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Babylonian Mathematics
Babylonian mathematics (also known as ''Assyro-Babylonian mathematics'') are the mathematics developed or practiced by the people of Mesopotamia, from the days of the early Sumerians to the centuries following the fall of Babylon in 539 BC. Babylonian mathematical texts are plentiful and well edited. With respect to time they fall in two distinct groups: one from the Old Babylonian period (1830–1531 BC), the other mainly Seleucid from the last three or four centuries BC. With respect to content, there is scarcely any difference between the two groups of texts. Babylonian mathematics remained constant, in character and content, for nearly two millennia. In contrast to the scarcity of sources in Egyptian mathematics, knowledge of Babylonian mathematics is derived from some 400 clay tablets unearthed since the 1850s. Written in Cuneiform script, tablets were inscribed while the clay was moist, and baked hard in an oven or by the heat of the sun. The majority of recovered clay tab ...
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Akkadian Language
Akkadian (, Akkadian: )John Huehnergard & Christopher Woods, "Akkadian and Eblaite", ''The Cambridge Encyclopedia of the World's Ancient Languages''. Ed. Roger D. Woodard (2004, Cambridge) Pages 218-280 is an extinct East Semitic language that was spoken in ancient Mesopotamia ( Akkad, Assyria, Isin, Larsa and Babylonia) from the third millennium BC until its gradual replacement by Akkadian-influenced Old Aramaic among Mesopotamians by the 8th century BC. It is the earliest documented Semitic language. It used the cuneiform script, which was originally used to write the unrelated, and also extinct, Sumerian (which is a language isolate). Akkadian is named after the city of Akkad, a major centre of Mesopotamian civilization during the Akkadian Empire (c. 2334–2154 BC). The mutual influence between Sumerian and Akkadian had led scholars to describe the languages as a '' Sprachbund''. Akkadian proper names were first attested in Sumerian texts from around the mi ...
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Clay Tablet, Mathematical, Geometric-algebraic, Similar To The Euclidean Geometry
Clay is a type of fine-grained natural soil material containing clay minerals (hydrous aluminium phyllosilicates, e.g. kaolin, Al2 Si2 O5( OH)4). Clays develop plasticity when wet, due to a molecular film of water surrounding the clay particles, but become hard, brittle and non–plastic upon drying or firing. Most pure clay minerals are white or light-coloured, but natural clays show a variety of colours from impurities, such as a reddish or brownish colour from small amounts of iron oxide. Clay is the oldest known ceramic material. Prehistoric humans discovered the useful properties of clay and used it for making pottery. Some of the earliest pottery shards have been dated to around 14,000 BC, and clay tablets were the first known writing medium. Clay is used in many modern industrial processes, such as paper making, cement production, and chemical filtering. Between one-half and two-thirds of the world's population live or work in buildings made with clay, ofte ...
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Clay Tablet, Mathematical, Geometric-algebraic, Similar To The Pythagorean Theorem
Clay is a type of fine-grained natural soil material containing clay minerals (hydrous aluminium phyllosilicates, e.g. kaolin, Al2 Si2 O5( OH)4). Clays develop plasticity when wet, due to a molecular film of water surrounding the clay particles, but become hard, brittle and non–plastic upon drying or firing. Most pure clay minerals are white or light-coloured, but natural clays show a variety of colours from impurities, such as a reddish or brownish colour from small amounts of iron oxide. Clay is the oldest known ceramic material. Prehistoric humans discovered the useful properties of clay and used it for making pottery. Some of the earliest pottery shards have been dated to around 14,000 BC, and clay tablets were the first known writing medium. Clay is used in many modern industrial processes, such as paper making, cement production, and chemical filtering. Between one-half and two-thirds of the world's population live or work in buildings made with clay, often bak ...
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Division (mathematics)
Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication. At an elementary level the division of two natural numbers is, among other possible interpretations, the process of calculating the number of times one number is contained within another. This number of times need not be an integer. For example, if 20 apples are divided evenly between 4 people, everyone receives 5 apples (see picture). The division with remainder or Euclidean division of two natural numbers provides an integer ''quotient'', which is the number of times the second number is completely contained in the first number, and a ''remainder'', which is the part of the first number that remains, when in the course of computing the quotient, no further full chunk of the size of the second number can be allocated. For example, if 21 apples are divided between 4 people, everyone receives 5 ...
