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Positional Notation
Positional notation, also known as place-value notation, positional numeral system, or simply place value, 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 values may be modified when combined). 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 sy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abacus 6
An abacus ( abaci or abacuses), also called a counting frame, is a hand-operated calculating tool which was used from ancient times in the ancient Near East, Europe, China, and Russia, until the adoption of the Hindu–Arabic numeral system. An abacus consists of a two-dimensional array of slidable beads (or similar objects). In their earliest designs, the beads could be loose on a flat surface or sliding in grooves. Later the beads were made to slide on rods and built into a frame, allowing faster manipulation. Each rod typically represents one digit of a multi-digit number laid out using a positional numeral system such as base ten (though some cultures used different numerical bases). Roman and East Asian abacuses use a system resembling bi-quinary coded decimal, with a top deck (containing one or two beads) representing fives and a bottom deck (containing four or five beads) representing ones. Natural numbers are normally used, but some allow simple fractional compone ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chinese Numerals
Chinese numerals are words and characters used to denote numbers in written Chinese. Today, speakers of Chinese languages use three written numeral systems: the system of Arabic numerals used worldwide, and two indigenous systems. The more familiar indigenous system is based on Chinese characters that correspond to numerals in the spoken language. These may be shared with other languages of the Chinese cultural sphere such as Korean, Japanese, and Vietnamese. Most people and institutions in China primarily use the Arabic or mixed Arabic-Chinese systems for convenience, with traditional Chinese numerals used in finance, mainly for writing amounts on cheques, banknotes, some ceremonial occasions, some boxes, and on commercials. The other indigenous system consists of the Suzhou numerals, or ''huama'', a positional system, the only surviving form of the rod numerals. These were once used by Chinese mathematicians, and later by merchants in Chinese markets, such as those in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sign-value Notation
A sign-value notation represents numbers using a sequence of numerals which each represent a distinct quantity, regardless of their position in the sequence. Sign-value notations are typically additive, subtractive, or multiplicative depending on their conventions for grouping signs together to collectively represent numbers. Although the absolute value of each sign is independent of its position, the value of the sequence as a whole may depend on the order of the signs, as with numeral systems which combine additive and subtractive notation, such as Roman numerals. There is no need for zero in sign-value notation. Additive notation Additive notation represents numbers by a series of numerals that added together equal the value of the number represented, much as tally marks are added together to represent a larger number. To represent multiples of the sign value, the same sign is simply repeated. In Roman numerals, for example, means ten and means fifty, so means eighty ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Roman Empire
The Roman Empire ruled the Mediterranean and much of Europe, Western Asia and North Africa. The Roman people, Romans conquered most of this during the Roman Republic, Republic, and it was ruled by emperors following Octavian's assumption of effective sole rule in 27 BC. The Western Roman Empire, western empire collapsed in 476 AD, but the Byzantine Empire, eastern empire lasted until the fall of Constantinople in 1453. By 100 BC, the city of Rome had expanded its rule from the Italian peninsula to most of the Mediterranean Sea, Mediterranean and beyond. However, it was severely destabilised by List of Roman civil wars and revolts, civil wars and political conflicts, which culminated in the Wars of Augustus, victory of Octavian over Mark Antony and Cleopatra at the Battle of Actium in 31 BC, and the subsequent conquest of the Ptolemaic Kingdom in Egypt. In 27 BC, the Roman Senate granted Octavian overarching military power () and the new title of ''Augustus (title), Augustus'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hellenistic Period
In classical antiquity, the Hellenistic period covers the time in Greek history after Classical Greece, between the death of Alexander the Great in 323 BC and the death of Cleopatra VII in 30 BC, which was followed by the ascendancy of the Roman Empire, as signified by the Battle of Actium in 31 BC and the Roman conquest of Ptolemaic Egypt the following year, which eliminated the last major Hellenistic kingdom. Its name stems from the Ancient Greek word ''Hellas'' (, ''Hellás''), which was gradually recognized as the name for Greece, from which the modern historiographical term ''Hellenistic'' was derived. The term "Hellenistic" is to be distinguished from "Hellenic" in that the latter refers to Greece itself, while the former encompasses all the ancient territories of the period that had come under significant Greek influence, particularly the Hellenized Middle East, after the conquests of Alexander the Great. After the Macedonian conquest of the Achaemenid Empire in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Karl Menninger (mathematics)
