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194 (number)
194 (one hundred ndninety-four) is the natural number following 193 and preceding 195. In mathematics * 194 is the smallest Markov number that is neither a Fibonacci number nor a Pell number * 194 is the smallest number written as the sum of three squares in five ways * 194 is the number of irreducible representations of the Monster group In the area of abstract algebra known as group theory, the monster group M (also known as the Fischer–Griess monster, or the friendly giant) is the largest sporadic simple group; it has order : : = 2463205976112133171923293 ... * 194!! - 1 is prime See also * 194 (other) References Integers {{Num-stub ... [...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] |
193 (number)
193 (one hundred ndninety-three) is the natural number following 192 and preceding 194. In mathematics 193 is the number of compositions of 14 into distinct parts. In decimal, it is the seventeenth full repetend prime, or ''long prime''. * It is the only odd prime p known for which 2 is not a primitive root of 4p^2 + 1. * It is the thirteenth Pierpont prime, which implies that a regular 193-gon can be constructed using a compass, straightedge, and angle trisector. * It is part of the fourteenth pair of twin primes (191, 193), the seventh trio of prime triplets (193, 197, 199), and the fourth set of prime quadruplets (191, 193, 197, 199). Aside from itself, the '' friendly giant'' (the largest sporadic group) holds a total of 193 conjugacy classes. It also holds at least 44 maximal subgroups aside from the double cover of \mathbb (the forty-fourth prime number is 193). 193 is also the eighth numerator of convergents to Euler's number; correct to three decimal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
195 (number)
195 (one hundred ndninety-five) is the natural number following 194 and preceding 196. In mathematics 195 is: * the sum of eleven consecutive primes: 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 * the smallest number expressed as a sum of distinct square In geometry, a square is a regular polygon, regular quadrilateral. It has four straight sides of equal length and four equal angles. Squares are special cases of rectangles, which have four equal angles, and of rhombuses, which have four equal si ...s in 16 different ways * a centered tetrahedral number * in the middle of a prime quadruplet (191, 193, 197, 199). See also * 195 (other) References Integers {{Num-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Markov Number
A Markov number or Markoff number is a positive integer ''x'', ''y'' or ''z'' that is part of a solution to the Markov Diophantine equation :x^2 + y^2 + z^2 = 3xyz,\, studied by . The first few Markov numbers are :1 (number), 1, 2 (number), 2, 5 (number), 5, 13 (number), 13, 29 (number), 29, 34 (number), 34, 89 (number), 89, 169 (number), 169, 194 (number), 194, 233 (number), 233, 433, 610, 985, 1325, ... appearing as coordinates of the Markov triples :(1, 1, 1), (1, 1, 2), (1, 2, 5), (1, 5, 13), (2, 5, 29), (1, 13, 34), (1, 34, 89), (2, 29, 169), (5, 13, 194), (1, 89, 233), (5, 29, 433), (1, 233, 610), (2, 169, 985), (13, 34, 1325), ... There are infinitely many Markov numbers and Markov triples. Markov tree There are two simple ways to obtain a new Markov triple from an old one (''x'', ''y'', ''z''). First, one may permutation, permute the 3 numbers ''x'',''y'',''z'', so in particular one can normalize the triples so that ''x'' ≤ ''y'' ≤&nbs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fibonacci Number
In mathematics, the Fibonacci sequence is a Integer sequence, sequence in which each element is the sum of the two elements that precede it. Numbers that are part of the Fibonacci sequence are known as Fibonacci numbers, commonly denoted . Many writers begin the sequence with 0 and 1, although some authors start it from 1 and 1 and some (as did Fibonacci) from 1 and 2. Starting from 0 and 1, the sequence begins : 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ... The Fibonacci numbers were first described in Indian mathematics as early as 200 BC in work by Pingala on enumerating possible patterns of Sanskrit poetry formed from syllables of two lengths. They are named after the Italian mathematician Leonardo of Pisa, also known as Fibonacci, who introduced the sequence to Western European mathematics in his 1202 book . Fibonacci numbers appear unexpectedly often in mathematics, so much so that there is an entire journal dedicated to their study, the ''Fibonacci Quarterly''. Appli ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pell Number
