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186 (number)
186 (one hundred ndeighty-six) is the natural number following 185 and preceding 187. In mathematics There is no integer with exactly 186 coprimes less than it, so 186 is a nontotient. It is also never the difference between an integer and the total of coprimes below it, so it is a noncototient. There are 186 different pentahexes, shapes formed by gluing together five regular hexagons, when rotations of shapes are counted as distinct from each other. 186 is a Fine number. See also * The year AD 186 or 186 BC * List of highways numbered 186 The following highways are numbered 186: Ireland R186 regional road Japan * Japan National Route 186 United States * Alabama State Route 186 * Arizona State Route 186 * Arkansas Highway 186 * California State Route 186 * Connecticut Route 18 ... * References {{DEFAULTSORT:186 (Number) Integers ... [...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 numbers'', and numbers used for ordering are called '' 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 jersey numbers). Some definitions, including the standard 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 numbers form a set. Many other number sets are built by succ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
185 (number)
185 (one hundred ndeighty-five) is the natural number following 184 and preceding 186. In mathematics There are 185 different directed graphs on four unlabeled vertices that have at least one sink vertex, with no outgoing edges, 185 ways of permuting the squares of a 2\times 4 grid of squares in such a way that each square is one unit away from its original position horizontally, vertically, or diagonally, and 185 matroids on five labeled elements in which each element participates in at least one basis. The Spiral of Theodorus is formed by unit-length line segments that, together with the center point of the spiral, form right triangles. 185 of these right triangles fit within the first four turns of this spiral. See also * The year AD 185 or 185 BC __NOTOC__ Year 185 BC was a year of the pre-Julian Roman calendar. At the time it was known as the Year of the Consulship of Pulcher and Puditanus (or, less frequently, year 569 ''Ab urbe condita''). The denomination 185 B ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
187 (number)
187 (one hundred ndeighty-seven) is the natural number following 186 and preceding 188. In mathematics There are 187 ways of forming a sum of positive integers that adds to 11, counting two sums as equivalent when they are cyclic permutations of each other. There are also 187 unordered triples of 5-bit binary numbers whose bitwise exclusive or is zero. Per Miller's rules, the triakis tetrahedron produces 187 distinct stellations. It is the smallest Catalan solid, dual to the truncated tetrahedron, which only has 9 distinct stellations. In other fields There are 187 chapters in the Hebrew Torah. See also * 187 (other) 187 is a year on the Julian calendar. 187 may also refer to: Entertainment *'' One Eight Seven'', a 1997 American crime thriller film released by Warner Bros. Music *'' Deep Cover (song)'', also known as ''187'' and ''187um'', a 1992 song b ... References {{DEFAULTSORT:187 (Number) Integers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coprime
In mathematics, two integers and are coprime, relatively prime or mutually prime if the only positive integer that is a divisor of both of them is 1. Consequently, any prime number that divides does not divide , and vice versa. This is equivalent to their greatest common divisor (GCD) being 1. One says also '' is prime to '' or '' is coprime with ''. The numbers 8 and 9 are coprime, despite the fact that neither considered individually is a prime number, since 1 is their only common divisor. On the other hand, 6 and 9 are not coprime, because they are both divisible by 3. The numerator and denominator of a reduced fraction are coprime, by definition. Notation and testing Standard notations for relatively prime integers and are: and . In their 1989 textbook '' Concrete Mathematics'', Ronald Graham, Donald Knuth, and Oren Patashnik proposed that the notation a\perp b be used to indicate that and are relatively prime and that the term "prime" be used instead of coprime ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nontotient
