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43 (number)
43 (forty-three) is the natural number following 42 and preceding 44. In mathematics Forty-three is the 14th smallest prime number. The previous is forty-one, with which it comprises a twin prime, and the next is forty-seven. 43 is the smallest prime that is not a Chen prime. It is also the third Wagstaff prime. 43 is the fourth term of Sylvester's sequence, one more than the product of the previous terms (2 × 3 × 7). 43 is a centered heptagonal number. Let ''a'' = ''a'' = 1, and thenceforth ''a'' = (''a'' + ''a'' + ... + ''a''). This sequence continues 1, 1, 2, 3, 5, 10, 28, 154... . ''a'' is the first term of this sequence that is not an integer. 43 is a Heegner number. 43 is the largest prime which divides the order of the Janko group J4. 43 is a repdigit in base 6 (111). 43 is the number of triangles inside the Sri Yantra. 43 is the largest natural number that is not an (original) McNugget number. 43 is the smallest prime number expressible as the sum of 2, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prime Number
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime because the only ways of writing it as a product, or , involve 5 itself. However, 4 is composite because it is a product (2 × 2) in which both numbers are smaller than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself or can be factorized as a product of primes that is unique up to their order. The property of being prime is called primality. A simple but slow method of checking the primality of a given number n, called trial division, tests whether n is a multiple of any integer between 2 and \sqrt. Faster algorithms include the Miller–Rabin primality test, which is fast but has a small chance of error, and the AKS primality test, which always pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Taylor Series
In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor series are equal near this point. Taylor series are named after Brook Taylor, who introduced them in 1715. A Taylor series is also called a Maclaurin series, when 0 is the point where the derivatives are considered, after Colin Maclaurin, who made extensive use of this special case of Taylor series in the mid-18th century. The partial sum formed by the first terms of a Taylor series is a polynomial of degree that is called the th Taylor polynomial of the function. Taylor polynomials are approximations of a function, which become generally better as increases. Taylor's theorem gives quantitative estimates on the error introduced by the use of such approximations. If the Taylor series of a function is convergent, its sum is the limit of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orion (constellation)
Orion is a prominent constellation located on the celestial equator and visible throughout the world. It is one of the most conspicuous and recognizable constellations in the night sky. It is named after Orion (mythology), Orion, a hunter in Greek mythology. Its brightest stars are the blue-white Rigel (Beta Orionis) and the red Betelgeuse (Alpha Orionis). Characteristics Orion is bordered by Taurus to the northwest, Eridanus to the southwest, Lepus to the south, Monoceros (constellation), Monoceros to the east, and Gemini to the northeast. Covering 594 square degrees, Orion ranks twenty-sixth of the 88 constellations in size. The constellation boundaries, as set by Belgian astronomer Eugène Joseph Delporte, Eugène Delporte in 1930, are defined by a polygon of 26 sides. In the equatorial coordinate system, the right ascension coordinates of these borders lie between and , while the declination coordinates are between and . The constellation's three-letter abbreviation, as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constellation
A constellation is an area on the celestial sphere in which a group of visible stars forms Asterism (astronomy), a perceived pattern or outline, typically representing an animal, mythological subject, or inanimate object. The origins of the earliest constellations likely go back to prehistory. People used them to relate stories of their beliefs, experiences, creation myth, creation, or mythology. Different cultures and countries adopted their own constellations, some of which lasted into the early 20th century before today's constellations were internationally recognized. The recognition of constellations has changed significantly over time. Many changed in size or shape. Some became popular, only to drop into obscurity. Some were limited to a single culture or nation. The 48 traditional Western constellations are Greek. They are given in Aratus' work ''Phenomena'' and Ptolemy's ''Almagest'', though their origin probably predates these works by several centuries. Constellation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
H II Region
An H II region or HII region is a region of interstellar atomic hydrogen that is ionized. It is typically in a molecular cloud of partially ionized gas in which star formation has recently taken place, with a size ranging from one to hundreds of light years, and density from a few to about a million particles per cubic centimetre. The Orion Nebula, now known to be an H II region, was observed in 1610 by Nicolas-Claude Fabri de Peiresc by telescope, the first such object discovered. The regions may be of any shape because the distribution of the stars and gas inside them is irregular. Hertzsprung-Russell diagram, The short-lived blue stars created in these regions emit copious amounts of ultraviolet light that ionize the surrounding gas. H II regions—sometimes several hundred light-years across—are often associated with giant molecular clouds. They often appear clumpy and filamentary, sometimes showing intricate shapes such as the Horsehead Nebula. H II regio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Visual Magnitude
Apparent magnitude () is a measure of the brightness of a star or other astronomical object observed from Earth. An object's apparent magnitude depends on its intrinsic luminosity, its distance from Earth, and any extinction of the object's light caused by interstellar dust along the line of sight to the observer. The word ''magnitude'' in astronomy, unless stated otherwise, usually refers to a celestial object's apparent magnitude. The magnitude scale dates back to the ancient Roman astronomer Claudius Ptolemy, whose star catalog listed stars from 1st magnitude (brightest) to 6th magnitude (dimmest). The modern scale was mathematically defined in a way to closely match this historical system. The scale is reverse logarithmic: the brighter an object is, the lower its magnitude number. A difference of 1.0 in magnitude corresponds to a brightness ratio of \sqrt /math>, or about 2.512. For example, a star of magnitude 2.0 is 2.512 times as bright as a star of magnitude 3.0, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
