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189 (number)
189 (one hundred ndeighty-nine) is the natural number following 188 and preceding 190. In mathematics 189 is a centered cube number and a heptagonal number. The centered cube numbers are the sums of two consecutive cubes, and 189 can be written as sum of two cubes in two ways: and The smallest number that can be written as the sum of two positive cubes in two ways is 1729. There are 189 zeros among the decimal digits of the positive integers with at most three digits. The largest prime number that can be represented in 256-bit arithmetic is the "ultra-useful prime" used in quasi-Monte Carlo methods and in some cryptographic Cryptography, or cryptology (from grc, , translit=kryptós "hidden, secret"; and ''graphein'', "to write", or '' -logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of adve ... systems. See Appendix B. See also * The year AD 189 or 189 BC * List of highways numbered 189 * R ... [...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] |
188 (number)
188 (one hundred ndeighty-eight) is the natural number following 187 and preceding 189. In mathematics There are 188 different four-element semigroups, and 188 ways a chess queen can move from one corner of a 4\times 4 board to the opposite corner by a path that always moves closer to its goal. The sides and diagonals of a regular dodecagon form 188 equilateral triangles. In other fields The number 188 figures prominently in the film ''The Parallel Street'' (1962) by German experimental film director . The opening frame of the film is just an image of this number. See also * The year AD 188 or 188 BC * List of highways numbered 188 The following highways are numbered 188: India * State Highway 188 (Andhra Pradesh) Japan * Japan National Route 188 United States * Alabama State Route 188 * Arizona State Route 188 * California State Route 188 * Connecticut Route 188 * Flori ... * References {{DEFAULTSORT:188 (Number) Integers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
190 (number)
190 (one hundred ndninety) is the natural number following 189 and preceding 191. In mathematics 190 is a triangular number, a hexagonal number, and a centered nonagonal number, the fourth figurate number (after 1, 28, and 91) with that combination of properties. It is also a truncated square pyramid number. Integers from 191 to 199 ;191 : 191 is a prime number. ;192 : 192 = 26 × 3 is a 3-smooth number, the smallest number with 14 divisors. ;193 : 193 is a prime number. ;194 : 194 = 2 × 97 is a Markov number, the smallest number written as the sum of three squares in five ways, and the number of irreducible representations of the Monster group. ;195 : 195 = 3 × 5 × 13 is the smallest number expressed as a sum of distinct squares in 16 different ways. ;196 :196 = 22 × 72 is a square number. ;197 :197 is a prime number and a Schröder–Hipparchus number. ;198 :198 = 2 × 32 × 11 is the smallest number written as the sum of four squares in ten ways :No integer factorial eve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Centered Cube Number
A centered cube number is a centered figurate number that counts the number of points in a three-dimensional pattern formed by a point surrounded by concentric cubical layers of points, with points on the square faces of the th layer. Equivalently, it is the number of points in a body-centered cubic pattern within a cube that has points along each of its edges. The first few centered cube numbers are : 1, 9, 35, 91, 189, 341, 559, 855, 1241, 1729, 2331, 3059, 3925, 4941, 6119, 7471, 9009, ... . Formulas The centered cube number for a pattern with concentric layers around the central point is given by the formula :n^3 + (n + 1)^3 = (2n+1)\left(n^2+n+1\right). The same number can also be expressed as a trapezoidal number (difference of two triangular numbers), or a sum of consecutive numbers, as :\binom-\binom = (n^2+1)+(n^2+2)+\cdots+(n+1)^2. Properties Because of the factorization , it is impossible for a centered cube number to be a prime number. The only centered ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heptagonal Number
A heptagonal number is a figurate number that is constructed by combining heptagons with ascending size. The ''n''-th heptagonal number is given by the formula :H_n=\frac. The first few heptagonal numbers are: : 0, 1, 7, 18, 34, 55, 81, 112, 148, 189, 235, 286, 342, 403, 469, 540, 616, 697, 783, 874, 970, 1071, 1177, 1288, 1404, 1525, 1651, 1782, … Parity The parity of heptagonal numbers follows the pattern odd-odd-even-even. Like square numbers, the digital root in base 10 of a heptagonal number can only be 1, 4, 7 or 9. Five times a heptagonal number, plus 1 equals a triangular number. Additional properties * The heptagonal numbers have several notable formulas: :H_=H_m+H_n+5mn :H_=H_m+H_n-5mn+3n :H_m-H_n=\frac :40H_n+9=(10n-3)^2 Sum of reciprocals A formula for the sum of the reciprocals of the heptagonal numbers is given by: : \begin\sum_^\infty \frac &= \frac+\frac\ln(5)+\frac\ln\left(\frac\sqrt\right)+\frac\ln\left(\frac\sqrt\right)\\ &=\frac13\left(\frac+\frac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cube (algebra)
