|
174 (number)
174 (one hundred ndseventy-four) is the natural number following 173 and preceding 175. In mathematics There are 174 7-crossing semi-meanders, ways of arranging a semi-infinite curve in the plane so that it crosses a straight line seven times. There are 174 invertible 3\times 3 (0,1)-matrices. There are also 174 combinatorially distinct ways of subdividing a topological cuboid into a mesh of tetrahedra, without adding extra vertices, although not all can be represented geometrically by flat-sided polyhedra. The Mordell curve y^2=x^3-174 has rank three, and 174 is the smallest positive integer for which y^2=x^3-k has this rank. The corresponding number for curves y^2=x^3+k is 113. In other fields In English draughts or checkers, a common variation is the "three-move restriction", in which the first three moves by both players are chosen at random. There are 174 different choices for these moves, although some systems for choosing these moves further restrict them to a subset th ... [...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] |
173 (number)
173 (one hundred ndseventy-three) is the natural number following 172 and preceding 174. In mathematics 173 is: *an odd number. *a deficient number. *an odious number. *a balanced prime. *an Eisenstein prime with no imaginary part. *a Sophie Germain prime. *an inconsummate number. *the sum of 2 squares: 22 + 132. *the sum of three consecutive prime numbers: 53 + 59 + 61. * Palindromic number in bases 3 (201023) and 9 (2129). In astronomy * 173 Ino is a large dark main belt asteroid * 173P/Mueller is a periodic comet in the Solar System * Arp 173 (VV 296, KPG 439) is a pair of galaxies in the constellation Boötes In the military * 173rd Air Refueling Squadron unit of the Nebraska Air National Guard * 173rd Airborne Brigade Combat Team of the United States Army based in Vicenza * 173rd Battalion unit of the Canadian Expeditionary Force during the World War I * 173rd Surveillance Squadron (Australia) of the Australian Army at Oakey, Queensland * K-173 ''Chelya ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
175 (number)
175 (one hundred ndseventy-five) is the natural number following 174 and preceding 176. In mathematics Raising the decimal digits of 175 to the powers of successive integers produces 175 back again: 175 is a figurate number for a rhombic dodecahedron, the difference of two consecutive fourth powers: It is also a decagonal number and a decagonal pyramid number, the smallest number after 1 that has both properties. In other fields In the Book of Genesis 25:7-8, Abraham is said to have lived to be 175 years old. 175 is the fire emergency number in Lebanon Lebanon ( , ar, لُبْنَان, translit=lubnān, ), officially the Republic of Lebanon () or the Lebanese Republic, is a country in Western Asia. It is located between Syria to Lebanon–Syria border, the north and east and Israel to Blue .... See also * The year AD 175 or 175 BC * List of highways numbered 175 * References {{DEFAULTSORT:175 (Number) Integers ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semi-meander
In mathematics, a meander or closed meander is a self-avoiding closed curve which intersects a line a number of times. Intuitively, a meander can be viewed as a road crossing a river through a number of bridges. Meander Given a fixed oriented line ''L'' in the Euclidean plane R2, a meander of order ''n'' is a non-self-intersecting closed curve in R2 which transversally intersects the line at 2''n'' points for some positive integer ''n''. The line and curve together form a meandric system. Two meanders are said to be equivalent if there is a homeomorphism of the whole plane that takes ''L'' to itself and takes one meander to the other. Examples The meander of order 1 intersects the line twice: : The meanders of order 2 intersect the line four times. : Meandric numbers The number of distinct meanders of order ''n'' is the meandric number ''Mn''. The first fifteen meandric numbers are given below . :''M''1 = 1 :''M''2 = 1 :''M''3 = 2 :''M''4 = 8 :''M''5 = 42 :''M''6 = 262 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical Matrix
A logical matrix, binary matrix, relation matrix, Boolean matrix, or (0, 1) matrix is a matrix with entries from the Boolean domain Such a matrix can be used to represent a binary relation between a pair of finite sets. Matrix representation of a relation If ''R'' is a binary relation between the finite indexed sets ''X'' and ''Y'' (so ), then ''R'' can be represented by the logical matrix ''M'' whose row and column indices index the elements of ''X'' and ''Y'', respectively, such that the entries of ''M'' are defined by :M_ = \begin 1 & (x_i, y_j) \in R, \\ 0 & (x_i, y_j) \not\in R. \end In order to designate the row and column numbers of the matrix, the sets ''X'' and ''Y'' are indexed with positive integers: ''i'' ranges from 1 to the cardinality (size) of ''X'', and ''j'' ranges from 1 to the cardinality of ''Y''. See the entry on indexed sets for more detail. Example The binary relation ''R'' on the set is defined so that ''aRb'' holds if and only if ''a'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cuboid
In geometry, a cuboid is a hexahedron, a six-faced solid. Its faces are quadrilaterals. Cuboid means "like a cube", in the sense that by adjusting the length of the edges or the angles between edges and faces a cuboid can be transformed into a cube. In mathematical language a cuboid is a convex polyhedron, whose polyhedral graph is the same as that of a cube. Special cases are a cube, with 6 squares as faces, a rectangular prism, rectangular cuboid or rectangular box, with 6 rectangles as faces, for both, cube and rectangular prism, adjacent faces meet in a right angle. General cuboids By Euler's formula the numbers of faces ''F'', of vertices ''V'', and of edges ''E'' of any convex polyhedron are related by the formula ''F'' + ''V'' = ''E'' + 2. In the case of a cuboid this gives 6 + 8 = 12 + 2; that is, like a cube, a cuboid has 6 faces, 8 vertices, and 12 edges. Along with the rectangular cuboids, any parallelepiped ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tetrahedron
