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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 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 carried o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integer
An integer is the number zero (), a positive natural number (, , , etc.) or a negative integer with a minus sign ( −1, −2, −3, etc.). The negative numbers are the additive inverses of the corresponding positive numbers. In the language of mathematics, the set of integers is often denoted by the boldface or blackboard bold \mathbb. 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 natural numbers, \mathbb is countably infinite. An integer may be regarded as a real number that can be written without a fractional component. For example, 21, 4, 0, and −2048 are integers, while 9.75, , and are not. The integers form the smallest group and the smallest ring containing the natural numbers. In algebraic number theory, the integers are sometimes qualified as rational integers to distinguish them from the more general algebraic in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transposition Error
A transcription error is a specific type of data entry error that is commonly made by human operators or by optical character recognition (OCR) programs. Human transcription errors are commonly the result of typographical mistakes; putting one’s fingers in the wrong place while touch typing is the easiest way to make this error. Electronic transcription errors occur when the scan of some printed matter is compromised or in an unusual font – for example, if the paper is crumpled, or the ink is smudged, the OCR may make transcription errors when reading. Transposition error Transposition errors are commonly mistaken for transcription errors, but they should not be confused. As the name suggests, transposition errors occur when characters have “transposed”—that is, they have switched places. Transposition errors are almost always human in origin. The most common way for characters to be transposed is when a user is touch typing at a speed that makes them input a later ch ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Error Detection
In information theory and coding theory with applications in computer science and telecommunication, error detection and correction (EDAC) or error control are techniques that enable reliable delivery of digital data over unreliable communication channels. Many communication channels are subject to channel noise, and thus errors may be introduced during transmission from the source to a receiver. Error detection techniques allow detecting such errors, while error correction enables reconstruction of the original data in many cases. Definitions ''Error detection'' is the detection of errors caused by noise or other impairments during transmission from the transmitter to the receiver. ''Error correction'' is the detection of errors and reconstruction of the original, error-free data. History In classical antiquity, copyists of the Hebrew Bible were paid for their work according to the number of stichs (lines of verse). As the prose books of the Bible were hardly ever wr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Signal Processing
Signal processing is an electrical engineering subfield that focuses on analyzing, modifying and synthesizing ''signals'', such as sound, images, and scientific measurements. Signal processing techniques are used to optimize transmissions, digital storage efficiency, correcting distorted signals, subjective video quality and to also detect or pinpoint components of interest in a measured signal. History According to Alan V. Oppenheim and Ronald W. Schafer, the principles of signal processing can be found in the classical numerical analysis techniques of the 17th century. They further state that the digital refinement of these techniques can be found in the digital control systems of the 1940s and 1950s. In 1948, Claude Shannon wrote the influential paper "A Mathematical Theory of Communication" which was published in the Bell System Technical Journal. The paper laid the groundwork for later development of information communication systems and the processing of signals ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Buckminster Fuller
Richard Buckminster Fuller (; July 12, 1895 – July 1, 1983) was an American architect, systems theorist, writer, designer, inventor, philosopher, and futurist. He styled his name as R. Buckminster Fuller in his writings, publishing more than 30 books and coining or popularizing such terms as " Spaceship Earth", " Dymaxion" (e.g., Dymaxion house, Dymaxion car, Dymaxion map), "ephemeralization", " synergetics", and "tensegrity". Fuller developed numerous inventions, mainly architectural designs, and popularized the widely known geodesic dome; carbon molecules known as fullerenes were later named by scientists for their structural and mathematical resemblance to geodesic spheres. He also served as the second World President of Mensa International from 1974 to 1983. Fuller was awarded 28 United States patents and many honorary doctorates. In 1960, he was awarded the Frank P. Brown Medal from The Franklin Institute. He was elected an honorary member of Phi Beta Kappa in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Synergetics (Fuller)
