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276 (number)
276 (two hundred ndseventy-six) is the natural number following 275 and preceding 277. In mathematics 276 is the sum of 3 consecutive fifth powers (276 = 15 + 25 + 35). As a figurate number it is a triangular number, a hexagonal number, and a centered pentagonal number, the third number after 1 and 6 to have this combination of properties. 276 is the size of the largest set of equiangular lines in 23 dimensions. The maximal set of such lines, derived from the Leech lattice, provides the highest dimension in which the "Gerzon bound" of \binom is known to be attained; its symmetry group is the third Conway group, Co3. 276 is the smallest number for which it is not known if the corresponding aliquot sequence either terminates or ends in a repeating cycle. In other fields In the Christian calendar, there are 276 days from the Annunciation on March 25 to Christmas on December 25, a number considered significant by some authors. See also *The years 276 and 276 BC *List of highway ... [...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] |
Conway Group Co3
In the area of modern algebra known as group theory, the Conway group ''\mathrm_3'' is a sporadic simple group of order Order, ORDER or Orders may refer to: * Categorization, the process in which ideas and objects are recognized, differentiated, and understood * Heterarchy, a system of organization wherein the elements have the potential to be ranked a number of d ... : 210375371123 : = 495766656000 : ≈ 5. History and properties ''\mathrm_3'' is one of the 26 sporadic groups and was discovered by as the group of automorphisms of the Leech lattice \Lambda fixing a lattice vector of type 3, thus length . It is thus a subgroup of \mathrm_0. It is isomorphic to a subgroup of \mathrm_1. The direct product 2\times \mathrm_3 is maximal in \mathrm_0. The Schur multiplier and the outer automorphism group are both trivial. Representations Co3 acts on the unique 23-dimensional even lattice of determinant 4 with no roots, given by the orthogonal complement ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Highways Numbered 276
The following highways are numbered 276: Canada * Manitoba Provincial Road 276 * Nova Scotia Route 276 * Quebec Route 276 Japan * Japan National Route 276 United States * Interstate 276 * U.S. Route 276 * Arkansas Highway 276 ** Arkansas Highway 276S * California State Route 276 * Florida State Road 276 * Georgia State Route 276 (former) * Iowa Highway 276 (former) * K-276 (Kansas highway) * Kentucky Route 276 * Maryland Route 276 * Montana Secondary Highway 276 * New Mexico State Road 276 * New York State Route 276 * Ohio State Route 276 * Pennsylvania Route 276 (former) * Tennessee State Route 276 * Texas State Highway 276 ** Texas State Highway Spur 276 (former) ** Farm to Market Road 276 (Texas) * Utah State Route 276 * Virginia State Route 276 * Washington State Route 276 State Route 276 (SR 276) was a legislated, but not constructed, state highway located in the U.S. state of Washington. The highway was meant to serve as a northern bypass of Pul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
276 BC
__NOTOC__ Year 276 BC was a year of the pre-Julian Roman calendar. At the time it was known as the Year of the Consulship of Gurges and Clepsina (or, less frequently, year 478 ''Ab urbe condita''). The denomination 276 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 Egypt * The Egyptian King Ptolemy II's first wife, Arsinoe I (daughter of the late King Lysimachus of Thrace) is accused, probably at instigation of Ptolemy II's sister (who also has the name Arsinoe), of plotting his murder and is exiled by the King. Arsinoe then marries her own brother, a customary practice in Egypt, but scandalous to the Greeks. The suffix "Philadelphoi" ("Brother-Loving") consequently is added to the names of King Ptolemy II and Queen Arsinoe II. The former queen, Arsinoe I, is banished to Coptos, a city of Upper Egypt near the Wadi Hammamat, while her rival adopts her ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Christmas
Christmas is an annual festival commemorating the birth of Jesus Christ, observed primarily on December 25 as a religious and cultural celebration among billions of people around the world. A feast central to the Christian liturgical year, it is preceded by the season of Advent or the Nativity Fast and initiates the season of Christmastide, which historically in the West lasts twelve days and culminates on Twelfth Night. Christmas Day is a public holiday in many countries, is celebrated religiously by a majority of Christians, as well as culturally by many non-Christians, and forms an integral part of the holiday season organized around it. The traditional Christmas narrative recounted in the New Testament, known as the Nativity of Jesus, says that Jesus was born in Bethlehem, in accordance with messianic prophecies. When Joseph and Mary arrived in the city, the inn had no room and so they were offered a stable where the Christ Child was soon born, with angel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Annunciation
The Annunciation (from Latin '), also referred to as the Annunciation to the Blessed Virgin Mary, the Annunciation of Our Lady, or the Annunciation of the Lord, is the Christian celebration of the biblical tale of the announcement by the angel Gabriel to Mary that she would conceive and bear a son through a virgin birth and become the mother of Jesus Christ, the Christian Messiah and Son of God, marking the Incarnation. Gabriel told Mary to name her son Jesus, meaning " YHWH is salvation". According to , the Annunciation occurred "in the sixth month" of Elizabeth's pregnancy with John the Baptist. Many Christians observe this event with the Feast of the Annunciation on 25 March, an approximation of the northern vernal equinox nine full months before Christmas, the ceremonial birthday of Jesus. The Annunciation is a key topic in Christian art in general, as well as in Marian art in the Catholic Church, having been especially prominent during the Middle Ages and Re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Liturgical Year
