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294 (number)
294 is the natural number following 293 and preceding 295. In mathematics *294 is an even composite number with three prime factors. *294 is the number of planar biconnected graphs with 7 vertices. Biconnected graphs are two dimensional graphs with a given number of points and 294 is the number of ways to organize 7 vertices in different ways. *11115² - 294² = 123456789 *The Magic Inscribed Lotus was created by Nārāyaṇa, and Indian Mathematician in the 14th century The 14th century lasted from 1 January 1301 (represented by the Roman numerals MCCCI) to 31 December 1400 (MCD). It is estimated that the century witnessed the death of more than 45 million lives from political and natural disasters in both Euro .... In this inscription, each group of 12 numbers has a sum of 294. It was constructed with a 12 x 4 magic rectangle. *In 1930, George A. Miller determined that there are 294 isomorphic groups in the order of 64. Isomorphism is making a map that preserves relation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Natural Number
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive integers Some authors acknowledge both definitions whenever convenient. Sometimes, the whole numbers are the natural numbers as well as zero. In other cases, the ''whole numbers'' refer to all of the integers, including negative integers. The counting numbers are another term for the natural numbers, particularly in primary education, and are ambiguous as well although typically start at 1. The natural numbers are used for counting things, like "there are ''six'' coins on the table", in which case they are called ''cardinal numbers''. They are also used to put things in order, like "this is the ''third'' largest city in the country", which are called ''ordinal numbers''. Natural numbers are also used as labels, like Number (sports), jersey ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
293 (number)
293 is the natural number following 292 and preceding 294. In mathematics 293 is: *a prime number, *a Pythagorean prime, *a Sophie Germain prime *a Chen prime *strictly trivially polygonal (number n that is polygonal in only 2 ways: 2-gonal and n-gonal) *equivalent to the sum of the first three tetradic primes. Tetradic numbers are numbers that are the same if written backwards, flipped upside-down, or mirrored upside-down and tetradic primes are tetradic numbers that are also prime 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 .... It is the sum of 11 + 101 + 181. *the sum of perfect cubes 23+23+33+53+53 References {{DEFAULTSORT:293 (Number) Integers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
295 (number)
295 is the natural number following 294 and preceding 296. In mathematics *295 is an odd composite number with two prime factors. *295 is a centered tetrahedral number meaning that it can be represented as a tetrahedron In geometry, a tetrahedron (: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular Face (geometry), faces, six straight Edge (geometry), edges, and four vertex (geometry), vertices. The tet .... *295 Is a structured deltoidal hexecontahedral number which can be represented as a deltoidal hexecontahedron. *295 can be written as the sum of 4 nonzero perfect squares. *295 is the second suspected Lychrel number. References {{Improve categories, date=November 2023 Integers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Composite Number
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Accordingly it is a positive integer that has at least one divisor other than 1 and itself. Every positive integer is composite, prime number, prime, or the Unit (ring theory), unit 1, so the composite numbers are exactly the numbers that are not prime and not a unit. E.g., the integer 14 is a composite number because it is the product of the two smaller integers 2 × 7 but the integers 2 and 3 are not because each can only be divided by one and itself. The composite numbers up to 150 are: :4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100, 102, 104, 105, 106, 108, 110, 111, 112, 114, 115, 116, 117, 118, 119, 120, 121, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Biconnected Graph
In graph theory, a biconnected graph is a connected and "nonseparable" graph Graph may refer to: Mathematics *Graph (discrete mathematics), a structure made of vertices and edges **Graph theory, the study of such graphs and their properties *Graph (topology), a topological space resembling a graph in the sense of discret ..., meaning that if any one vertex were to be removed, the graph will remain connected. Therefore a biconnected graph has no articulation vertices. The property of being k-vertex-connected graph, 2-connected is equivalent to biconnectivity, except that the complete graph of two vertices is usually not regarded as 2-connected. This property is especially useful in maintaining a graph with a two-fold Redundancy (engineering), redundancy, to prevent disconnection upon the removal of a single edge (graph theory), edge (or connection). The use of biconnected graphs is very important in the field of networking (see Flow network, Network flow), because of this pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Two Dimensional
