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Bhāskara I
Bhāskara () (commonly called Bhāskara I to avoid confusion with the 12th-century mathematician Bhāskara II) was a 7th-century Indian mathematician and astronomer who was the first to write numbers in the Hindu–Arabic decimal system with a circle for the zero, and who gave a unique and remarkable rational approximation of the sine function in his commentary on Aryabhata's work. This commentary, ''Āryabhaṭīyabhāṣya'', written in 629 CE, is among the oldest known prose works in Sanskrit on mathematics and astronomy. He also wrote two astronomical works in the line of Aryabhata's school: the ''Mahābhāskarīya'' (“Great Book of Bhaskara”) and the ''Laghubhāskarīya'' (“Small Book of Bhaskara”). On 7 June 1979, the Indian Space Research Organisation launched the Bhāskara I satellite, named in honour of the mathematician. Biography Little is known about Bhāskara's life, except for what can be deduced from his writings. He was born in India in the 7th centu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bhaskara I's Sine Approximation Formula
In mathematics, Bhaskara I's sine approximation formula is a rational expression in one variable for the computation of the approximate values of the trigonometric sines discovered by Bhaskara I (c. 600 – c. 680), a seventh-century Indian mathematician. This formula is given in his treatise titled ''Mahabhaskariya''. It is not known how Bhaskara I arrived at his approximation formula. However, several historians of mathematics have put forward different hypotheses as to the method Bhaskara might have used to arrive at his formula. The formula is elegant, simple and enables one to compute reasonably accurate values of trigonometric sines without using any geometry whatsoever. The approximation formula The formula is given in verses 17 – 19, Chapter VII, Mahabhaskariya of Bhaskara I. A translation of the verses is given below: *(Now) I briefly state the rule (for finding the ''bhujaphala'' and the ''kotiphala'', etc.) without making use of the Rsine-differences 225, e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vallabhi
Vallabhi (or Valabhi or Valabhipur, modern Vala; Devanāgarī: वल्लभी) is an ancient city located in the Saurashtra peninsula of Gujarat, near Bhavnagar in western India. It is also known as Vallabhipura and was the capital of the Suryavanshi Maitraka Dynasty. History Vallabhi was occupied as early as the Harappan period, and was later part of the Maurya Empire from about 322 BCE until 185 BCE. The Satavahana dynasty ruled the area, off and on, from the late second century BCE until the early third century CE. The Gupta Empire held the area from approximately 319 CE to 467 CE. The Great Council of Vallabhi, which codified the Śvētāmbaras Jain texts, was held there in 454 CE, during the decline of the Gupta Empire. In the fifth century (CE), the first two Maitraka rulers, Bhatarka and Dharasena I, only used the title of ''Senapati'' (general). The third ruler, Dronasimha (Dronasena ), declared himself ''Maharaja'' (literally "Great King").Roychaudhuri, H.C ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wilson's Theorem
In algebra and number theory, Wilson's theorem states that a natural number ''n'' > 1 is a prime number if and only if the product of all the positive integers less than ''n'' is one less than a multiple of ''n''. That is (using the notations of modular arithmetic), the factorial (n - 1)! = 1 \times 2 \times 3 \times \cdots \times (n - 1) satisfies :(n-1)!\ \equiv\; -1 \pmod n exactly when ''n'' is a prime number. In other words, any number ''n'' is a prime number if, and only if, (''n'' − 1)! + 1 is divisible by ''n''. History This theorem was stated by Ibn al-Haytham (c. 1000 AD), and, in the 18th century, by John Wilson. Edward Waring announced the theorem in 1770, although neither he nor his student Wilson could prove it. Lagrange gave the first proof in 1771. There is evidence that Leibniz was also aware of the result a century earlier, but he never published it. Example For each of the values of ''n'' from 2 to 30, the following table shows the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fibonacci
