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Most-perfect Magic Square
A most-perfect magic square of order ''n'' is a magic square containing the numbers 1 to ''n''2 with two additional properties: # Each 2 × 2 subsquare sums to 2''s'', where ''s'' = ''n''2 + 1. # All pairs of integers distant ''n''/2 along a (major) diagonal sum to ''s''. __TOC__ Examples Two 12 × 12 most-perfect magic squares can be obtained adding 1 to each element of: 1 2 3 4 5 6 7 8 9 10 11 12'' ,'' 64 92 81 94 48 77 67 63 50 61 83 78 ,'' 31 99 14 97 47 114 28 128 45 130 12 113 ,'' 24 132 41 134 8 117 27 103 10 101 43 118 ,'' 23 107 6 105 39 122 20 136 37 138 4 121 ,'' 16 140 33 142 0 125 19 111 2 109 35 126 ,'' 75 55 58 53 91 70 72 84 89 86 56 69 ,'' 76 80 93 82 60 65 79 51 62 49 95 66 ,'' 115 15 98 13 131 30 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Fifteen or 15 may refer to: *15 (number), the natural number following 14 and preceding 16 *one of the years 15 BC, AD 15, 1915, 2015 Music *Fifteen (band), a punk rock band Albums * 15 (Buckcherry album), ''15'' (Buckcherry album), 2005 * 15 (Ani Lorak album), ''15'' (Ani Lorak album), 2007 * 15 (Phatfish album), ''15'' (Phatfish album), 2008 * 15 (mixtape), ''15'' (mixtape), a 2018 mixtape by Bhad Bhabie * Fifteen (Green River Ordinance album), ''Fifteen'' (Green River Ordinance album), 2016 * Fifteen (The Wailin' Jennys album), ''Fifteen'' (The Wailin' Jennys album), 2017 * ''Fifteen'', a 2012 album by Colin James Songs *Fifteen (song), "Fifteen" (song), a 2008 song by Taylor Swift *"Fifteen", a song by Harry Belafonte from the album ''Love Is a Gentle Thing'' *"15", a song by Rilo Kiley from the album ''Under the Blacklight'' *"15", a song by Marilyn Manson from the album ''The High End of Low'' *"The 15th", a 1979 song by Wire Other uses *Fifteen, Ohio, a community in th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transcription (linguistics)
Transcription in the linguistic sense is the systematic representation of spoken language in written form. The source can either be utterances (''speech'' or ''sign language'') or preexisting text in another writing system. Transcription should not be confused with translation, which means representing the meaning of text from a source-language in a target language, (e.g. ''Los Angeles'' (from source-language Spanish) means ''The Angels'' in the target language English); or with transliteration, which means representing the spelling of a text from one script to another. In the academic discipline of linguistics, transcription is an essential part of the methodologies of (among others) phonetics, conversation analysis, dialectology, and sociolinguistics. It also plays an important role for several subfields of speech technology. Common examples for transcriptions outside academia are the proceedings of a court hearing such as a criminal trial (by a court reporter) or a physicia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Indian Numerals
Indian or Indians may refer to: Peoples South Asia * Indian people, people of Indian nationality, or people who have an Indian ancestor ** Non-resident Indian, a citizen of India who has temporarily emigrated to another country * South Asian ethnic groups, referring to people of the Indian subcontinent, as well as the greater South Asia region prior to the 1947 partition of India * Anglo-Indians, people with mixed Indian and British ancestry, or people of British descent born or living in the Indian subcontinent * East Indians, a Christian community in India Europe * British Indians, British people of Indian origin The Americas * Indo-Canadians, Canadian people of Indian origin * Indian Americans, American people of Indian origin * Indigenous peoples of the Americas, the pre-Columbian inhabitants of the Americas and their descendants ** Plains Indians, the common name for the Native Americans who lived on the Great Plains of North America ** Native Americans in the U ... [...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. A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Panmagic Square
A pandiagonal magic square or panmagic square (also diabolic square, diabolical square or diabolical magic square) is a magic square with the additional property that the broken diagonals, i.e. the diagonals that wrap round at the edges of the square, also add up to the magic constant. A pandiagonal magic square remains pandiagonally magic not only under rotation or reflection, but also if a row or column is moved from one side of the square to the opposite side. As such, an n \times n pandiagonal magic square can be regarded as having 8n^2 orientations. 3×3 pandiagonal magic squares It can be shown that non-trivial pandiagonal magic squares of order 3 do not exist. Suppose the square :\begin \hline \!\!\!\; a_ \!\!\! & \!\! a_\!\!\!\!\; & \!\! a_ \!\!\\ \hline \!\!\!\; a_ \!\!\! & \!\! a_\!\!\!\!\; & \!\! a_ \!\!\\ \hline \!\!\!\; a_ \!\!\! & \!\! a_\!\!\!\!\; & \!\! a_ \!\!\\ \hline \end is pandiagonally magic with magic constant . Adding sums and results in . Subtracting ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kathleen Ollerenshaw
