gas Commission, Ahmedabad has refuted this popular opinion and claims that based on his interpretation of Aryabhatta's system of measurements and writings, it is highly likely that he belonged to the modern Ponnani-Chamravattom area (latitude 10N51 and longitude 75E45) in Kerala in the 6th Century AD
Aryabhata was the first in the line of brilliant mathematician-astronomers of classical Indian mathematics, whose major work was the Aryabhatiya and the Aryabhatta-siddhanta. The Aryabhatiya presented a number of innovations in mathematics and astronomy in verse form, which were influential for many centuries. The extreme brevity of the text was elaborated in commentaries by his disciple Bhaskara I (Bhashya, ca. 600) and by Nilakantha Somayaji in his Aryabhatiya Bhasya, (1465). The number place-value system, first seen in the 3rd century Bakhshali Manuscript was clearly in place in his work.[1] He may have been the first mathematician to use letters of the alphabet to denote unknown quantities.[2]
Aryabhata's system of astronomy was called the audAyaka system (days are reckoned from uday, dawn at lanka, equator). Some of his later writings on astronomy, which...

...Aryabhata (IAST: Āryabhaṭa; Sanskrit: आर्यभटः) (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 Aryabhatiya (499 CE, when he was 23 years old) and the Arya-siddhanta.
Biography
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...

...Causes of Floods
Floods are caused by many factors: heavy precipitation, severe winds over water, unusual high tides, tsunamis, or failure of dams, levels, retention ponds, or other structures that contained the water.
Periodic floods occur on many rivers, forming a surrounding region known as the flood plain.
During times of rain or snow, some of the water is retained in ponds or soil, some is absorbed by grass and vegetation, some evaporates, and the rest travels over the land as surface runoff. Floods occur when ponds, lakes, riverbeds, soil, and vegetation cannot absorb all the water. Water then runs off the land in quantities that cannot be carried within stream channels or retained in natural ponds, lakes, and man-made reservoirs. About 30 percent of all precipitation is in the form of runoff small and that amount might be increased by water from melting snow. River flooding is often caused by heavy rain, sometimes increased by melting snow. A flood that rises rapidly, with little or no advance warning, is called a flash flood. Flash floods usually result from intense rainfall over a relatively small area, or if the area was already saturated from previous precipitation.
Severe winds over water
Even when rainfall is relatively light, the shorelines of lakes and bays can be flooded by severe winds—such as during hurricanes—that blow water into the shore areas.
Unusual high tides
Coastal areas are sometimes flooded by unusually high tides, such as spring tides,...

...Aryabhata (Sanskrit: आर्यभट; IAST: Āryabhaṭa) or Aryabhata I[1][2] (476–550 CE)[3][4] was the first in the line of great mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy. His works include the Āryabhaṭīya (499 CE, when he was 23 years old)[5] and the Arya-siddhanta.
The works of Aryabhata dealt with mainly mathematics and astronomy.
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[13]
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.[14]
Approximation of π
Aryabhata worked on the approximation for pi ( ), and may have come to the conclusion that is irrational. In the second part of the Aryabhatiyam (gaṇitapāda 10), 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."
[15]
This implies that the ratio of the circumference to the diameter is...

...Aryabhatta Biography Wikipedia.ame
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, including Brahmagupta's references to him "in more than a hundred places by name". Furthermore, in most instances "Aryabhatta" does not fit the metre either.
Time and place of birth
Aryabhata mentions in the Aryabhatiya that it was composed 3,630 years into the Kali Yuga, when he was 23 years old. This corresponds to 499 CE, and implies that he was born in 476.
Aryabhata was born in Taregna (literally, song of the stars), which is a small town in Bihar, India, about 30 km (19 mi) from Patna (then known as Pataliputra), the capital city of Bihar State. Evidences justify his birth there. In Taregna Aryabhata set up an Astronomical Observatory in the Sun Temple 6th century.
There is no evidence that he was born outside Patliputra and traveled to Magadha, the centre of instruction, culture and knowledge for his studies where he even set up a coaching institute. 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.
Education
It is fairly certain that, at some point, he went to Kusumapura for advanced studies and lived there for some time. Both Hindu and Buddhist tradition, as...