Fibonacci (; also , ; – ), also known as Leonardo Bonacci, Leonardo of Pisa, or Leonardo Bigollo Pisano ('Leonardo the Traveller from Pisa'), was an Italian mathematician from the Republic of Pisa, considered to be "the most talented Western mathematician of the Middle Ages". The name he is commonly called, ''Fibonacci'', was made up in 1838 by the Franco-Italian historian Guillaume Libri and is short for ('son of Bonacci'). However, even earlier in 1506 a notary of the Holy Roman Empire, Perizolo mentions Leonardo as "Lionardo Fibonacci". Fibonacci popularized the Indo–Arabic numeral system in the Western world primarily through his composition in 1202 of ''Liber Abaci'' (''Book of Calculation''). He also introduced Europe to the sequence of Fibonacci numbers, which he used as an example in ''Liber Abaci''. Biography Fibonacci was born around 1170 to Guglielmo, an Italian merchant and customs official. Guglielmo directed a trading post in Bugia (Béjaïa) in modern- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alhazen
Ḥasan Ibn al-Haytham, Latinized as Alhazen (; full name ; ), was a medieval mathematician, astronomer, and physicist of the Islamic Golden Age from present-day Iraq.For the description of his main fields, see e.g. ("He is one of the principal Arab mathematicians and, without any doubt, the best physicist.") , ("Ibn al-Ḥaytam was an eminent eleventh-century Arab optician, geometer, arithmetician, algebraist, astronomer, and engineer."), ("Ibn al-Haytham (d. 1039), known in the West as Alhazan, was a leading Arab mathematician, astronomer, and physicist. His optical compendium, Kitab al-Manazir, is the greatest medieval work on optics.") Referred to as "the father of modern optics", he made significant contributions to the principles of optics and visual perception in particular. His most influential work is titled '' Kitāb al-Manāẓir'' (Arabic: , "Book of Optics"), written during 1011–1021, which survived in a Latin edition. Ibn al-Haytham was an early propo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Āryabhaṭīya
''Aryabhatiya'' (IAST: ') or ''Aryabhatiyam'' ('), a Sanskrit astronomical treatise, is the ''magnum opus'' and only known surviving work of the 5th century Indian mathematician Aryabhata. Philosopher of astronomy Roger Billard estimates that the book was composed around 510 CE based on historical references it mentions. Structure and style Aryabhatiya is written in Sanskrit and divided into four sections; it covers a total of 121 verses describing different moralitus via a mnemonic writing style typical for such works in India (see definitions below): 1. Gitikapada (13 verses): large units of time—kalpa, manvantara, and yuga—which present a cosmology different from earlier texts such as Lagadha's Vedanga Jyotisha (ca. 1st century BCE). There is also a table of ine (jya), given in a single verse. The duration of the planetary revolutions during a mahayuga is given as 4.32 million years. 2. Ganitapada (33 verses): covering mensuration (kṣetra vyāvahāra); arithmetic and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brahmi Numeral
The Brahmi numerals are a numeral system attested from the 3rd century BCE (somewhat later in the case of most of the tens). They are a non positional decimal system. They are the direct graphic ancestors of the modern Hindu–Arabic numeral system. However, they were conceptually distinct from these later systems, as they were not used as a positional system with a zero. Rather, there were separate numerals for each of the tens (10, 20, 30, etc.). There were also symbols for 100 and 1000 which were combined in ligatures with the units to signify 200, 300, 2000, 3000, etc. In computers, these ligatures are written with the Brahmi Number Joiner at U+1107F. Origins The source of the first three numerals seems clear: they are collections of 1, 2, and 3 strokes, in Ashoka's era vertical I, II, III like Roman numerals, but soon becoming horizontal like the ancient Han Chinese numerals. In the oldest inscriptions, 4 looks like a +, reminiscent of the X of neighboring , and perh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decimal
The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers of the Hindu–Arabic numeral system. The way of denoting numbers in the decimal system is often referred to as ''decimal notation''. A ''decimal numeral'' (also often just ''decimal'' or, less correctly, ''decimal number''), refers generally to the notation of a number in the decimal numeral system. Decimals may sometimes be identified by a decimal separator (usually "." or "," as in or ). ''Decimal'' may also refer specifically to the digits after the decimal separator, such as in " is the approximation of to ''two decimals''". Zero-digits after a decimal separator serve the purpose of signifying the precision of a value. The numbers that may be represented in the decimal system are the decimal fractions. That is, fractions of the form , where is an integer, and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Positional Numeral System
