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124 (number)
124 (one hundred ndtwenty-four) is the natural number following 123 and preceding 125. In mathematics 124 is an untouchable number, meaning that it is not the sum of proper divisors of any positive number. It is a stella octangula number, the number of spheres packed in the shape of a stellated octahedron. It is also an icosahedral number. There are 124 different polygons of length 12 formed by edges of the integer lattice, counting two polygons as the same only when one is a translated copy of the other. 124 is a perfectly partitioned number, meaning that it divides the number of partitions of 124. It is the first number to do so after 1, 2, and 3. See also * The year AD 124 Year 124 ( CXXIV) was a leap year starting on Friday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Glabrio and Flaccus (or, less frequently, year 877 ''Ab urbe condita'' ... or 124 BC * 124th (other) * List of h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called ''Cardinal number, cardinal numbers'', and numbers used for ordering are called ''Ordinal number, ordinal numbers''. Natural numbers are sometimes used as labels, known as ''nominal numbers'', having none of the properties of numbers in a mathematical sense (e.g. sports Number (sports), jersey numbers). Some definitions, including the standard ISO/IEC 80000, ISO 80000-2, begin the natural numbers with , corresponding to the non-negative integers , whereas others start with , corresponding to the positive integers Texts that exclude zero from the natural numbers sometimes refer to the natural numbers together with zero as the whole numbers, while in other writings, that term is used instead for the integers (including negative integers). The natural ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
123 (number)
123 (one hundred ndtwenty-three) is the natural number following 122 and preceding 124. In mathematics *123 is a Lucas number. It is the eleventh member of the Mian-Chowla sequence. *Along with 6, 123 is one of only two positive integers that is simultaneously two more than a perfect square and two less than a perfect cube (123 = 112 + 2 = 53 - 2). In religion The Book of Numbers says that Aaron died at the age of 123. In telephony *The emergency telephone number in Colombia *The telephone number of the speaking clock for the correct time in the United Kingdom *The electricity ( PLN) emergency telephone number in Indonesia *The medical emergency telephone number in Egypt *The Notation for national and international telephone numbers Recommendation ITU-T Recommendation E.123 defines a standard way to write telephone numbers, e-mail addresses, and web addresses In other fields 123 is also: * ''123'' (film), a 2002 Indian film *123 (interbank network), shared cash network ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
125 (number)
125 (one hundred ndtwenty-five) is the natural number following 124 and preceding 126. In mathematics 125 is the cube of 5. It can be expressed as a sum of two squares in two different ways, 125 = 10² + 5² = 11² + 2². 125 and 126 form a Ruth-Aaron pair under the second definition in which repeated prime factors are counted as often as they occur. Like many other powers of 5, it is a Friedman number in base 10 since 125 = 51 + 2. 125 is the center of a close triplet of perfect powers, (121 = 112, 125 = 53, 128 = 27). Excluding the trivial cases of 0 and 1, the only closer such triplet is (4,8,9) and the only other equally close is (25, 27, 32). U.S. military * Air National Guard 125th Special Tactics Squadron unit in Portland, Oregon * US Air Force 125th Fighter Wing, Air National Guard unit at Jacksonville International Airport, Florida * US Navy VAW-125 squadron at Naval Station Norfolk, Virginia * US Navy VFA-125 strike fighter squadron at Naval Air Station Lemoore ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Untouchable Number
An untouchable number is a positive integer that cannot be expressed as the sum of all the proper divisors of any positive integer (including the untouchable number itself). That is, these numbers are not in the image of the aliquot sum function. Their study goes back at least to Abu Mansur al-Baghdadi (circa 1000 AD), who observed that both 2 and 5 are untouchable. Examples For example, the number 4 is not untouchable as it is equal to the sum of the proper divisors of 9: 1 + 3 = 4. The number 5 is untouchable as it is not the sum of the proper divisors of any positive integer: 5 = 1 + 4 is the only way to write 5 as the sum of distinct positive integers including 1, but if 4 divides a number, 2 does also, so 1 + 4 cannot be the sum of all of any number's proper divisors (since the list of factors would have to contain both 4 and 2). The first few untouchable numbers are: : 2, 5, 52, 88, 96, 120, 124, 146, 162, 188, 2 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stella Octangula Number
In mathematics, a stella octangula number is a figurate number based on the stella octangula, of the form .. The sequence of stella octangula numbers is :0, 1, 14, 51, 124, 245, 426, 679, 1016, 1449, 1990, ... Only two of these numbers are square. Ljunggren's equation There are only two positive square stella octangula numbers, and , corresponding to and respectively.. The elliptic curve describing the square stella octangula numbers, :m^2 = n (2n^2 - 1) may be placed in the equivalent Weierstrass form :x^2 = y^3 - 2y by the change of variables , . Because the two factors and of the square number are relatively prime, they must each be squares themselves, and the second change of variables X=m/\sqrt and Y=\sqrt leads to Ljunggren's equation :X^2 = 2Y^4 - 1 A theorem of Siegel Siegel (also Segal or Segel), is a German and Ashkenazi Jewish surname. it can be traced to 11th century Bavaria and was used by people who made wax seals for or sealed official documents (each su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stellated Octahedron
