Casting Out Nines
Casting out nines is any of three arithmetical procedures: *Adding the decimal digits of a positive whole number, while optionally ignoring any 9s or digits which sum to 9 or a multiple of 9. The result of this procedure is a number which is smaller than the original whenever the original has more than one digit, leaves the same remainder as the original after division by nine, and may be obtained from the original by subtracting a multiple of 9 from it. The name of the procedure derives from this latter property. *Repeated application of this procedure to the results obtained from previous applications until a single-digit number is obtained. This single-digit number is called the "digital root" of the original. If a number is divisible by 9, its digital root is 9. Otherwise, its digital root is the remainder it leaves after being divided by 9. *A sanity test in which the above-mentioned procedures are used to check for errors in arithmetical calculations. The test is car ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Integer
An integer is the number zero (0), a positive natural number (1, 2, 3, ...), or the negation of a positive natural number (−1, −2, −3, ...). The negations or additive inverses of the positive natural numbers are referred to as negative integers. The set (mathematics), set of all integers is often denoted by the boldface or blackboard bold The set of natural numbers \mathbb is a subset of \mathbb, which in turn is a subset of the set of all rational numbers \mathbb, itself a subset of the real numbers \mathbb. Like the set of natural numbers, the set of integers \mathbb is Countable set, countably infinite. An integer may be regarded as a real number that can be written without a fraction, fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, , 5/4, and Square root of 2, are not. The integers form the smallest Group (mathematics), group and the smallest ring (mathematics), ring containing the natural numbers. In algebraic number theory, the ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Remainder
In mathematics, the remainder is the amount "left over" after performing some computation. In arithmetic, the remainder is the integer "left over" after dividing one integer by another to produce an integer quotient ( integer division). In algebra of polynomials, the remainder is the polynomial "left over" after dividing one polynomial by another. The ''modulo operation'' is the operation that produces such a remainder when given a dividend and divisor. Alternatively, a remainder is also what is left after subtracting one number from another, although this is more precisely called the '' difference''. This usage can be found in some elementary textbooks; colloquially it is replaced by the expression "the rest" as in "Give me two dollars back and keep the rest." However, the term "remainder" is still used in this sense when a function is approximated by a series expansion, where the error expression ("the rest") is referred to as the remainder term. Integer division Gi ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Brady Haran
Brady John Haran (born 18 June 1976) is an Australian-British independent filmmaker and video journalist who produces educational videos and documentary films for his YouTube channels, the most notable being ''Computerphile'' and ''Numberphile''. Haran is also the co-host of the'' Hello Internet'' podcast along with fellow educational YouTuber CGP Grey. On 22 August 2017, Haran launched his second podcast, called ''The Unmade Podcast'', and on 11 November 2018, he launched his third podcast, '' The Numberphile Podcast'', based on his mathematics-centered channel of the same name. Reporter and filmmaker Brady Haran studied journalism for a year before being hired by '' The Adelaide Advertiser''. In 2002, he moved from Australia to Nottingham, United Kingdom. In Nottingham, he worked for the BBC, began to work with film, and reported for '' East Midlands Today'', BBC News Online and BBC radio stations. In 2007, Haran worked as a filmmaker-in-residence for Nottingham Science C ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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The Mathematical Association Of America
The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university, college, and high school teachers; graduate and undergraduate students; pure and applied mathematicians; computer scientists; statisticians; and many others in academia, government, business, and industry. The MAA was founded in 1915 and is headquartered at 11 Dupont in the Dupont Circle neighborhood of Washington, D.C. The organization publishes mathematics journals and books, including the ''American Mathematical Monthly'' (established in 1894 by Benjamin Finkel), the most widely read mathematics journal in the world according to records on JSTOR. Meetings The MAA sponsors the annual summer MathFest and cosponsors with the American Mathematical Society the Joint Mathematics Meeting, held in early January of each year. On occasion the Society for Industrial and Applied Mathematics joins in these meetings. Twe ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Fibonacci
Leonardo Bonacci ( – ), commonly known as Fibonacci, was an Italians, 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'', is first found in a modern source in a 1838 text by the Franco-Italian mathematician Guglielmo Libri Carucci dalla Sommaja, Guglielmo Libri and is short for ('son of Bonacci'). However, even as early as 1506, Perizolo, a notary of the Holy Roman Empire, mentions him as "Lionardo Fibonacci". Fibonacci popularized the Hindu–Arabic numeral system, Indo–Arabic numeral system in the Western world primarily through his composition in 1202 of (''Book of Calculation'') and also introduced Europe to the sequence of Fibonacci numbers, which he used as an example in . Biography Fibonacci was born around 1170 to Guglielmo, an Italian merchant and customs official who directed a trading post in Béjaïa, Bugia, modern-day Béjaïa, Algeria ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Avicenna
Ibn Sina ( – 22 June 1037), commonly known in the West as Avicenna ( ), was a preeminent philosopher and physician of the Muslim world, flourishing during the Islamic Golden Age, serving in the courts of various Iranian peoples, Iranian rulers. He is often described as the father of early modern medicine. His philosophy was of the Peripatetic school derived from Aristotelianism. His most famous works are ''The Book of Healing'', a philosophical and scientific encyclopedia, and ''The Canon of Medicine'', a medical encyclopedia which became a standard medical text at many medieval European University, universities and remained in use as late as 1650. Besides philosophy and medicine, Avicenna's corpus includes writings on Astronomy in medieval Islam, astronomy, Alchemy and chemistry in medieval Islam, alchemy, Geography and cartography in medieval Islam, geography and geology, Psychology in medieval Islam, psychology, Islamic theology, Logic in Islamic philosophy, logic, Mat ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Aryabhata II