In mathematics, the Pell numbers are an infinite sequence of integers, known since ancient times, that comprise the denominators of the closest rational approximations to the square root of 2. This sequence of approximations begins , , , , and , so the sequence of Pell numbers begins with 1, 2, 5, 12, and 29. The numerators of the same sequence of approximations are half the companion Pell numbers or Pell–Lucas numbers; these numbers form a second infinite sequence that begins with 2, 6, 14, 34, and 82. Both the Pell numbers and the companion Pell numbers may be calculated by means of a recurrence relation similar to that for the Fibonacci numbers, and both sequences of numbers grow exponentially, proportionally to powers of the silver ratio 1 + . As well as being used to approximate the square root of two, Pell numbers can be used to find square triangular numbers, to construct integer approximations to the right isosceles triangle, and to solve certain combina ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Square Number
In mathematics, a square number or perfect square is an integer that is the square (algebra), square of an integer; in other words, it is the multiplication, product of some integer with itself. For example, 9 is a square number, since it equals and can be written as . The usual notation for the square of a number is not the product , but the equivalent exponentiation , usually pronounced as " squared". The name ''square'' number comes from the name of the shape. The unit of area is defined as the area of a unit square (). Hence, a square with side length has area . If a square number is represented by ''n'' points, the points can be arranged in rows as a square each side of which has the same number of points as the square root of ''n''; thus, square numbers are a type of Figurate number, figurate numbers (other examples being Cube (algebra), cube numbers and triangular numbers). In the Real number, real number system, square numbers are non-negative. A non-negative integer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Irreducible Representation
In mathematics, specifically in the representation theory of groups and algebras, an irreducible representation (\rho, V) or irrep of an algebraic structure A is a nonzero representation that has no proper nontrivial subrepresentation (\rho, _W,W), with W \subset V closed under the action of \. Every finite-dimensional unitary representation on a Hilbert space V is the direct sum of irreducible representations. Irreducible representations are always indecomposable (i.e. cannot be decomposed further into a direct sum of representations), but the converse may not hold, e.g. the two-dimensional representation of the real numbers acting by upper triangular unipotent matrices is indecomposable but reducible. History Group representation theory was generalized by Richard Brauer from the 1940s to give modular representation theory, in which the matrix operators act on a vector space over a field K of arbitrary characteristic, rather than a vector space over the field of real number ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monster Group
In the area of abstract algebra known as group theory, the monster group M (also known as the Fischer–Griess monster, or the friendly giant) is the largest sporadic simple group; it has order : : = 2463205976112133171923293141475971 : ≈ . The finite simple groups have been completely classified. Every such group belongs to one of 18 countably infinite families or is one of 26 sporadic groups that do not follow such a systematic pattern. The monster group contains 20 sporadic groups (including itself) as subquotients. Robert Griess, who proved the existence of the monster in 1982, has called those 20 groups the ''happy family'', and the remaining six exceptions '' pariahs''. It is difficult to give a good constructive definition of the monster because of its complexity. Martin Gardner wrote a popular account of the monster group in his June 1980 Mathematical Games column in ''Scientific American''. History The monster was predi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
194 (other)
194 A.D. is a year. 194 may also refer to: * 194 (number) * Connecticut Route 194 * Kentucky Route 194 * Maryland Route 194 * Oregon Route 194 * Pennsylvania Route 194 * Georgia State Route 194 * Maine State Route 194 * New York State Route 194 * Virginia State Route 194 * Washington State Route 194 * Japan National Route 194 * K-194 (Kansas highway) * North Carolina Highway 194 * Wisconsin Highway 194 * Wyoming Highway 194 * Colorado State Highway 194 * Minnesota State Highway 194 * Texas State Highway 194 * State Highway 194 (Maharashtra) * Interstate 194 (other) * Interstate 194 (Michigan) * Minuscule 194 * Jordan 194 * Palestine 194 * 194th Fighter Squadron * 194th Intelligence Squadron * 194th Armored Brigade (United States) * 194th Engineer Brigade * 194th Regional Support Wing * 194th Ohio Infantry * 194th Battalion (Edmonton Highlanders), CEF * 194th (2/1st South Scottish) Brigade * No. 194 Squadron RAF 194 Squadron RAF, though formed as a training ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