Dame Kathleen Mary Ollerenshaw, (''née'' Timpson; 1 October 1912 – 10 August 2014) was a British mathematician and politician who was Lord Mayor of Manchester from 1975 to 1976 and an advisor on educational matters to Margaret Thatcher's government in the 1980s. Early life and education She was born Kathleen Mary Timpson in Withington, Manchester, where she attended Lady Barn House School (1918–26). She was a grandchild of the founder of the Timpson shoe repair business, who had moved to Manchester from Kettering and established the business there by 1870. She became fascinated with mathematics, inspired by the Lady Barn headmistress, Miss Jenkin Jones. While at Lady Barn, she met her future husband, Robert Ollerenshaw. Ollerenshaw became completely deaf at age eight and was taught to lip read. She gravitated toward the study of mathematics as it is not dependent on hearing. She was further inspired by a headmistress at Lady Barn House School who studied mathematics a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
David S
David (; , "beloved one") (traditional spelling), , ''Dāwūd''; grc-koi, Δαυΐδ, Dauíd; la, Davidus, David; gez , ዳዊት, ''Dawit''; xcl, Դաւիթ, ''Dawitʿ''; cu, Давíдъ, ''Davidŭ''; possibly meaning "beloved one". was, according to the Hebrew Bible, the third king of the United Kingdom of Israel. In the Books of Samuel, he is described as a young shepherd and harpist who gains fame by slaying Goliath, a champion of the Philistines, in southern Canaan. David becomes a favourite of Saul, the first king of Israel; he also forges a notably close friendship with Jonathan, a son of Saul. However, under the paranoia that David is seeking to usurp the throne, Saul attempts to kill David, forcing the latter to go into hiding and effectively operate as a fugitive for several years. After Saul and Jonathan are both killed in battle against the Philistines, a 30-year-old David is anointed king over all of Israel and Judah. Following his rise to power, David ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bijection
In mathematics, a bijection, also known as a bijective function, one-to-one correspondence, or invertible function, is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set. There are no unpaired elements. In mathematical terms, a bijective function is a one-to-one (injective) and onto (surjective) mapping of a set ''X'' to a set ''Y''. The term ''one-to-one correspondence'' must not be confused with ''one-to-one function'' (an injective function; see figures). A bijection from the set ''X'' to the set ''Y'' has an inverse function from ''Y'' to ''X''. If ''X'' and ''Y'' are finite sets, then the existence of a bijection means they have the same number of elements. For infinite sets, the picture is more complicated, leading to the concept of cardinal number—a way to distinguish the various sizes of infinite sets. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reversible Square
Reversibility can refer to: * Time reversibility, a property of some mathematical or physical processes and systems for which time-reversed dynamics are well defined :* Reversible diffusion, an example of a reversible stochastic process * Reversible process (thermodynamics), a process or cycle such that the net change at each stage in the combined entropy of the system and its surroundings is zero * Reversible reaction, a chemical reaction for which the position of the chemical equilibrium is very sensitive to the imposed physical conditions; so the reaction can be made to run either forwards or in reverse by changing those conditions * Reversible computing, logical reversibility of a computation; a computational step for which a well-defined inverse exists * Reversible error, a legal mistake invalidating a trial * Reversible garment, a garment that can be worn two ways * Piaget's theory of cognitive development Piaget's theory of cognitive development is a comprehensive theory ab ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frénicle Standard Form
A magic square is in the Frénicle standard form, named for Bernard Frénicle de Bessy, if the following two conditions hold: # the element at position ,1(top left corner) is the smallest of the four corner elements; and # the element at position ,2(top edge, second from left) is smaller than the element in ,1 In 1693, Frénicle described all the 880 essentially different order-4 magic squares. Properties This standard form was devised since a magic square remains "essentially similar" if it is rotated or transposed, or flipped so that the order of rows is reversed. There exist 8 different magic squares sharing one standard form. For example, the following magic squares are all essentially similar, with only the final square being in the Frénicle standard form: 8 1 6 8 3 4 4 9 2 4 3 8 6 7 2 6 1 8 2 9 4 2 7 6 3 5 7 1 5 9 3 5 7 9 5 1 1 5 9 7 5 3 7 5 3 9 5 1 4 9 2 6 7 2 8 1 6 2 7 6 8 3 4 2 9 4 6 1 8 4 3 8 Generali ... [...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 punched cards ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