Āryabhaṭa (c. 920 – c. 1000) was an Indian mathematician and astronomer, and the author of the ''Maha-Siddhanta''. The numeral II is given to him to distinguish him from the earlier and more influential Āryabhaṭa I. Scholars are unsure of when exactly he was born, though David Pingree dates of his main publications between 950–1100. The manuscripts of his ''Maha-Siddhanta'' have been discovered from Gujarat, Rajasthan, Uttar Pradesh, and Bengal, so he probably lived in northern India. Maha Siddhanta Aryabhata wrote ''Maha-Siddhanta'', also known as ''Arya-siddhanta'', Sanskrit language work containing 18 chapters. It summarizes a lost work attributed to Parashara, and is probably based on Shridhara's work. The initial twelve chapters deal with topics related to mathematical astronomy and cover the topics that Indian mathematicians of that period had already worked on. The various topics that have been included in these twelve chapters are: the longitud ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Greek Numerals
Greek numerals, also known as Ionic, Ionian, Milesian, or Alexandrian numerals, is a numeral system, system of writing numbers using the letters of the Greek alphabet. In modern Greece, they are still used for ordinal number (linguistics), ordinal numbers and in contexts similar to those in which Roman numerals are still used in the Western world. For ordinary cardinal number (linguistics), cardinal numbers, however, modern Greece uses Arabic numerals. History The Minoans, Minoan and Mycenaean civilizations' Linear A and Linear B alphabets used a different system, called Aegean numerals, which included number-only symbols for powers of ten: = 1, = 10, = 100, = 1000, and = 10000. Attic numerals composed another system that came into use perhaps in the 7th century BC. They were acrophonic, derived (after the initial one) from the first letters of the names of the numbers represented. They ran = 1, = ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Nicomachus
Nicomachus of Gerasa (; ) was an Ancient Greek Neopythagorean philosopher from Gerasa, in the Roman province of Syria (now Jerash, Jordan). Like many Pythagoreans, Nicomachus wrote about the mystical properties of numbers, best known for his works ''Introduction to Arithmetic'' and ''Manual of Harmonics'', which are an important resource on Ancient Greek mathematics and Ancient Greek music in the Roman period. Nicomachus' work on arithmetic became a standard text for Neoplatonic education in Late antiquity, with philosophers such as Iamblichus and John Philoponus writing commentaries on it. A Latin paraphrase by Boethius of Nicomachus's works on arithmetic and music became standard textbooks in medieval education. Life Little is known about the life of Nicomachus except that he was a Pythagorean who came from Gerasa. His ''Manual of Harmonics'' was addressed to a lady of noble birth, at whose request Nicomachus wrote the book, which suggests that he was a respected schola ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Introduction To Arithmetic
Nicomachus of Gerasa (; ) was an Ancient Greek Neopythagoreanism, Neopythagorean philosopher from Gerasa, in the Syria (Roman province), Roman province of Syria (now Jerash, Jordan). Like many Pythagoreans, Nicomachus wrote about the mystical properties of numbers, best known for his works ''Introduction to Arithmetic'' and ''Manual of Harmonics'', which are an important resource on Ancient Greek mathematics and Ancient Greek music in the Roman period. Nicomachus' work on arithmetic became a standard text for Neoplatonic education in Late antiquity, with philosophers such as Iamblichus and John Philoponus writing commentaries on it. A Latin paraphrase by Boethius of Nicomachus's works on arithmetic and music became standard textbooks in medieval education. Life Little is known about the life of Nicomachus except that he was a Pythagoreanism, Pythagorean who came from Gerasa. His ''Manual of Harmonics'' was addressed to a lady of noble birth, at whose request Nicomachus wrote the ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Iamblichus
Iamblichus ( ; ; ; ) was a Neoplatonist philosopher who determined a direction later taken by Neoplatonism. Iamblichus was also the biographer of the Greek mystic, philosopher, and mathematician Pythagoras. In addition to his philosophical contributions, his is important for the study of the sophists because it preserved about ten pages of an otherwise unknown sophist known as the Anonymus Iamblichi. Life According to the and Iamblichus' biographer, Eunapius, Iamblichus was born in Chalcis (later called Qinnašrīn) in Coele, now in northwest Syria. Iamblichus was descended from the Emesene dynasty. He initially studied under Anatolius of Laodicea and later studied under Porphyry, a pupil of Plotinus (the founder of Neoplatonism). Iamblichus disagreed with Porphyry about theurgy, reportedly responding to Porphyry's criticism of the practice in '' On the Mysteries of the Egyptians, Chaldeans, and Assyrians''. He returned to Coele Syria around 304 to found a school i ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |
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Refutation Of All Heresies
The ''Refutation of All Heresies'' (; ), also called the ''Elenchus'' or ''Philosophumena'', is a compendious Christian polemical work of the early third century, whose attribution to Hippolytus of Rome or an unknown " Pseudo-Hippolytus" is disputed. It catalogues both pagan beliefs and 33 gnostic Christian systems deemed heretical by the author/s and/or compiler/s, making it a major source of information on contemporary opponents of Christian orthodoxy as understood today. The first book, a synopsis of Greek philosophy, circulated separately in several manuscripts and was known as the ''Philosophoumena'' ( "philosophical teachings"), a title which some extend to the whole work. Books IV-X were recovered in 1842 in a manuscript at Mount Athos, while books II and III remain lost. The work was long attributed to the early Christian theologian Origen. Contents This work is divided into ten books, 8 of which have survived more or less intact. Books II and III, however, have not been ... [...More Info...]       [...Related Items...]     OR:     [Wikipedia]   [Google]   [Baidu]   |