In number theory, a nontotient is a positive integer ''n'' which is not a totient number: it is not in the range of Euler's totient function φ, that is, the equation φ(''x'') = ''n'' has no solution ''x''. In other words, ''n'' is a nontotient if there is no integer ''x'' that has exactly ''n'' coprimes below it. All odd numbers are nontotients, except 1, since it has the solutions ''x'' = 1 and ''x'' = 2. The first few even nontotients are : 14, 26, 34, 38, 50, 62, 68, 74, 76, 86, 90, 94, 98, 114, 118, 122, 124, 134, 142, 146, 152, 154, 158, 170, 174, 182, 186, 188, 194, 202, 206, 214, 218, 230, 234, 236, 242, 244, 246, 248, 254, 258, 266, 274, 278, 284, 286, 290, 298, ... Least ''k'' such that the totient of ''k'' is ''n'' are (0 if no such ''k'' exists) :1, 3, 0, 5, 0, 7, 0, 15, 0, 11, 0, 13, 0, 0, 0, 17, 0, 19, 0, 25, 0, 23, 0, 35, 0, 0, 0, 29, 0, 31, 0, 51, 0, 0, 0, 37, 0, 0, 0, 41, 0, 43, 0, 69, 0, 47, 0, 65, 0, 0, 0, 53, 0, 81, 0, 87, 0, 59, 0, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Noncototient
In mathematics, a noncototient is a positive integer ''n'' that cannot be expressed as the difference between a positive integer ''m'' and the number of coprime integers below it. That is, ''m'' − φ(''m'') = ''n'', where φ stands for Euler's totient function, has no solution for ''m''. The '' cototient'' of ''n'' is defined as ''n'' − φ(''n''), so a noncototient is a number that is never a cototient. It is conjectured that all noncototients are even. This follows from a modified form of the slightly stronger version of the Goldbach conjecture: if the even number ''n'' can be represented as a sum of two distinct primes ''p'' and ''q,'' then :pq - \varphi(pq) = pq - (p-1)(q-1) = p+q-1 = n-1. \, It is expected that every even number larger than 6 is a sum of two distinct primes, so probably no odd number larger than 5 is a noncototient. The remaining odd numbers are covered by the observations 1=2-\phi(2), 3 = 9 - \phi(9) and 5 = 25 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polyhex (mathematics)
In recreational mathematics, a polyhex is a polyform with a regular hexagon (or 'hex' for short) as the base form, constructed by joining together 1 or more hexagons. Specific forms are named by their number of hexagons: ''monohex'', ''dihex'', ''trihex'', ''tetrahex'', etc. They were named by David Klarner who investigated them. Each individual polyhex tile and tessellation polyhexes and can be drawn on a regular hexagonal tiling. Construction rules The rules for joining hexagons together may vary. Generally, however, the following rules apply: #Two hexagons may be joined only along a common edge, and must share the entirety of that edge. #No two hexagons may overlap. #A polyhex must be connected. Configurations of disconnected basic polygons do not qualify as polyhexes. #The mirror image of an asymmetric polyhex is not considered a distinct polyhex (polyhex are "double sided"). Tessellation properties All of the polyhexes with fewer than five hexagons can form at least one ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
186 BC
__NOTOC__ Year 186 BC was a year of the pre-Julian Roman calendar. At the time it was known as the Year of the Consulship of Albinus and Philippus (or, less frequently, year 568 ''Ab urbe condita''). The denomination 186 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 * The rapid spread of the Bacchanalia cult throughout the Roman Republic, which, it is claimed, indulges in all kinds of crimes and political conspiracies at its nocturnal meetings, leads to the Roman Senate issuing a decree, the ''Senatus consultum de Bacchanalibus'', by which the Bacchanalia are prohibited throughout all Italy except in certain special cases which must be approved specifically by the Senate. Asia Minor * Eumenes II of Pergamum defeats Prusias I of Bithynia. China * The first burial at the famous archaeological site of Mawangdui is made during th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Highways Numbered 186
The following highways are numbered 186: Ireland R186 regional road Japan * Japan National Route 186 United States * Alabama State Route 186 * Arizona State Route 186 * Arkansas Highway 186 * California State Route 186 * Connecticut Route 186 * Georgia State Route 186 * Illinois Route 186 (former) * K-186 (Kansas highway) * Kentucky Route 186 * Maine State Route 186 * Maryland Route 186 * Massachusetts Route 186 * M-186 (Michigan highway) * New Mexico State Road 186 * New York State Route 186 * North Carolina Highway 186 * Ohio State Route 186 * South Carolina Highway 186 * Tennessee State Route 186 * Texas State Highway 186 ** Texas State Highway Spur 186 ** Farm to Market Road 186 (Texas) * Utah State Route 186 * Virginia State Route 186 * Wisconsin Highway 186 State Trunk Highway 186 (often called Highway 186, STH-186 or WIS 186) is a state highway (US), state highway in the U.S. state of Wisconsin. It runs from its southern terminus at Wisconsin Highway 7 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