M43 (nebula)
Messier 43 or M43, also known as De Mairan's Nebula and NGC 1982, is a star-forming nebula with a prominent H II region in the equatorial constellation of Orion. It was discovered by the French scientist Jean-Jacques Dortous de Mairan some time before 1731, then catalogued by Charles Messier in 1769. It is physically part of the Orion Nebula (Messier 42), separate from that main nebula by a dense lane of dust known as the northeast dark lane. It is part of the much larger Orion molecular cloud complex. The main ionizing star in this nebula is HD 37061 (variable star designation NU Ori), the focus of the H II region, away. This is a triple star system with the brighter component being a single-lined spectroscopic binary. The main component is a blue-white hued B-type main-sequence star with a stellar classification of B0.5V or B1V. It has times the mass of the Sun () and times the Sun's radius (). It is radiating over 26,000 times the Sun's luminosity () from its photo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Messier Object
The Messier objects are a set of 110 astronomical objects catalogued by the French astronomer Charles Messier in his ''Catalogue des Nébuleuses et des Amas d'Étoiles'' (''Catalogue of Nebulae and Star Clusters''). Because Messier was only interested in finding comets, he created a list of those non-comet objects that frustrated his hunt for them. The compilation of this list, in collaboration with his assistant Pierre Méchain, is known as ''the Messier catalogue''. This catalogue of objects is one of the most famous lists of astronomical objects, and many Messier objects are still referenced by their Messier numbers. The catalogue includes most of the astronomical deep-sky objects that can easily be observed from Earth's Northern Hemisphere; many Messier objects are popular targets for amateur astronomers. A preliminary version first appeared in 1774 in the ''Memoirs'' of the French Academy of Sciences for the year 1771. The first version of Messier's catalogue contain ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stable Isotope
The term stable isotope has a meaning similar to stable nuclide, but is preferably used when speaking of nuclides of a specific element. Hence, the plural form stable isotopes usually refers to isotopes of the same element. The relative abundance of such stable isotopes can be measured experimentally (isotope analysis), yielding an isotope ratio that can be used as a research tool. Theoretically, such stable isotopes could include the radiogenic daughter products of radioactive decay, used in radiometric dating. However, the expression stable-isotope ratio is preferably used to refer to isotopes whose relative abundances are affected by isotope fractionation in nature. This field is termed stable isotope geochemistry. Stable-isotope ratios Measurement of the ratios of naturally occurring stable isotopes (isotope analysis) plays an important role in isotope geochemistry, but stable isotopes (mostly hydrogen, carbon, nitrogen, oxygen and sulfur) are also finding uses in ecological ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Technetium
Technetium is a chemical element with the symbol Tc and atomic number 43. It is the lightest element whose isotopes are all radioactive. All available technetium is produced as a synthetic element. Naturally occurring technetium is a spontaneous fission product in uranium ore and thorium ore, the most common source, or the product of neutron capture in molybdenum ores. This silvery gray, crystalline transition metal lies between manganese and rhenium in group 7 of the periodic table, and its chemical properties are intermediate between those of both adjacent elements. The most common naturally occurring isotope is 99Tc, in traces only. Many of technetium's properties had been predicted by Dmitri Mendeleev before it was discovered. Mendeleev noted a gap in his periodic table and gave the undiscovered element the provisional name '' ekamanganese'' (''Em''). In 1937, technetium (specifically the technetium-97 isotope) became the first predominantly artificial element to be produ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Atomic Number
The atomic number or nuclear charge number (symbol ''Z'') of a chemical element is the charge number of an atomic nucleus. For ordinary nuclei, this is equal to the proton number (''n''p) or the number of protons found in the nucleus of every atom of that element. The atomic number can be used to uniquely identify ordinary chemical elements. In an ordinary uncharged atom, the atomic number is also equal to the number of electrons. For an ordinary atom, the sum of the atomic number ''Z'' and the neutron number ''N'' gives the atom's atomic mass number ''A''. Since protons and neutrons have approximately the same mass (and the mass of the electrons is negligible for many purposes) and the mass defect of the nucleon binding is always small compared to the nucleon mass, the atomic mass of any atom, when expressed in unified atomic mass units (making a quantity called the "relative isotopic mass"), is within 1% of the whole number ''A''. Atoms with the same atomic number but dif ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
15 Puzzle
The 15 puzzle (also called Gem Puzzle, Boss Puzzle, Game of Fifteen, Mystic Square and many others) is a sliding puzzle having 15 square tiles numbered 1–15 in a frame that is 4 tiles high and 4 tiles wide, leaving one unoccupied tile position. Tiles in the same row or column of the open position can be moved by sliding them horizontally or vertically, respectively. The goal of the puzzle is to place the tiles in numerical order. Named for the number of tiles in the frame, the 15 puzzle may also be called a 16 puzzle, alluding to its total tile capacity. Similar names are used for different sized variants of the 15 puzzle, such as the 8 puzzle that has 8 tiles in a 3×3 frame. The ''n'' puzzle is a classical problem for modelling algorithms involving heuristics. Commonly used heuristics for this problem include counting the number of misplaced tiles and finding the sum of the taxicab distances between each block and its position in the goal configuration. Note that both are '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
