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369 (number)
Three hundred sixty-nine is the natural number following three hundred sixty-eight and preceding three hundred seventy. In mathematics 369 is the magic constant of the ''9'' × ''9'' magic squareSequence A006003 in OEIS. and the ''n''-Queens Problem for ''n'' = 9. There are 369 free octominoes ( polyominoes of order 8).Sequence A000105 in OEIS. Other uses 369 is also: * The year 369 or 369 BC * A Singapore gang, also known as Salakau in Hokkien * "3-6-9", a song by Cupid featuring B.o.B from '' Time for a Change'' * "369", a song by Buzzcocks Buzzcocks are an English punk rock band formed in Bolton, England in 1976 by singer-songwriter-guitarist Pete Shelley and singer-songwriter Howard Devoto. They are regarded as a seminal influence on the Manchester music scene, the independen ... References {{reflist 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 suc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magic Constant
The magic constant or magic sum of a magic square is the sum of numbers in any row, column, or diagonal of the magic square. For example, the magic square shown below has a magic constant of 15. For a normal magic square of order ''n'' – that is, a magic square which contains the numbers 1, 2, ..., ''n''2 – the magic constant is M = n \cdot \frac. For normal magic squares of orders ''n'' = 3, 4, 5, 6, 7, and 8, the magic constants are, respectively: 15, 34, 65, 111, 175, and 260 (sequence A006003 in the OEIS). For example, a normal 8 × 8 square will always equate to 260 for each row, column, or diagonal. The normal magic constant of order n is (n^3+n)/2. The largest magic constant of normal magic square which is also a: * triangular number is 15 (solve the Diophantine equation x^2=y^3+16y+16, where y is divisible by 4); *square number is 1 (solve the Diophantine equation x^2=y^3+4y, where y is even); * generalized pentagonal number is 171535 (solve the Dioph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Magic Square
In recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same. The 'order' of the magic square is the number of integers along one side (''n''), and the constant sum is called the ' magic constant'. If the array includes just the positive integers 1,2,...,n^2, the magic square is said to be 'normal'. Some authors take magic square to mean normal magic square. Magic squares that include repeated entries do not fall under this definition and are referred to as 'trivial'. Some well-known examples, including the Sagrada Família magic square and the Parker square are trivial in this sense. When all the rows and columns but not both diagonals sum to the magic constant this gives a ''semimagic square (sometimes called orthomagic square). The mathematical study of magic squares typically deals with their construction, classification, and enumeration. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
A006003
A, or a, is the first letter and the first vowel of the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages and others worldwide. Its name in English is ''a'' (pronounced ), plural ''aes''. It is similar in shape to the Ancient Greek letter alpha, from which it derives. The uppercase version consists of the two slanting sides of a triangle, crossed in the middle by a horizontal bar. The lowercase version can be written in two forms: the double-storey a and single-storey ɑ. The latter is commonly used in handwriting and fonts based on it, especially fonts intended to be read by children, and is also found in italic type. In English grammar, " a", and its variant " an", are indefinite articles. History The earliest certain ancestor of "A" is aleph (also written 'aleph), the first letter of the Phoenician alphabet, which consisted entirely of consonants (for that reason, it is also called an abjad to distinguish it fro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
On-Line Encyclopedia Of Integer Sequences
The On-Line Encyclopedia of Integer Sequences (OEIS) is an online database of integer sequences. It was created and maintained by Neil Sloane while researching at AT&T Labs. He transferred the intellectual property and hosting of the OEIS to the OEIS Foundation in 2009. Sloane is chairman of the OEIS Foundation. OEIS records information on integer sequences of interest to both professional and amateur mathematicians, and is widely cited. , it contains over 350,000 sequences, making it the largest database of its kind. Each entry contains the leading terms of the sequence, keywords, mathematical motivations, literature links, and more, including the option to generate a graph or play a musical representation of the sequence. The database is searchable by keyword, by subsequence, or by any of 16 fields. History Neil Sloane started collecting integer sequences as a graduate student in 1965 to support his work in combinatorics. The database was at first stored on punche ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eight Queens Puzzle
The eight queens puzzle is the problem of placing eight chess queens on an 8×8 chessboard so that no two queens threaten each other; thus, a solution requires that no two queens share the same row, column, or diagonal. There are 92 solutions. The problem was first posed in the mid-19th century. In the modern era, it is often used as an example problem for various computer programming techniques. The eight queens puzzle is a special case of the more general ''n'' queens problem of placing ''n'' non-attacking queens on an ''n''×''n'' chessboard. Solutions exist for all natural numbers ''n'' with the exception of ''n'' = 2 and ''n'' = 3. Although the exact number of solutions is only known for ''n'' ≤ 27, the asymptotic growth rate of the number of solutions is (0.143 ''n'')''n''. History Chess composer Max Bezzel published the eight queens puzzle in 1848. Franz Nauck published the first solutions in 1850. W. W. Rouse Ball (1960) "The Eight Queens Problem", in ''Mathem ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Octomino