Positional notation (or place-value notation, or positional numeral system) usually denotes the extension to any radix, base of the Hindu–Arabic numeral system (or decimal, decimal system). More generally, a positional system is a numeral system in which the contribution of a digit to the value of a number is the value of the digit multiplied by a factor determined by the position of the digit. In early numeral systems, such as Roman numerals, a digit has only one value: I means one, X means ten and C a hundred (however, the value may be negated if placed before another digit). In modern positional systems, such as the decimal, decimal system, the position of the digit means that its value must be multiplied by some value: in 555, the three identical symbols represent five hundreds, five tens, and five units, respectively, due to their different positions in the digit string. The Babylonian Numerals, Babylonian numeral system, base 60, was the first positional system to be deve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brahmagupta
Brahmagupta ( – ) was an Indian mathematician and astronomer. He is the author of two early works on mathematics and astronomy: the ''Brāhmasphuṭasiddhānta'' (BSS, "correctly established doctrine of Brahma", dated 628), a theoretical treatise, and the '' Khaṇḍakhādyaka'' ("edible bite", dated 665), a more practical text. Brahmagupta was the first to give rules for computing with ''zero''. The texts composed by Brahmagupta were in elliptic verse in Sanskrit, as was common practice in Indian mathematics. As no proofs are given, it is not known how Brahmagupta's results were derived. In 628 CE, Brahmagupta first described gravity as an attractive force, and used the term "gurutvākarṣaṇam (गुरुत्वाकर्षणम्)" in Sanskrit to describe it. Life and career Brahmagupta was born in 598 CE according to his own statement. He lived in ''Bhillamāla'' in Gurjaradesa (modern Bhinmal in Rajasthan, India) during the reign of the Chavda dynasty ruler, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Harsha
Harshavardhana ( IAST Harṣa-vardhana; c. 590–647 CE) was a Pushyabhuti emperor who ruled northern India from 606 to 647 CE. He was the son of Prabhakaravardhana who had defeated the Alchon Huna invaders, and the younger brother of Rajyavardhana, a king of Thanesar, present-day Haryana. At the height of Harsha's power, his territory covered much of north and northwestern India, with the Narmada River as its southern boundary. He eventually made Kannauj (in present Uttar Pradesh state) his capital, and ruled till 647 CE.International Dictionary of Historic Places: Asia and Oceania by Trudy Ring, Robert M. Salkin, Sharon La Boda p.507 Harsha was defeated by the Emperor Pulakeshin II of the Chalukya dynasty in the Battle of Narmada, when he tried to expand his empire into the southern peninsula of India. The peace and prosperity that prevailed made his court a centre of cosmopolitanism, attracting scholars, artists and religious visitors from far and wide. The Chinese tra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thanesar
Thanesar city or old Kurukshetra city is a historic town and an important Hindu pilgrimage sites, Hindu pilgrimage centre in Kurukshetra district of the States and territories of India, state of Haryana in North India, northern India. It is located in Kurukshetra district, approximately 160 km northwest of Delhi. Thanesar city means old name of kurukshetra city. Kurukshetra (Sthanishwar city ) was the capital and seat of power of the Pushyabhuti dynasty, whose rulers conquered most of Aryavarta following the fall of the Gupta Empire. The Pushyabhuti emperor Prabhakarvardhana was a ruler of Thanesar in the early seventh century CE. He was succeeded by his sons, Rajyavardhana and Harsha. Harsha, also known as Harshavardhana, consolidated a vast empire over much of North India by defeating independent kings that fragmented from the Later Guptas. History The name Thanesar is derived from its name in Sanskrit language, Sanskrit, ''Sthanishvara'' which means ''Place/Abode of G ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