In arithmetic and algebra, the cube of a number is its third power, that is, the result of multiplying three instances of together. The cube of a number or any other mathematical expression is denoted by a superscript 3, for example or . The cube is also the number multiplied by its square: :. The ''cube function'' is the function (often denoted ) that maps a number to its cube. It is an odd function, as :. The volume of a geometric cube is the cube of its side length, giving rise to the name. The inverse operation that consists of finding a number whose cube is is called extracting the cube root of . It determines the side of the cube of a given volume. It is also raised to the one-third power. The graph of the cube function is known as the cubic parabola. Because the cube function is an odd function, this curve has a center of symmetry at the origin, but no axis of symmetry. In integers A cube number, or a perfect cube, or sometimes just a cube, is a number wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1729 (number)
1729 is the natural number following 1728 and preceding 1730. It is a taxicab number, and is variously known as Ramanujan's number and the Ramanujan-Hardy number, after an anecdote of the British mathematician G. H. Hardy when he visited Indian mathematician Srinivasa Ramanujan in hospital. He related their conversation: The two different ways are: : 1729 = 13 + 123 = 93 + 103 The quotation is sometimes expressed using the term "positive cubes", since allowing negative perfect cubes (the cube of a negative integer) gives the smallest solution as 91 (which is a divisor of 1729; 1991 = 1729). :91 = 63 + (−5)3 = 43 + 33 Numbers that are the smallest number that can be expressed as the sum of two cubes in ''n'' distinct ways have been dubbed "taxicab numbers". The number was also found in one of Ramanujan's notebooks dated years before the incident, and was noted by Frénicle de Bessy in 1657. A commemorative plaque now appears at the site of the Ramanujan-Hardy inciden ... [...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] |
Quasi-Monte Carlo Method
In numerical analysis, the quasi-Monte Carlo method is a method for numerical integration and solving some other problems using low-discrepancy sequences (also called quasi-random sequences or sub-random sequences). This is in contrast to the regular Monte Carlo method or Monte Carlo integration, which are based on sequences of pseudorandom numbers. Monte Carlo and quasi-Monte Carlo methods are stated in a similar way. The problem is to approximate the integral of a function ''f'' as the average of the function evaluated at a set of points ''x''1, ..., ''x''''N'': : \int_ f(u)\,u \approx \frac\,\sum_^N f(x_i). Since we are integrating over the ''s''-dimensional unit cube, each ''x''''i'' is a vector of ''s'' elements. The difference between quasi-Monte Carlo and Monte Carlo is the way the ''x''''i'' are chosen. Quasi-Monte Carlo uses a low-discrepancy sequence such as the Halton sequence, the Sobol sequence, or the Faure sequence, whereas Monte Carlo uses a pseudorandom sequence ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cryptography
Cryptography, or cryptology (from grc, , translit=kryptós "hidden, secret"; and ''graphein'', "to write", or ''-logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of adversarial behavior. More generally, cryptography is about constructing and analyzing protocols that prevent third parties or the public from reading private messages. Modern cryptography exists at the intersection of the disciplines of mathematics, computer science, information security, electrical engineering, digital signal processing, physics, and others. Core concepts related to information security ( data confidentiality, data integrity, authentication, and non-repudiation) are also central to cryptography. Practical applications of cryptography include electronic commerce, chip-based payment cards, digital currencies, computer passwords, and military communications. Cryptography prior to the modern age was effectively synonymo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
189 BC
__NOTOC__ Year 189 BC was a year of the pre-Julian Roman calendar. At the time it was known as the Year of the Consulship of Nobilior and Vulso (or, less frequently, year 565 ''Ab urbe condita''). The denomination 189 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 * Cato the Elder criticizes the consul Marcus Fulvius Nobilior for giving awards to Roman soldiers for doing ordinary tasks, such as digging wells. Greece * The defeat of Antiochus III by the Romans in the Battle of Magnesia robs the Aetolian League of its principal foreign ally and makes it impossible for them to stand alone in continued opposition to Rome. The League is forced to sign a peace treaty with Rome that makes it a subject ally of the Republic. Although the League continues to exist in name, the power of the League is broken by the treaty and it never again const ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Highways Numbered 189
The following highways are numbered 189: Japan * Japan National Route 189 United States * Interstate 189 * U.S. Route 189 * Alabama State Route 189 * Arizona State Route 189 * California State Route 189 * Connecticut Route 189 * Florida State Road 189 * Georgia State Route 189 * K-189 (Kansas highway) * Kentucky Route 189 * Maine State Route 189 * Maryland Route 189 * Massachusetts Route 189 Massachusetts (Massachusett: ''Muhsachuweesut Massachusett_writing_systems.html" ;"title="nowiki/> məhswatʃəwiːsət.html" ;"title="Massachusett writing systems">məhswatʃəwiːsət">Massachusett writing systems">məhswatʃəwiːsət'' En ... * M-189 (Michigan highway) * New Mexico State Road 189 * New York State Route 189 * Ohio State Route 189 * Pennsylvania Route 189 (former) * Tennessee State Route 189 * Texas State Highway 189 (former) ** Ranch to Market Road 189 (Texas) * Utah State Route 189 (1935–1969), Utah State Route 189 (former) * Virginia State Route 189 * Wiscon ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