An octomino (or 8-omino) is a polyomino of order 8, that is, a polygon in the plane made of 8 equal-sized squares connected edge-to-edge. When rotations and reflections are not considered to be distinct shapes, there are 369 different ''free'' octominoes. When reflections are considered distinct, there are 704 ''one-sided'' octominoes. When rotations are also considered distinct, there are 2,725 ''fixed'' octominoes. Symmetry The figure shows all possible free octominoes, coloured according to their symmetry groups: * 316 octominoes (coloured grey) have no symmetry. Their symmetry group consists only of the identity mapping. * 23 octominoes (coloured red) have an axis of reflection symmetry aligned with the gridlines. Their symmetry group has two elements, the identity and the reflection in a line parallel to the sides of the squares. :: * 5 octominoes (coloured green) have an axis of reflection symmetry at 45° to the gridlines. Their symmetry group has two elements, the i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polyomino
A polyomino is a plane geometric figure formed by joining one or more equal squares edge to edge. It is a polyform whose cells are squares. It may be regarded as a finite subset of the regular square tiling. Polyominoes have been used in popular puzzles since at least 1907, and the enumeration of pentominoes is dated to antiquity. Many results with the pieces of 1 to 6 squares were first published in '' Fairy Chess Review'' between the years 1937 to 1957, under the name of "dissection problems." The name ''polyomino'' was invented by Solomon W. Golomb in 1953, and it was popularized by Martin Gardner in a November 1960 " Mathematical Games" column in ''Scientific American''. Related to polyominoes are polyiamonds, formed from equilateral triangles; polyhexes, formed from regular hexagons; and other plane polyforms. Polyominoes have been generalized to higher dimensions by joining cubes to form polycubes, or hypercubes to form polyhypercubes. In statistical physics, the s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
A000105
A, or a, is the first letter and the first vowel of the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages and others worldwide. Its name in English is ''a'' (pronounced ), plural ''aes''. It is similar in shape to the Ancient Greek letter alpha, from which it derives. The uppercase version consists of the two slanting sides of a triangle, crossed in the middle by a horizontal bar. The lowercase version can be written in two forms: the double-storey a and single-storey ɑ. The latter is commonly used in handwriting and fonts based on it, especially fonts intended to be read by children, and is also found in italic type. In English grammar, " a", and its variant " an", are indefinite articles. History The earliest certain ancestor of "A" is aleph (also written 'aleph), the first letter of the Phoenician alphabet, which consisted entirely of consonants (for that reason, it is also called an abjad to distinguish it fr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
369 BC
__NOTOC__ Year 369 BC was a year of the pre-Julian Roman calendar. At the time, it was known as the Year of the Tribunate of Fidenas, Cicurinus, Cossus, Cornelius, Cincinnatus and Ambustus (or, less frequently, year 385 ''Ab urbe condita''). The denomination 369 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 Greece * After driving off the Spartan army that has threatened Mantinea, Epaminondas of Thebes moves south and crosses the Evrotas River (the frontier of Sparta), which no hostile army has breached in historical memory. The Spartans, unwilling to engage the massive Theban army in battle, remain inside their city while the Thebans and their allies ravage Laconia. * Epaminondas briefly returns to Arcadia, then marches south to Messenia, a territory which the Spartans had conquered some 200 years before. There, Epaminondas starts the rebuilding o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Singapore
Singapore (), officially the Republic of Singapore, is a sovereign island country and city-state in maritime Southeast Asia. It lies about one degree of latitude () north of the equator, off the southern tip of the Malay Peninsula, bordering the Strait of Malacca to the west, the Singapore Strait to the south, the South China Sea to the east, and the Straits of Johor to the north. The country's territory is composed of one Singapore Island, main island, List of islands of Singapore, 63 satellite islands and islets, and Pedra Branca, Singapore, one outlying islet; the combined area of these has increased by 25% since the country's independence as a result of extensive land reclamation projects. It has the List of countries and dependencies by population density, third highest population density in the world. With a multicultural population and recognising the need to respect cultural identities of the major ethnic groups within the nation, Singapore has four Languages ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Salakau
Salakau ( zh, s=三六九, poj=Saⁿ-la̍k-káu), which means 369 in Hokkien, also known as "Sah Lak Kau", is a street gang or secret society based in Singapore. The numbers 3, 6 and 9 add up to 18, which was the name of an older gang; the number signified the 18 arhats (principal disciples) of Shaolin Monastery. As one of the oldest and most prominent gangs in the country, they are known to take part in many illicit activities such as narcotics, extortion, prostitution and white-collar crime — and many of their members have been in and out of prison for violent attacks and rioting. They have a renowned gang chant sung in Hokkien that's usually accompanied by techno beats. It was reproduced for Royston Tan's teenage gangster flick '' 15'', albeit with direct references to the gang edited out.Ooi Boon, Tan (18 May 1993). "The name game : from sports teams and rock bands to secret societies". ''Straits Times'' History In the early 1970s till late 1980s, Salakau attacked riv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