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Geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is called a '' geometer''. Until the 19th century, geometry was almost exclusively devoted to Euclidean geometry, which includes the notions of point, line, plane, distance, angle, surface, and curve, as fundamental concepts. During the 19th century several discoveries enlarged dramatically the scope of geometry. One of the oldest such discoveries is Carl Friedrich Gauss' ("remarkable theorem") that asserts roughly that the Gaussian curvature of a surface is independent from any specific embedding in a Euclidean space. This implies that surfaces can be studied ''intrinsically'', that is, as stand-alone spaces, and has been expanded into the theory of manifolds and Riemannian geometry. Later in the 19th century, it appeared that ...
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Multiplication Table
In mathematics, a multiplication table (sometimes, less formally, a times table) is a mathematical table used to define a multiplication operation for an algebraic system. The decimal multiplication table was traditionally taught as an essential part of elementary arithmetic around the world, as it lays the foundation for arithmetic operations with base-ten numbers. Many educators believe it is necessary to memorize the table up to 9 × 9. History In pre-modern time The oldest known multiplication tables were used by the Babylonians about 4000 years ago. However, they used a base of 60. The oldest known tables using a base of 10 are the Chinese decimal multiplication table on bamboo strips dating to about 305 BC, during China's Warring States period. The multiplication table is sometimes attributed to the ancient Greek mathematician Pythagoras (570–495 BC). It is also called the Table of Pythagoras in many languages (for example French, Italian and Russian), ...
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Metrology
Metrology is the scientific study of measurement. It establishes a common understanding of units, crucial in linking human activities. Modern metrology has its roots in the French Revolution's political motivation to standardise units in France when a length standard taken from a natural source was proposed. This led to the creation of the decimal-based metric system in 1795, establishing a set of standards for other types of measurements. Several other countries adopted the metric system between 1795 and 1875; to ensure conformity between the countries, the Bureau International des Poids et Mesures (BIPM) was established by the Metre Convention. This has evolved into the International System of Units (SI) as a result of a resolution at the 11th General Conference on Weights and Measures (CGPM) in 1960. Metrology is divided into three basic overlapping activities: * The definition of units of measurement * The realisation of these units of measurement in practice * Traceabil ...
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Positional Notation
Positional notation (or place-value notation, or positional numeral system) usually denotes the extension to any base of the Hindu–Arabic numeral system (or 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 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 numeral system, base 60, was the first positional system to be developed, and its influence is present toda ...
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Superior Highly Composite Number
In mathematics, a superior highly composite number is a natural number which has the highest ratio of its number of divisors to ''some'' positive power of itself than any other number. It is a stronger restriction than that of a highly composite number, which is defined as having more divisors than any smaller positive integer. The first 10 superior highly composite numbers and their factorization are listed. For a superior highly composite number ''n'' there exists a positive real number ''ε'' such that for all natural numbers ''k'' smaller than ''n'' we have :\frac\geq\frac and for all natural numbers ''k'' larger than ''n'' we have :\frac>\frac where ''d(n)'', the divisor function, denotes the number of divisors of ''n''. The term was coined by Ramanujan (1915). For example, the number with the most divisors per square root of the number itself is 12; this can be demonstrated using some highly composites near 12. \frac\approx 1.414, \frac=1.5, \frac\approx 1.633, ...
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Numeral System
A numeral system (or system of numeration) is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner. The same sequence of symbols may represent different numbers in different numeral systems. For example, "11" represents the number ''eleven'' in the decimal numeral system (used in common life), the number ''three'' in the binary numeral system (used in computers), and the number ''two'' in the unary numeral system (e.g. used in tallying scores). The number the numeral represents is called its value. Not all number systems can represent all numbers that are considered in the modern days; for example, Roman numerals have no zero. Ideally, a numeral system will: *Represent a useful set of numbers (e.g. all integers, or rational numbers) *Give every number represented a unique representation (or at least a standard representation) *Reflect the algebraic and arithme ...
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Sexagesimal
Sexagesimal, also known as base 60 or sexagenary, is a numeral system with sixty as its base. It originated with the ancient Sumerians in the 3rd millennium BC, was passed down to the ancient Babylonians, and is still used—in a modified form—for measuring time, angles, and geographic coordinates. The number 60, a superior highly composite number, has twelve factors, namely 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60, of which 2, 3, and 5 are prime numbers. With so many factors, many fractions involving sexagesimal numbers are simplified. For example, one hour can be divided evenly into sections of 30 minutes, 20 minutes, 15 minutes, 12 minutes, 10 minutes, 6 minutes, 5 minutes, 4 minutes, 3 minutes, 2 minutes, and 1 minute. 60 is the smallest number that is divisible by every number from 1 to 6; that is, it is the lowest common multiple of 1, 2, 3, 4, 5, and 6. ''In this article, all sexagesimal digits are represented as decimal numbers, except where otherwise noted. ...
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