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YBC 7289
YBC 7289 is a Babylonian clay tablet notable for containing an accurate sexagesimal approximation to the square root of 2, the length of the diagonal of a unit square. This number is given to the equivalent of six decimal digits, "the greatest known computational accuracy ... in the ancient world". The tablet is believed to be the work of a student in southern Mesopotamia from some time between 1800 and 1600 BC. It was donated to the Yale Babylonian Collection by J. P. Morgan. Content The tablet depicts a square with its two diagonals. One side of the square is labeled with the sexagesimal number 30. The diagonal of the square is labeled with two sexagesimal numbers. The first of these two, 1;24,51,10 represents the number 305470/216000 ≈ 1.414213, a numerical approximation of the square root of two that is off by less than one part in two million. The second of the two numbers is 42;25,35 = 30547/720 ≈ 42.426. This number is the result of multiplying 30 by the given appr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heptagon
In geometry, a heptagon or septagon is a seven-sided polygon or 7-gon. The heptagon is sometimes referred to as the septagon, using "sept-" (an elision of ''septua-'', a Latin-derived numerical prefix, rather than ''hepta-'', a Greek-derived numerical prefix; both are cognate) together with the Greek suffix "-agon" meaning angle. Regular heptagon A regular heptagon, in which all sides and all angles are equal, has internal angles of 5π/7 radians (128 degrees). Its Schläfli symbol is . Area The area (''A'') of a regular heptagon of side length ''a'' is given by: :A = \fraca^2 \cot \frac \simeq 3.634 a^2. This can be seen by subdividing the unit-sided heptagon into seven triangular "pie slices" with vertices at the center and at the heptagon's vertices, and then halving each triangle using the apothem as the common side. The apothem is half the cotangent of \pi/7, and the area of each of the 14 small triangles is one-fourth of the apothem. The area of a regular heptago ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics Manuscripts
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Historia Mathematica
''Historia Mathematica: International Journal of History of Mathematics'' is an academic journal on the history of mathematics published by Elsevier. It was established by Kenneth O. May in 1971 as the free newsletter ''Notae de Historia Mathematica'', but by its sixth issue in 1974 had turned into a full journal. The International Commission on the History of Mathematics began awarding the Montucla Prize, for the best article by an early career scholar in ''Historia Mathematica'', in 2009. The award is given every four years. Editors The editors of the journal have been: * Kenneth O. May, 1974–1977 * Joseph W. Dauben, 1977–1985 * Eberhard Knobloch, 1985–1994 * David E. Rowe, 1994–1996 * Karen Hunger Parshall, 1996–2000 * Craig Fraser and Umberto Bottazzini, 2000–2004 * Craig Fraser, 2004–2007 * Benno van Dalen, 2007–2009 * June Barrow-Green and Niccolò Guicciardini, 2010–2013 * Niccolò Guicciardini and Tom Archibald, 2013-2015 * Tom Archibald and Reinha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
IM 67118
IM 67118, also known as Db2-146, is an Old Babylonian clay tablet in the collection of the National Museum of Iraq that contains the solution to a problem in plane geometry concerning a rectangle with given area and diagonal. In the last part of the text the solution is proved correct by means of the Pythagorean theorem. The steps of the solution are believed to represent cut-and-paste geometry operations involving a diagram from which, it has been suggested, ancient Mesopotamians might, at an earlier time, have derived the Pythagorean theorem. Description The tablet was excavated in 1962 at Tell edh-Dhiba'i, an Old Babylonian settlement near modern Baghdad that was once part of the kingdom of Eshnunna, and was published by Taha Baqir in the same year. It dates to approximately 1770 BCE (according to the middle chronology), during the reign of Ibal-pi-el II, who ruled Eshnunna at the same time that Hammurabi ruled Babylon. The tablet measures 11.5×6.8×3.3 cm. Its langu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plimpton 322
Plimpton 322 is a Babylonian clay tablet, notable as containing an example of Babylonian mathematics. It has number 322 in the G.A. Plimpton Collection at Columbia University. This tablet, believed to have been written about 1800 BC, has a table of four columns and 15 rows of numbers in the cuneiform script of the period. This table lists two of the three numbers in what are now called Pythagorean triples, i.e., integers , , and satisfying . From a modern perspective, a method for constructing such triples is a significant early achievement, known long before the Greek and Indian mathematicians discovered solutions to this problem. At the same time, one should recall the tablet's author was a scribe, rather than a professional mathematician; it has been suggested that one of his goals may have been to produce examples for school problems. There has been significant scholarly debate on the nature and purpose of the tablet. For readable popular treatments of this tablet see rec ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