The stellated octahedron is the only stellation of the octahedron. It is also called the stella octangula (Latin for "eight-pointed star"), a name given to it by Johannes Kepler in 1609, though it was known to earlier geometers. It was depicted in Pacioli's ''De Divina Proportione,'' 1509. It is the simplest of five regular polyhedral compounds, and the only regular compound of two tetrahedra. It is also the least dense of the regular polyhedral compounds, having a density of 2. It can be seen as a 3D extension of the hexagram: the hexagram is a two-dimensional shape formed from two overlapping equilateral triangles, centrally symmetric to each other, and in the same way the stellated octahedron can be formed from two centrally symmetric overlapping tetrahedra. This can be generalized to any desired amount of higher dimensions; the four-dimensional equivalent construction is the compound of two 5-cells. It can also be seen as one of the stages in the construction of a 3D Koch ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Icosahedral Number
An icosahedral number is a figurate number that represents an icosahedron. The ''n''th icosahedral number is given by the formula : The first such numbers are 1, 12, 48, 124, 255, 456, 742, 1128, 1629, 2260, 3036, 3972, 5083, … . History The first study of icosahedral numbers appears to have been by René Descartes, around 1630, in his ''De solidorum elementis''. Prior to Descartes, figurate numbers had been studied by the ancient Greeks and by Johann Faulhaber, but only for polygonal numbers, pyramidal numbers, and cubes. Descartes introduced the study of figurate numbers based on the Platonic solids and some semiregular polyhedra; his work included the icosahedral numbers. However, ''De solidorum elementis'' was lost, and not rediscovered until 1860. In the meantime, icosahedral numbers had been studied again by other mathematicians, including Friedrich Wilhelm Marpurg Friedrich Wilhelm Marpurg (21 November 1718 – 22 May 1795) was a German music critic, music theorist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Integer Lattice
In mathematics, the -dimensional integer lattice (or cubic lattice), denoted , is the lattice in the Euclidean space whose lattice points are -tuples of integers. The two-dimensional integer lattice is also called the square lattice, or grid lattice. is the simplest example of a root lattice. The integer lattice is an odd unimodular lattice. Automorphism group The automorphism group (or group of congruences) of the integer lattice consists of all permutations and sign changes of the coordinates, and is of order 2''n'' ''n''!. As a matrix group it is given by the set of all ''n''×''n'' signed permutation matrices. This group is isomorphic to the semidirect product :(\mathbb Z_2)^n \rtimes S_n where the symmetric group ''S''''n'' acts on (Z2)''n'' by permutation (this is a classic example of a wreath product). For the square lattice, this is the group of the square, or the dihedral group of order 8; for the three-dimensional cubic lattice, we get the group of the cube, o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Partition Number
In number theory, the partition function represents the number of possible partitions of a non-negative integer . For instance, because the integer 4 has the five partitions , , , , and . No closed-form expression for the partition function is known, but it has both asymptotic expansions that accurately approximate it and recurrence relations by which it can be calculated exactly. It grows as an exponential function of the square root of its argument. The multiplicative inverse of its generating function is the Euler function; by Euler's pentagonal number theorem this function is an alternating sum of pentagonal number powers of its argument. Srinivasa Ramanujan first discovered that the partition function has nontrivial patterns in modular arithmetic, now known as Ramanujan's congruences. For instance, whenever the decimal representation of ends in the digit 4 or 9, the number of partitions of will be divisible by 5. Definition and examples For a positive integer , is t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
AD 124
Year 124 ( CXXIV) was a leap year starting on Friday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Glabrio and Flaccus (or, less frequently, year 877 ''Ab urbe condita''). The denomination 124 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years. Events By place Roman Empire * Emperor Hadrian begins to rebuild the Olympeion in Athens. * Antinous becomes Hadrian's beloved companion on his journeys through the Roman Empire. * During a voyage to Greece, Hadrian is initiated in the ancient rites known as the Eleusinian Mysteries. Asia * In northern India, Nahapana, ruler of the Scythians, is defeated and dies in battle while fighting against King Gautamiputra Satakarni. This defeat destroys the Scythian dynasty of the Western Kshatrapas. Births * Apuleius, Numidian novelist, writer, public speake ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
124 BC
__NOTOC__ Year 124 BC was a year of the pre-Julian Roman calendar. At the time it was known as the Year of the Consulship of Longinus and Calvinus (or, less frequently, year 630 ''Ab urbe condita'') and the Fifth Year of Yuanshuo. The denomination 124 BC for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years. Events By place Roman Republic * Fregellae's revolt against Rome begins in Latium. Later the city is captured and destroyed by the Romans. Parthia * Mithridates II succeeds Artabanus II as King of Parthia. Egypt * Cleopatra II of Egypt and her brother Ptolemy VIII of Egypt reconcile. China * Spring: The Han general Wei Qing, with an army of 30,000 cavalry, proceeds from Gaoque into Xiongnu territory, and in a night attack surrounds the Tuqi King of the Right in his camp. The Tuqi escapes, but numerous petty chiefs are captured in this and a second engagement. * Li ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