Karl Menninger (October 6, 1898 – October 2, 1963) was a German teacher of and writer about mathematics. His major work was ''Zahlwort und Ziffer'' (1934; English trans., ''Number Words and Number Symbols''), about non-academic mathematics in much of the world. (The omission of Africa Africa is the world's second-largest and second-most populous continent after Asia. At about 30.3 million km2 (11.7 million square miles) including adjacent islands, it covers 20% of Earth's land area and 6% of its total surfac ... was rectified by Claudia Zaslavsky in her book ''Africa Counts''.) References *Dauben, Joseph Warren, and Christoph Scriba, eds. (2002), ''Writing the History of Mathematics'', Birkhäuser, Basel, page 483. *Menninger, Karl (1934), ''Zahlwort und Ziffer''. Revised edition (1958). Göttingen: Vandenhoeck and Ruprecht. *Menninger, Karl (1969), ''Number Words and Number Symbols''. Cambridge, Mass.: The M.I.T. Press. German historians ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carl Friedrich Gauss
Johann Carl Friedrich Gauss (; ; ; 30 April 177723 February 1855) was a German mathematician, astronomer, geodesist, and physicist, who contributed to many fields in mathematics and science. He was director of the Göttingen Observatory and professor of astronomy from 1807 until his death in 1855. While studying at the University of Göttingen, he propounded several mathematical theorems. As an independent scholar, he wrote the masterpieces '' Disquisitiones Arithmeticae'' and ''Theoria motus corporum coelestium''. Gauss produced the second and third complete proofs of the fundamental theorem of algebra. In number theory, he made numerous contributions, such as the composition law, the law of quadratic reciprocity and the Fermat polygonal number theorem. He also contributed to the theory of binary and ternary quadratic forms, the construction of the heptadecagon, and the theory of hypergeometric series. Due to Gauss' extensive and fundamental contributions to science ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Sand Reckoner
''The Sand Reckoner'' (, ''Psammites'') is a work by Archimedes, an Ancient Greek mathematician of the 3rd century BC, in which he set out to determine an upper bound for the number of grains of sand that fit into the universe. In order to do this, Archimedes had to estimate the size of the universe according to the contemporary model, and invent a way to talk about extremely large numbers. The work, also known in Latin as ''Arenarius'', is about eight pages long in translation and is addressed to the Syracusan king Gelo II (son of Hiero II). It is considered the most accessible work of Archimedes.Archimedes, The Sand Reckoner 511 R U, by Ilan Vardi accessed 28-II-2007. Naming large numbers [Baidu] |
Archimedes
Archimedes of Syracuse ( ; ) was an Ancient Greece, Ancient Greek Greek mathematics, mathematician, physicist, engineer, astronomer, and Invention, inventor from the ancient city of Syracuse, Sicily, Syracuse in History of Greek and Hellenistic Sicily, Sicily. Although few details of his life are known, based on his surviving work, he is considered one of the leading scientists in classical antiquity, and one of the greatest mathematicians of all time. Archimedes anticipated modern calculus and mathematical analysis, analysis by applying the concept of the Cavalieri's principle, infinitesimals and the method of exhaustion to derive and rigorously prove many geometry, geometrical theorem, theorems, including the area of a circle, the surface area and volume of a sphere, the area of an ellipse, the area under a parabola, the volume of a segment of a paraboloid of revolution, the volume of a segment of a hyperboloid of revolution, and the area of a spiral. Archimedes' other math ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variable (mathematics)
In mathematics, a variable (from Latin language, Latin ) is a Mathematical symbol, symbol, typically a letter, that refers to an unspecified mathematical object. One says colloquially that the variable ''represents'' or ''denotes'' the object, and that any valid candidate for the object is the value (mathematics), value of the variable. The values a variable can take are usually of the same kind, often numbers. More specifically, the values involved may form a Set (mathematics), set, such as the set of real numbers. The object may not always exist, or it might be uncertain whether any valid candidate exists or not. For example, one could represent two integers by the variables and and require that the value of the square of is twice the square of , which in algebraic notation can be written . A definitive proof that this relationship is impossible to satisfy when and are restricted to integer numbers isn't obvious, but it has been known since ancient times and has had a big ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zero
0 (zero) is a number representing an empty quantity. Adding (or subtracting) 0 to any number leaves that number unchanged; in mathematical terminology, 0 is the additive identity of the integers, rational numbers, real numbers, and complex numbers, as well as other algebraic structures. Multiplying any number by 0 results in 0, and consequently division by zero has no meaning in arithmetic. As a numerical digit, 0 plays a crucial role in decimal notation: it indicates that the power of ten corresponding to the place containing a 0 does not contribute to the total. For example, "205" in decimal means two hundreds, no tens, and five ones. The same principle applies in place-value notations that uses a base other than ten, such as binary and hexadecimal. The modern use of 0 in this manner derives from Indian mathematics that was transmitted to Europe via medieval Islamic mathematicians and popularized by Fibonacci. It was independently used by the Maya. Common name ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
