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183 (number)
183 (one hundred ndeighty-three) is the natural number following 182 and preceding 184. In mathematics 183 is a perfect totient number, a number that is equal to the sum of its iterated totients Because 183 = 13^2 + 13 + 1, it is the number of points in a projective plane over the finite field \mathbb_. 183 is the fourth element of a divisibility sequence 1,3,13,183,\dots in which the nth number a_n can be computed as a_n=a_^2+a_+1=\bigl\lfloor x^\bigr\rfloor, for a transcendental number x\approx 1.38509. This sequence counts the number of trees of height \le n in which each node can have at most two children. There are 183 different semiorders on four labeled elements. See also * The year AD 183 or 183 BC __NOTOC__ Year 183 BC was a year of the pre-Julian Roman calendar. At the time it was known as the Year of the Consulship of Marcellus and Labeo (or, less frequently, year 571 ''Ab urbe condita''). The denomination 183 BC for this year has been ... * List of highways ... [...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] |
182 (number)
182 (one hundred ndeighty-two) is the natural number following 181 and preceding 183. In mathematics * 182 is an even number * 182 is a composite number, as it is a positive integer with a positive divisor other than one or itself * 182 is a deficient number, as the sum of its proper divisors, 154, is less than 182 * 182 is a member of the Mian–Chowla sequence: 1, 2, 4, 8, 13, 21, 31, 45, 66, 81, 97, 123, 148, 182 * 182 is a nontotient number, as there is no integer with exactly 182 coprimes below it * 182 is an odious number * 182 is a pronic number, oblong number or heteromecic number, a number which is the product of two consecutive integers ( 13 × 14) * 182 is a repdigit in the D'ni numeral system ( 77), and in base 9 ( 222) * 182 is a sphenic number, the product of three prime factors * 182 is a square-free number * 182 is an Ulam number * Divisors of 182: 1, 2, 7, 13, 14, 26, 91, 182 In astronomy * 182 Elsa is a S-type main belt asteroid * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
184 (number)
184 (one hundred ndeighty-four) is the natural number following 183 and preceding 185. In mathematics There are 184 different Eulerian graphs on eight unlabeled vertices, and 184 paths by which a chess rook can travel from one corner of a 4 × 4 chessboard to the opposite corner without passing through the same square twice. 184 is also a refactorable number. In other fields Some physicists have proposed that 184 is a magic number for neutrons in atomic nuclei. In poker, with one or more jokers as wild cards, there are 184 different straight flushes. See also * The year AD 184 or 184 BC * List of highways numbered 184 The following highways are numbered 184: Ireland * R184 road (Ireland) Japan * Japan National Route 184 Poland * Voivodeship road 184 (Poland), Voivodeship road 184 United States * Interstate 184 * Alabama State Route 184 * Arkansas Highway ... * References {{DEFAULTSORT:184 (Number) Integers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perfect Totient Number
In number theory, a perfect totient number is an integer that is equal to the sum of its iterated totients. That is, we apply the totient function to a number ''n'', apply it again to the resulting totient, and so on, until the number 1 is reached, and add together the resulting sequence of numbers; if the sum equals ''n'', then ''n'' is a perfect totient number. For example, there are six positive integers less than 9 and relatively prime to it, so the totient of 9 is 6; there are two numbers less than 6 and relatively prime to it, so the totient of 6 is 2; and there is one number less than 2 and relatively prime to it, so the totient of 2 is 1; and , so 9 is a perfect totient number. The first few perfect totient numbers are : 3, 9, 15, 27, 39, 81, 111, 183, 243, 255, 327, 363, 471, 729, 2187, 2199, 3063, 4359, 4375, ... . In symbols, one writes :\varphi^i(n) = \begin \varphi(n), &\text i = 1 \\ \varphi(\varphi^(n)), &\text i \geq 2 \end for the iterated totient function ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Iteration
Iteration is the repetition of a process in order to generate a (possibly unbounded) sequence of outcomes. Each repetition of the process is a single iteration, and the outcome of each iteration is then the starting point of the next iteration. In mathematics and computer science, iteration (along with the related technique of recursion) is a standard element of algorithms. Mathematics In mathematics, iteration may refer to the process of iterating a function, i.e. applying a function repeatedly, using the output from one iteration as the input to the next. Iteration of apparently simple functions can produce complex behaviors and difficult problems – for examples, see the Collatz conjecture and juggler sequences. Another use of iteration in mathematics is in iterative methods which are used to produce approximate numerical solutions to certain mathematical problems. Newton's method is an example of an iterative method. Manual calculation of a number's square root is a co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euler's Totient Function
In number theory, Euler's totient function counts the positive integers up to a given integer that are relatively prime to . It is written using the Greek letter phi as \varphi(n) or \phi(n), and may also be called Euler's phi function. In other words, it is the number of integers in the range for which the greatest common divisor is equal to 1. The integers of this form are sometimes referred to as totatives of . For example, the totatives of are the six numbers 1, 2, 4, 5, 7 and 8. They are all relatively prime to 9, but the other three numbers in this range, 3, 6, and 9 are not, since and . Therefore, . As another example, since for the only integer in the range from 1 to is 1 itself, and . Euler's totient function is a multiplicative function, meaning that if two numbers and are relatively prime, then . This function gives the order of the multiplicative group of integers modulo (the group of units of the ring \Z/n\Z). It is also used for defining the RSA e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Point (geometry)