The liturgical year, also called the church year, Christian year or kalendar, consists of the cycle of liturgical seasons in Christian churches that determines when feast days, including celebrations of saints, are to be observed, and which portions of Scripture are to be read either in an annual cycle or in a cycle of several years. Distinct liturgical colours may be used in connection with different seasons of the liturgical year. The dates of the festivals vary somewhat among the different churches, although the sequence and logic is largely the same. Liturgical cycle The liturgical cycle divides the year into a series of seasons, each with their own mood, theological emphases, and modes of prayer, which can be signified by different ways of decorating churches, colours of paraments and vestments for clergy, scriptural readings, themes for preaching and even different traditions and practices often observed personally or in the home. In churches that follow the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aliquot Sequence
In mathematics, an aliquot sequence is a sequence of positive integers in which each term is the sum of the proper divisors of the previous term. If the sequence reaches the number 1, it ends, since the sum of the proper divisors of 1 is 0. Definition and overview The aliquot sequence starting with a positive integer ''k'' can be defined formally in terms of the sum-of-divisors function σ1 or the aliquot sum function ''s'' in the following way: : ''s''0 = ''k'' : ''s''n = ''s''(''s''''n''−1) = σ1(''s''''n''−1) − ''s''''n''−1 if ''s''''n''−1 > 0 : ''s''n = 0 if ''s''''n''−1 = 0 ---> (if we add this condition, then the terms after 0 are all 0, and all aliquot sequences would be infinite sequence, and we can conjecture that all aliquot sequences are convergent, the limit of these sequences are usually 0 or 6) and ''s''(0) is undefined. For example, the aliquot sequence of 10 is 10, 8, 7, 1, 0 because: :σ1(10) − 10 = 5 + 2 + 1 = 8 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leech Lattice
In mathematics, the Leech lattice is an even unimodular lattice Λ24 in 24-dimensional Euclidean space, which is one of the best models for the kissing number problem. It was discovered by . It may also have been discovered (but not published) by Ernst Witt in 1940. Characterization The Leech lattice Λ24 is the unique lattice in 24-dimensional Euclidean space, E24, with the following list of properties: *It is unimodular; i.e., it can be generated by the columns of a certain 24×24 matrix with determinant 1. *It is even; i.e., the square of the length of each vector in Λ24 is an even integer. *The length of every non-zero vector in Λ24 is at least 2. The last condition is equivalent to the condition that unit balls centered at the points of Λ24 do not overlap. Each is tangent to 196,560 neighbors, and this is known to be the largest number of non-overlapping 24-dimensional unit balls that can simultaneously touch a single unit ball. This arrangement of 196,560 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
275 (number)
270 (two hundred ndseventy) is the natural number following 269 and preceding 271. In mathematics *270 is a harmonic divisor number *270 is the fourth number that is divisible by its average integer divisor *270 is a practical number, by the second definition *The sum of the coprime counts for the first 29 integers is 270 *270 is a sparsely totient number, the largest integer with 72 as its totient *Given 6 elements, there are 270 square permutations *10! has 270 divisors *270 is a Harshad number in base 10 *270 is the smallest positive integer that has divisors ending by digits 1, 2, ..., 9. *270 is the smallest sum of a set of even numbers that contain every digit once. In other fields *The year 270 BC *The year 270 AD *The caliber of the .270 Winchester rifle *The number of U.S. Electoral College votes needed to be elected President of the United States *The average number of days in human pregnancy Integers from 271 to 279 271 272 272 = 24·17, sum of four consecutiv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Equiangular Lines
In geometry, a set of lines is called equiangular if all the lines intersect at a single point, and every pair of lines makes the same angle. Equiangular lines in Euclidean space Computing the maximum number of equiangular lines in ''n''-dimensional Euclidean space is a difficult problem, and unsolved in general, though bounds are known. The maximal number of equiangular lines in 2-dimensional Euclidean space is 3: we can take the lines through opposite vertices of a regular hexagon, each at an angle 120 degrees from the other two. The maximum in 3 dimensions is 6: we can take lines through opposite vertices of an icosahedron. It is known that the maximum number in any dimension n is less than or equal to \binom. This upper bound is tight up to a constant factor to a construction by de Caen. The maximum in dimensions 1 through 16 is listed in the ''On-Line Encyclopedia of Integer Sequences'' as follows: :1, 3, 6, 6, 10, 16, 28, 28, 28, 28, 28, 28, 28, 28, 36, 40, ... In particul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Centered Pentagonal Number
A centered pentagonal number is a centered figurate number that represents a pentagon with a dot in the center and all other dots surrounding the center in successive pentagonal layers. The centered pentagonal number for ''n'' is given by the formula :P_=, n\geq1 The first few centered pentagonal numbers are 1, 6, 16, 31, 51, 76, 106, 141, 181, 226, 276, 331, 391, 456, 526, 601 __NOTOC__ Year 601 ( DCI) was a common year starting on Sunday (link will display the full calendar) of the Julian calendar. The denomination 601 for this year has been used since the early medieval period, when the Anno Domini calendar era bec ..., 681, 766, 856, 951, 1051, 1156, 1266, 1381, 1501, 1626, 1756, 1891, 2031, 2176, 2326, 2481, 2641, 2806, 2976 . Properties *The parity of centered pentagonal numbers follows the pattern odd-even-even-odd, and in base 10 the units follow the pattern 1-6-6-1. *Centered pentagonal numbers follow the following Recurrence relations: :P_=P_+5n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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