...solar system 4.2 Eclipses 4.3 Sidereal periods 4.4 Heliocentrism 5 Legacy 6 See also 7 References 8 External links
Statue of Aryabhata on the grounds of IUCAA, Pune. As there is no known information regarding his appearance, any image of Aryabhata originates from an artist's conception. Born Died Era Region Main interests Major works 476 CE prob. Ashmaka 550 CE Gupta era India Mathematics, Astronomy Āryabhaṭīya, Arya-siddhanta
Biography
Name
en.wikipedia.org/wiki/Aryabhata
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Aryabhata - Wikipedia, the free encyclopedia
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,[6] including Brahmagupta's references to him "in more than a hundred places by name".[7] Furthermore, in most instances "Aryabhatta" does not fit the metre either.[6] Time and place of birth Aryabhata mentions in the Aryabhatiya that it was composed 3,630 years into the Kali Yuga, when he was 23 years old. This corresponds to 499 CE, and implies that he was born in 476.[4] Aryabhata's birthplace is uncertain, but it may have been in the area known in ancient texts as Ashmaka India which may have been Maharashtra or Dhaka.[6]
Education
It is fairly certain that, at some point, he went to Kusumapura for advanced studies and lived there for some time.[8] Both Hindu and Buddhist tradition, as...

...Aryabhatta is the first of the great astronomers of the classical age of India. He was born in Kerala, South India in 476 AD but later lived in Kusumapura, which his commentator Bhaskara I (629 AD) identifies with pataliputra (modern Patna) in Bihar. His first name “Arya” is hardly a south Indian name while “Bhatt” (or Bhatta) is a typical north Indian name even found today specially among the trader community.
Aryabhatta studied at the University of Nalanda. One of his major works was Aryabhatiya written in 499 AD. His book aryabhatiya covers astronomical and mathematical theories in which the earth was taken to be spinning on its axis and the periods of the planets were given with respect to the sun. Aryabhatta believes that the moon and planets shine by reflected sunlight and he also believes that the orbits of the planets are ellipses. He correctly explains the causes of eclipses of the Sun and the Moon. His value for the length of the year at 365 days 6 hours 12 minutes 30 seconds is remarkably close to the true value which is about 365 days 6 hours. In this book, the day was reckoned from one sunrise to the next, whereas in his Aryabhata-siddhanta he took the day from one midnight to another. There was also difference in some astronomical parameters.
Aryabhatta was the first to explain how the Lunar Eclipse and the Solar Eclipse happened. Aryabhatta also gave close approximation for Pi. In the...

...during the Islamic Golden Age (c. 820 CE). Al-Khwarizmi cited some of his results and in the 10th century Al-Biruni stated that Aryabhata's followers believed that the Earth rotated on its axis. Aryabhata's astronomical calculation methods were also very influential. Islamic world widely used the trigonometric tables to compute many Arabic astronomical tables (zijes). Calendric calculations devised by Aryabhata and his followers contributed the practical purposes of fixing the Panchangam (the Hindu calendar). Other cultures used this for forming the calendar systems.
India honored Aryabhata by naming India's first satellite as Aryabhata. An Institute for conducting research in astronomy, astrophysics, and atmospheric sciences is the Aryabhatta Research Institute of Observational Sciences (ARIOS) near Nainital, India. Indian authorities named the inter-school math competition as ‘Aryabhata Maths Competition’, as is Bacillus Aryabhata, a species of bacteria discovered by ISRO scientists in 2009.
References
Indian Streams Research General: Avhale, P. S; Waghmare, R. V.; Kolhe, S. B. Indian Streams Research Journal. Sep2012, Vol. 2 Issue 8, Special section p1-5. 5p. Retrieved from https://ehis.ebscohost.com/eds/detail?vid=2&hid=117&sid=d84c9078-6d85-4131-9209-e44cdb4cba58%40sessionmgr110&bdata=JnNpdGU9ZWRzLWxpdmU%3d#db=a9h&AN=82351338
Aryabhata – Indian mathematician : Retrieved from...