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Plimpton 322
Plimpton 322 is a Babylonian clay tablet, believed to have been written around 1800 BC, that contains a mathematical table written in cuneiform script. Each row of the table relates to a Pythagorean triple, that is, a triple of integers (s,\ell,d) that satisfies the Pythagorean theorem, s^2+\ell^2=d^2, the rule that equates the sum of the squares of the legs of a right triangle to the square of the hypotenuse. The era in which Plimpton 322 was written was roughly 13 to 15 centuries prior to the era in which the major Greek discoveries in geometry were made. At the time that Otto Neugebauer and Abraham Sachs first realized the mathematical significance of the tablet in the 1940s, a few Old Babylonian tablets making use of the Pythagorean rule were already known. In addition to providing further evidence that Mesopotamian scribes knew and used the rule, Plimpton 322 strongly suggested that they had a systematic method for generating Pythagorean triples as some of the tripl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
New York City
New York, often called New York City (NYC), is the most populous city in the United States, located at the southern tip of New York State on one of the world's largest natural harbors. The city comprises five boroughs, each coextensive with a respective county. The city is the geographical and demographic center of both the Northeast megalopolis and the New York metropolitan area, the largest metropolitan area in the United States by both population and urban area. New York is a global center of finance and commerce, culture, technology, entertainment and media, academics, and scientific output, the arts and fashion, and, as home to the headquarters of the United Nations, international diplomacy. With an estimated population in 2024 of 8,478,072 distributed over , the city is the most densely populated major city in the United States. New York City has more than double the population of Los Angeles, the nation's second-most populous city. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edgar James Banks
Edgar James Banks (May 23, 1866 – May 5, 1945), was an American diplomat, antiquarian and novelist. Biography Banks was an antiquities enthusiast and entrepreneurial roving archaeologist in the closing days of the Ottoman Empire, who has been held up as an original for the fictional composite figure of Indiana Jones. Starting from his position as American consul in Baghdad in 1898, Banks bought hundreds of cuneiform tablets on the market in the closing days of the Ottoman Empire and resold them in small batches to museums, libraries, universities, and theological seminaries, several in Utah and the Southwestern United States and across the United States. These tablets had been dug up by locals at sites like Telloh and the many other tells of central Mesopotamia. Banks purchased many more cuneiform inscriptions from a dealer in Constantinople. His export of antiquities was an infringement of Article 8 of the 1884 Ottoman Antiquities Law. He wrote a book, published in 1912, about ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trigonometry
Trigonometry () is a branch of mathematics concerned with relationships between angles and side lengths of triangles. In particular, the trigonometric functions relate the angles of a right triangle with ratios of its side lengths. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. The Greeks focused on the calculation of chords, while mathematicians in India created the earliest-known tables of values for trigonometric ratios (also called trigonometric functions) such as sine. Throughout history, trigonometry has been applied in areas such as geodesy, surveying, celestial mechanics, and navigation. Trigonometry is known for its many identities. These trigonometric identities are commonly used for rewriting trigonometrical expressions with the aim to simplify an expression, to find a more useful form of an expression, or to solve an equation. History Sumerian astronomers studied angle me ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Number Theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example, rational numbers), or defined as generalizations of the integers (for example, algebraic integers). Integers can be considered either in themselves or as solutions to equations (Diophantine geometry). Questions in number theory can often be understood through the study of Complex analysis, analytical objects, such as the Riemann zeta function, that encode properties of the integers, primes or other number-theoretic objects in some fashion (analytic number theory). One may also study real numbers in relation to rational numbers, as for instance how irrational numbers can be approximated by fractions (Diophantine approximation). Number theory is one of the oldest branches of mathematics alongside geometry. One quirk of number theory is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schøyen Collection
__NOTOC__ The Schøyen Collection is one of the largest private manuscript collections in the world, mostly located in Oslo and London. Formed in the 20th century by the father of current owner Martin Schøyen, it comprises manuscripts of global provenance, spanning 5,000 years of history. It contains more than 13,000 manuscript items; the oldest is about 5,300 years old. There are manuscripts from 134 different countries and territories, representing 120 languages and 185 scripts. The Collection procures and preserves diverse manuscripts, from all over the world, irrespective of the geography, culture, linguistic, race and religious background. It declares that its interest is in "advancing the study of human culture and civilization" over many millennia. Some of its recent acquisitions have been obtained from the civil war-affected regions of the Middle East and Afghanistan, where warlords and smugglers have destroyed ancient sites to find a buyer for ancient manuscript fragment ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadratic Equation
In mathematics, a quadratic equation () is an equation that can be rearranged in standard form as ax^2 + bx + c = 0\,, where the variable (mathematics), variable represents an unknown number, and , , and represent known numbers, where . (If and then the equation is linear equation, linear, not quadratic.) The numbers , , and are the ''coefficients'' of the equation and may be distinguished by respectively calling them, the ''quadratic coefficient'', the ''linear coefficient'' and the ''constant coefficient'' or ''free term''. The values of that satisfy the equation are called ''solution (mathematics), solutions'' of the equation, and ''zero of a function, roots'' or ''zero of a function, zeros'' of the quadratic function on its left-hand side. A quadratic equation has at most two solutions. If there is only one solution, one says that it is a double root. If all the coefficients are real numbers, there are either two real solutions, or a single real double root, or two comple ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coprime