In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all the ordinary convex polyhedra and the only one that has fewer than 5 faces. The tetrahedron is the three-dimensional case of the more general concept of a Euclidean simplex, and may thus also be called a 3-simplex. The tetrahedron is one kind of pyramid, which is a polyhedron with a flat polygon base and triangular faces connecting the base to a common point. In the case of a tetrahedron the base is a triangle (any of the four faces can be considered the base), so a tetrahedron is also known as a "triangular pyramid". Like all convex polyhedra, a tetrahedron can be folded from a single sheet of paper. It has two such nets. For any tetrahedron there exists a sphere (called the circumsphere) on which all four vertices lie, and another sphere ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mordell Curve
In algebra, a Mordell curve is an elliptic curve of the form ''y''2 = ''x''3 + ''n'', where ''n'' is a fixed non-zero integer. These curves were closely studied by Louis Mordell, from the point of view of determining their integer points. He showed that every Mordell curve contains only finitely many integer points (''x'', ''y''). In other words, the differences of perfect squares and perfect cubes tend to infinity. The question of how fast was dealt with in principle by Baker's method. Hypothetically this issue is dealt with by Marshall Hall's conjecture In mathematics, Hall's conjecture is an open question, , on the differences between perfect squares and perfect cubes. It asserts that a perfect square ''y''2 and a perfect cube ''x''3 that are not equal must lie a substantial distance apart. This .... Properties If (''x'', ''y'') is an integer point on a Mordell curve, then so is (''x'', ''-y''). There are certain values of ''n'' for which the corresponding Mordell curve has ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rank Of An Elliptic Curve
In mathematics, the rank of an elliptic curve is the rational Mordell–Weil rank of an elliptic curve E defined over the field of rational numbers. Mordell's theorem says the group of rational points on an elliptic curve has a finite basis. This means that for any elliptic curve there is a finite subset of the rational points on the curve, from which all further rational points may be generated. If the number of rational points on a curve is infinite then some point in a finite basis must have infinite order. The number of ''independent'' basis points with infinite order is the rank of the curve. The rank is related to several outstanding problems in number theory, most notably the Birch–Swinnerton-Dyer conjecture. It is widely believed that there is no maximum rank for an elliptic curve, and it has been shown that there exist curves with rank as large as 28, but it is widely believed that such curves are rare. Indeed, Goldfeld and later Katz– Sarnak conjectured that in a su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
English Draughts
English draughts (British English) or checkers (American English), also called straight checkers or simply draughts, is a form of the strategy board game checkers (or draughts). It is played on an 8×8 checkerboard with 12 pieces per side. The pieces move and capture diagonally forward, until they reach the opposite end of the board, when they are crowned and can thereafter move and capture both backward and forward. As in all forms of draughts, English draughts is played by two opponents, alternating turns on opposite sides of the board. The pieces are traditionally black, red, or white. Enemy pieces are captured by jumping over them. The 8×8 variant of draughts was weakly solved in 2007 by a team of Canadian computer scientists led by Jonathan Schaeffer. From the standard starting position, both players can guarantee a draw with perfect play. Pieces Though pieces are traditionally made of wood, now many are made of plastic, though other materials may be used. Pieces are t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
174 BC
__NOTOC__ Year 174 BC was a year of the Roman calendar, pre-Julian Roman calendar. At the time it was known as the Year of the Consulship of Paullulus and Scaevola (or, less frequently, year 580 ''Ab urbe condita''). The denomination 174 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 Mongolia * The Xiongnu attack the Yuezhi, and force them away from Gansu. Deaths * Modu Shanyu, Mete Khan, emperor and founder of the Xiongnu Empire, who has united various Hun confederations under his rule (b. 234 BC) * Publius Aelius Paetus (consul 201 BC), Publius Aelius Paetus, Roman Republic, Roman Roman consul, consul and Roman censor, censor * Titus Quinctius Flamininus, Roman Republic, Roman general and statesman whose skillful diplomacy has enabled him to establish a Roman protectorate over Ancient Greece, Greece (b. c. 227 BC) (approximate date) References ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Highways Numbered 174
The following highways are numbered 174: Brazil * BR-174 Canada *Ottawa Road 174 * Prince Edward Island Route 174 Costa Rica * National Route 174 Ireland * R174 road Japan * Route 174 (Japan) (Japan's shortest national highway) United States * Interstate 174 (proposed) * Alabama State Route 174 * California State Route 174 * Connecticut Route 174 * Georgia State Route 174 * Illinois Route 174 (former) * Kentucky Route 174 * Louisiana Highway 174 * Maine State Route 174 * Maryland Route 174 * M-174 (Michigan highway) * Missouri Route 174 * New Jersey Route 174 (former) * New Mexico State Road 174 * New York State Route 174 ** New York State Route 174X * Ohio State Route 174 * Pennsylvania Route 174 * South Carolina Highway 174 * Tennessee State Route 174 * Texas State Highway 174 ** Texas State Highway Spur 174 ** Farm to Market Road 174 * Utah State Route 174 * Virginia State Route 174 * Washington State Route 174 * Wisconsin Highway 174 (former) * Wyoming Highwa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
.jpg "Click for more on -> Tetrahedron")