Synergetics is the empirical study of systems in transformation, with an emphasis on whole system behaviors unpredicted by the behavior of any components in isolation. R. Buckminster Fuller (1895–1983) named and pioneered the field. His two-volume work ''Synergetics: Explorations in the Geometry of Thinking'', in collaboration with E. J. Applewhite, distills of a lifetime of research into book form. Since systems are identifiable at every scale, Synergetics is necessarily interdisciplinary, embracing a broad range of scientific and philosophical topics, especially in the area of geometry, wherein the tetrahedron features as Fuller's model of the simplest system. Despite mainstream endorsements such as the prologue by Arthur Loeb, and positive dust cover blurbs by U Thant and Arthur C. Clarke, along with the posthumous naming of the carbon allotrope "buckminsterfullerene", Synergetics remains an off-beat subject, ignored for decades by most traditional curricula and academic d ... [...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 mod ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Avicenna
Ibn Sina ( fa, ابن سینا; 980 – June 1037 CE), commonly known in the West as Avicenna (), was a Persian polymath who is regarded as one of the most significant physicians, astronomers, philosophers, and writers of the Islamic Golden Age, and the father of early modern medicine. Sajjad H. Rizvi has called Avicenna "arguably the most influential philosopher of the pre-modern era". He was a Muslim Peripatetic philosopher influenced by Greek Aristotelian philosophy. Of the 450 works he is believed to have written, around 240 have survived, including 150 on philosophy and 40 on medicine. 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 universities and remained in use as late as 1650. Besides philosophy and medicine, Avicenna's corpus includes writings on astronomy, alchemy, geography and geology, psycholo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aryabhata II
Āryabhaṭa (c. 920 – c. 1000) was an Indian mathematician and astronomer An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such as stars, planets, moons, comets and galaxies – in either ..., 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 some give dates of his main publications being between 950–1100. Maha Siddhanta Aryabhata's most eminent work was Maha Siddhanta. The treatise consists of eighteen chapters and was written in the form of verse in Sanskrit. The initial twelve chapters deals with topics related to mathematical astronomy and covers the topics that Indian mathematicians of that period had already worked on. The various topics that have been included in these tw ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Greek Numerals
Greek numerals, also known as Ionic, Ionian, Milesian, or Alexandrian numerals, are a system of writing numbers using the letters of the Greek alphabet. In modern Greece, they are still used for ordinal numbers and in contexts similar to those in which Roman numerals are still used in the Western world. For ordinary cardinal numbers, however, modern Greece uses Arabic numerals. History The Minoan and Mycenaean civilization Mycenaean Greece (or the Mycenaean civilization) was the last phase of the Bronze Age in Ancient Greece, spanning the period from approximately 1750 to 1050 BC.. It represents the first advanced and distinctively Greek civilization in mainland ...s' 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 comprised another system that came into use perhaps in th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nicomachus
Nicomachus of Gerasa ( grc-gre, Νικόμαχος; c. 60 – c. 120 AD) was an important ancient mathematician and music theorist, best known for his works ''Introduction to Arithmetic'' and ''Manual of Harmonics'' in Greek. He was born in Gerasa, in the Roman province of Syria (now Jerash, Jordan). He was a Neopythagorean, who wrote about the mystical properties of numbers.Eric Temple Bell (1940), ''The development of mathematics'', page 83.Frank J. Swetz (2013), ''The European Mathematical Awakening'', page 17, Courier Life Little is known about the life of Nicomachus except that he was a Pythagorean who came from Gerasa.} Historians consider him a Neopythagorean based on his tendency to view numbers as having mystical properties. The age in which he lived (c. 100 AD) is only known because he mentions Thrasyllus in his ''Manual of Harmonics'', and because his ''Introduction to Arithmetic'' was apparently translated into Latin in the mid 2nd century by Apuleius.Henrietta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Introduction To Arithmetic
The book ''Introduction to Arithmetic'' ( grc-gre, Ἀριθμητικὴ εἰσαγωγή, ''Arithmetike eisagoge'') is the only extant work on mathematics by Nicomachus (60–120 AD). Summary The work contains both philosophical prose and basic mathematical ideas. Nicomachus refers to Plato quite often, and writes that philosophy can only be possible if one knows enough about mathematics. Nicomachus also describes how natural numbers and basic mathematical ideas are eternal and unchanging, and in an abstract realm. It consists of two books, twenty-three and twenty-nine chapters, respectively. Although he was preceded by the Babylonians and the Chinese, Nicomachus provided one of the earliest Greco-Roman multiplication tables, whereas the oldest extant Greek multiplication table is found on a wax tablet dated to the 1st century AD (now found in the British Museum). Influence The ''Introduction to Arithmetic'' of Nicomachus was a standard textbook in Neoplatonic schoo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