In classical Euclidean geometry, a point is a primitive notion that models an exact location in space, and has no length, width, or thickness. In modern mathematics, a point refers more generally to an element of some set called a space. Being a primitive notion means that a point cannot be defined in terms of previously defined objects. That is, a point is defined only by some properties, called axioms, that it must satisfy; for example, ''"there is exactly one line that passes through two different points"''. Points in Euclidean geometry Points, considered within the framework of Euclidean geometry, are one of the most fundamental objects. Euclid originally defined the point as "that which has no part". In two-dimensional Euclidean space, a point is represented by an ordered pair (, ) of numbers, where the first number conventionally represents the horizontal and is often denoted by , and the second number conventionally represents the vertical and is often denoted by . ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Projective Plane
In mathematics, a projective plane is a geometric structure that extends the concept of a plane. In the ordinary Euclidean plane, two lines typically intersect in a single point, but there are some pairs of lines (namely, parallel lines) that do not intersect. A projective plane can be thought of as an ordinary plane equipped with additional "points at infinity" where parallel lines intersect. Thus ''any'' two distinct lines in a projective plane intersect at exactly one point. Renaissance artists, in developing the techniques of drawing in perspective, laid the groundwork for this mathematical topic. The archetypical example is the real projective plane, also known as the extended Euclidean plane. This example, in slightly different guises, is important in algebraic geometry, topology and projective geometry where it may be denoted variously by , RP2, or P2(R), among other notations. There are many other projective planes, both infinite, such as the complex projective plane, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Field
In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any field, a finite field is a set on which the operations of multiplication, addition, subtraction and division are defined and satisfy certain basic rules. The most common examples of finite fields are given by the integers mod when is a prime number. The ''order'' of a finite field is its number of elements, which is either a prime number or a prime power. For every prime number and every positive integer there are fields of order p^k, all of which are isomorphic. Finite fields are fundamental in a number of areas of mathematics and computer science, including number theory, algebraic geometry, Galois theory, finite geometry, cryptography and coding theory. Properties A finite field is a finite set which is a field; this means that multiplication, addition, subtraction and division (excluding division by zero) are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Divisibility Sequence
In mathematics, a divisibility sequence is an integer sequence (a_n) indexed by positive integers ''n'' such that :\textm\mid n\texta_m\mid a_n for all ''m'', ''n''. That is, whenever one index is a multiple of another one, then the corresponding term also is a multiple of the other term. The concept can be generalized to sequences with values in any ring where the concept of divisibility is defined. A strong divisibility sequence is an integer sequence (a_n) such that for all positive integers ''m'', ''n'', :\gcd(a_m,a_n) = a_. Every strong divisibility sequence is a divisibility sequence: \gcd(m,n) = m if and only if m\mid n. Therefore by the strong divisibility property, \gcd(a_m,a_n) = a_m and therefore a_m\mid a_n. Examples * Any constant sequence is a strong divisibility sequence. * Every sequence of the form a_n = kn, for some nonzero integer ''k'', is a divisibility sequence. * The numbers of the form 2^n-1 (Mersenne numbers) form a strong divisibi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transcendental Number
In mathematics, a transcendental number is a number that is not algebraic—that is, not the root of a non-zero polynomial of finite degree with rational coefficients. The best known transcendental numbers are and . Though only a few classes of transcendental numbers are known—partly because it can be extremely difficult to show that a given number is transcendental—transcendental numbers are not rare. Indeed, almost all real and complex numbers are transcendental, since the algebraic numbers comprise a countable set, while the set of real numbers and the set of complex numbers are both uncountable sets, and therefore larger than any countable set. All transcendental real numbers (also known as real transcendental numbers or transcendental irrational numbers) are irrational numbers, since all rational numbers are algebraic. The converse is not true: not all irrational numbers are transcendental. Hence, the set of real numbers consists of non-overlapping rational, algebrai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semiorder
In order theory, a branch of mathematics, a semiorder is a type of ordering for items with numerical scores, where items with widely differing scores are compared by their scores and where scores within a given margin of error are deemed incomparable. Semiorders were introduced and applied in mathematical psychology by as a model of human preference. They generalize strict weak orderings, in which items with equal scores may be tied but there is no margin of error. They are a special case of partial orders and of interval orders, and can be characterized among the partial orders by additional axioms, or by two forbidden four-item suborders. Utility theory The original motivation for introducing semiorders was to model human preferences without assuming that incomparability is a transitive relation. For instance, suppose that x, y, and z represent three quantities of the same material, and that x is larger than z by the smallest amount that is perceptible as a difference, while y ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