In number theory, two integers and are coprime, relatively prime or mutually prime if the only positive integer that is a divisor of both of them is 1. Consequently, any prime number that divides does not divide , and vice versa. This is equivalent to their greatest common divisor (GCD) being 1. One says also ''is prime to'' or ''is coprime with'' . The numbers 8 and 9 are coprime, despite the fact that neither—considered individually—is a prime number, since 1 is their only common divisor. On the other hand, 6 and 9 are not coprime, because they are both divisible by 3. The numerator and denominator of a reduced fraction are coprime, by definition. Notation and testing When the integers and are coprime, the standard way of expressing this fact in mathematical notation is to indicate that their greatest common divisor is one, by the formula or . In their 1989 textbook '' Concrete Mathematics'', Ronald Graham, Donald Knuth, and Oren Patashnik proposed an alte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sumerogram
A Sumerogram is the use of a Sumerian cuneiform character or group of characters as an ideogram or logogram rather than a syllabogram in the graphic representation of a language other than Sumerian, such as Akkadian, Eblaite, or Hittite. This type of logogram characterized, to a greater or lesser extent, every adaptation of the original Mesopotamian cuneiform system to a language other than Sumerian. The frequency and intensity of their use varied depending on period, style, and genre. In the same way, a written Akkadian word that is used ideographically to represent a language other than Akkadian (such as Hittite) is known as an ''Akkadogram''. In the transliteration of ancient texts Sumerograms are normally represented by majuscule letters. Most signs have a number of possible Sumerian sound values. The scribes and readers of texts using these Sumerograms would not necessarily have been aware of the Sumerian language, with the ''Sumerograms'' functioning as ideograms or lo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Akkadian Language
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 was an East Semitic language that is attested in ancient Mesopotamia ( Akkad, Assyria, Isin, Larsa, Babylonia and perhaps Dilmun) from the mid- third millennium BC until its gradual replacement in common use by Old Aramaic among Assyrians and Babylonians from the 8th century BC. Akkadian, which is the earliest documented Semitic language, is named after the city of Akkad, a major centre of Mesopotamian civilization during the Akkadian Empire (–2154 BC). It was written using the cuneiform script, originally used for Sumerian, but also used to write multiple languages in the region including Eblaite, Hurrian, Elamite, Old Persian and Hittite. The influence of Sumerian on Akkadian went beyond just the cuneiform script; owing to their close proximity, a lengthy span of con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hypotenuse
In geometry, a hypotenuse is the side of a right triangle opposite to the right angle. It is the longest side of any such triangle; the two other shorter sides of such a triangle are called '' catheti'' or ''legs''. Every rectangle can be divided into a pair of right triangles by cutting it along either diagonal; the diagonals are the hypotenuses of these triangles. The length of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the two legs. Mathematically, this can be written as a^2 + b^2 = c^2, where ''a'' is the length of one leg, ''b'' is the length of another leg, and ''c'' is the length of the hypotenuse. For example, if one of the legs of a right angle has a length of 3 and the other has a length of 4, then their squares add up to 25 = 9 + 16 = 3 × 3 + 4 × 4. Since 25 is the square of the hypotenuse, the length of the hypotenuse is the square r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Special Right Triangles
A special right triangle is a right triangle with some regular feature that makes calculations on the triangle easier, or for which simple formulas exist. For example, a right triangle may have angles that form simple relationships, such as 45°–45°–90°. This is called an "angle-based" right triangle. A "side-based" right triangle is one in which the lengths of the sides form ratios of Natural number, whole numbers, such as 3 : 4 : 5, or of other special numbers such as the golden ratio. Knowing the relationships of the angles or ratios of sides of these special right triangles allows one to quickly calculate various lengths in geometry, geometric problems without resorting to more advanced methods. Angle-based ''Angle-based'' special right triangles are specified by the relationships of the angles of which the triangle is composed. The angles of these triangles are such that the larger (right) angle, which is 90 degree (angle), degrees or radians, is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Middle Chronology
The chronology of the ancient Near East is a framework of dates for various events, rulers and dynasties. Historical inscriptions and texts customarily record events in terms of a succession of officials or rulers: "in the year X of king Y". Comparing many records pieces together a relative chronology relating dates in cities over a wide area. For the 3rd and 2nd millennia BC, this correlation is less certain but the following periods can be distinguished: * Early Bronze Age: Following the rise of cuneiform writing in the preceding Uruk period and Jemdet Nasr periods came a series of rulers and dynasties whose existence is based mostly on scant contemporary sources (e.g. En-me-barage-si), combined with archaeological cultures, some of which are considered problematic (e.g. Early Dynastic II). The lack of dendrochronology, astronomical correlations, and sparsity of modern, well-stratified sequences of radiocarbon dates from Southern Mesopotamia makes it difficult to assign a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