3D Printing
3D printing or additive manufacturing is the Manufacturing, construction of a three-dimensional object from a computer-aided design, CAD model or a digital 3D modeling, 3D model. It can be done in a variety of processes in which material is deposited, joined or solidified under Computer Numerical Control, computer control, with material being added together (such as plastics, liquids or powder grains being fused), typically layer by layer. In the 1980s, 3D printing techniques were considered suitable only for the production of functional or aesthetic prototypes, and a more appropriate term for it at the time was rapid prototyping. , the precision, repeatability, and material range of 3D printing have increased to the point that some 3D printing processes are considered viable as an industrial-production technology, whereby the term ''additive manufacturing'' can be used synonymously with ''3D printing''. One of the key advantages of 3D printing is the ability to produce very ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yale University
Yale University is a private research university in New Haven, Connecticut. Established in 1701 as the Collegiate School, it is the third-oldest institution of higher education in the United States and among the most prestigious in the world. It is a member of the Ivy League. Chartered by the Connecticut Colony, the Collegiate School was established in 1701 by clergy to educate Congregational ministers before moving to New Haven in 1716. Originally restricted to theology and sacred languages, the curriculum began to incorporate humanities and sciences by the time of the American Revolution. In the 19th century, the college expanded into graduate and professional instruction, awarding the first PhD in the United States in 1861 and organizing as a university in 1887. Yale's faculty and student populations grew after 1890 with rapid expansion of the physical campus and scientific research. Yale is organized into fourteen constituent schools: the original undergraduate col ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Almagest
The ''Almagest'' is a 2nd-century Greek-language mathematical and astronomical treatise on the apparent motions of the stars and planetary paths, written by Claudius Ptolemy ( ). One of the most influential scientific texts in history, it canonized a geocentric model of the Universe that was accepted for more than 1,200 years from its origin in Hellenistic Alexandria, in the medieval Byzantine and Islamic worlds, and in Western Europe through the Middle Ages and early Renaissance until Copernicus. It is also a key source of information about ancient Greek astronomy. Ptolemy set up a public inscription at Canopus, Egypt, in 147 or 148. N. T. Hamilton found that the version of Ptolemy's models set out in the ''Canopic Inscription'' was earlier than the version in the ''Almagest''. Hence the ''Almagest'' could not have been completed before about 150, a quarter-century after Ptolemy began observing. Names The name comes from Arabic ', with ' meaning "the", and ''magesti'' bei ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Claudius Ptolemy
Claudius Ptolemy (; grc-gre, Πτολεμαῖος, ; la, Claudius Ptolemaeus; AD) was a mathematician, astronomer, astrologer, geographer, and music theorist, who wrote about a dozen scientific treatises, three of which were of importance to later Byzantine, Islamic, and Western European science. The first is the astronomical treatise now known as the '' Almagest'', although it was originally entitled the ''Mathēmatikē Syntaxis'' or ''Mathematical Treatise'', and later known as ''The Greatest Treatise''. The second is the ''Geography'', which is a thorough discussion on maps and the geographic knowledge of the Greco-Roman world. The third is the astrological treatise in which he attempted to adapt horoscopic astrology to the Aristotelian natural philosophy of his day. This is sometimes known as the ''Apotelesmatika'' (lit. "On the Effects") but more commonly known as the '' Tetrábiblos'', from the Koine Greek meaning "Four Books", or by its Latin equivalent ''Quadripart ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algebraic Number
An algebraic number is a number that is a root of a non-zero polynomial in one variable with integer (or, equivalently, rational) coefficients. For example, the golden ratio, (1 + \sqrt)/2, is an algebraic number, because it is a root of the polynomial . That is, it is a value for x for which the polynomial evaluates to zero. As another example, the complex number 1 + i is algebraic because it is a root of . All integers and rational numbers are algebraic, as are all roots of integers. Real and complex numbers that are not algebraic, such as and , are called transcendental numbers. The set of algebraic numbers is countably infinite and has measure zero in the Lebesgue measure as a subset of the uncountable complex numbers. In that sense, almost all complex numbers are transcendental. Examples * All rational numbers are algebraic. Any rational number, expressed as the quotient of an integer and a (non-zero) natural number , satisfies the above definition, because is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