A two-dimensional space is a mathematical space with two dimensions, meaning points have two degrees of freedom: their locations can be locally described with two coordinates or they can move in two independent directions. Common two-dimensional spaces are often called '' planes'', or, more generally, ''surfaces''. These include analogs to physical spaces, like flat planes, and curved surfaces like spheres, cylinders, and cones, which can be infinite or finite. Some two-dimensional mathematical spaces are not used to represent physical positions, like an affine plane or complex plane. Flat The most basic example is the flat Euclidean plane, an idealization of a flat surface in physical space such as a sheet of paper or a chalkboard. On the Euclidean plane, any two points can be joined by a unique straight line along which the distance can be measured. The space is flat because any two lines transversed by a third line perpendicular to both of them are parallel, meaning they neve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
14th Century
The 14th century lasted from 1 January 1301 (represented by the Roman numerals MCCCI) to 31 December 1400 (MCD). It is estimated that the century witnessed the death of more than 45 million lives from political and natural disasters in both Europe and the Mongol Empire. West Africa experienced economic growth and prosperity. In Europe, the Black Death claimed 25 million lives wiping out one third of the European population while the Kingdom of England and the Kingdom of France fought in the protracted Hundred Years' War after the death of King Charles IV of France led to a claim to the French throne by King Edward III of England. This period is considered the height of chivalry and marks the beginning of strong separate identities for both England and France as well as the foundation of the Italian Renaissance and the Ottoman Empire. In Asia, Tamerlane (Timur), established the Timurid Empire, history's third largest empire to have been ever established by a single conqueror. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magic Rectangle
In mathematics, a magic hypercube is the ''k''-dimensional generalization of magic squares and magic cubes, that is, an ''n'' × ''n'' × ''n'' × ... × ''n'' array of integers such that the sums of the numbers on each pillar (along any axis) as well as on the main space diagonals are all the same. The common sum is called the magic constant of the hypercube, and is sometimes denoted ''M''''k''(''n''). If a magic hypercube consists of the numbers 1, 2, ..., ''n''''k'', then it has magic number :M_k(n) = \frac. For ''k'' = 4, a magic hypercube may be called a magic tesseract, with sequence of magic numbers given by . The side-length ''n'' of the magic hypercube is called its ''order''. Four-, five-, six-, seven- and eight-dimensional magic hypercubes of order three have been constructed by J. R. Hendricks. Marian Trenkler proved the following theorem: A ''p''-dimensional magic hypercube of order ''n'' exists if and only if ''p'' > 1 and ''n'' is different from 2 or ''p'' = ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Group Isomorphism
In abstract algebra, a group isomorphism is a function between two groups that sets up a bijection between the elements of the groups in a way that respects the given group operations. If there exists an isomorphism between two groups, then the groups are called isomorphic. From the standpoint of group theory, isomorphic groups have the same properties and need not be distinguished. Definition and notation Given two groups (G, *) and (H, \odot), a ''group isomorphism'' from (G, *) to (H, \odot) is a bijective group homomorphism from G to H. Spelled out, this means that a group isomorphism is a bijective function f : G \to H such that for all u and v in G it holds that f(u * v) = f(u) \odot f(v). The two groups (G, *) and (H, \odot) are isomorphic if there exists an isomorphism from one to the other. This is written (G, *) \cong (H, \odot). Often shorter and simpler notations can be used. When the relevant group operations are understood, they are omitted and one writes G \co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Incomplete Proofs
This page lists notable examples of incomplete or incorrect published mathematical proofs. Most of these were accepted as complete or correct for several years but later discovered to contain gaps or errors. There are both examples where a complete proof was later found, or where the alleged result turned out to be false. Results later proved rigorously * Euclid's ''Elements''. Euclid's proofs are essentially correct, but strictly speaking sometimes contain gaps because he tacitly uses some unstated assumptions, such as the existence of intersection points. In 1899 David Hilbert gave a complete set of ( second order) axioms for Euclidean geometry, called Hilbert's axioms, and between 1926 and 1959 Tarski gave some complete sets of first order axioms, called Tarski's axioms. * Isoperimetric inequality. For three dimensions it states that the shape enclosing the maximum volume for its surface area is the sphere. It was formulated by Archimedes but not proved rigorously until t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
