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Kirkman's Schoolgirl Problem
Kirkman's schoolgirl problem is a problem in combinatorics proposed by Thomas Penyngton Kirkman in 1850 as Query VI in '' The Lady's and Gentleman's Diary'' (pg.48). The problem states: Fifteen young ladies in a school walk out three abreast for seven days in succession: it is required to arrange them daily so that no two shall walk twice abreast. Solutions A solution to this problem is an example of a ''Kirkman triple system'', which is a Steiner triple system having a ''parallelism'', that is, a partition of the blocks of the triple system into parallel classes which are themselves partitions of the points into disjoint blocks. Such Steiner systems that have a parallelism are also called ''resolvable''. There are exactly seven non-isomorphic solutions to the schoolgirl problem, as originally listed by Frank Nelson Cole in ''Kirkman Parades'' in 1922. The seven solutions are summarized in the table below, denoting the 15 girls with the letters A to O. From the number o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kirkman Schoolgirl Problem
Kirkman's schoolgirl problem is a problem in combinatorics proposed by Thomas Penyngton Kirkman in 1850 as Query VI in ''The Lady's and Gentleman's Diary'' (pg.48). The problem states: Fifteen young ladies in a school walk out three abreast for seven days in succession: it is required to arrange them daily so that no two shall walk twice abreast. Solutions A solution to this problem is an example of a ''Kirkman triple system'', which is a Steiner triple system having a ''parallelism'', that is, a partition of the blocks of the triple system into parallel classes which are themselves partitions of the points into disjoint blocks. Such Steiner systems that have a parallelism are also called ''resolvable''. There are exactly seven non-isomorphic solutions to the schoolgirl problem, as originally listed by Frank Nelson Cole in ''Kirkman Parades'' in 1922. The seven solutions are summarized in the table below, denoting the 15 girls with the letters A to O. From the number of a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Proof
A mathematical proof is a deductive reasoning, deductive Argument-deduction-proof distinctions, argument for a Proposition, mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems; but every proof can, in principle, be constructed using only certain basic or original assumptions known as axioms, along with the accepted rules of inference. Proofs are examples of exhaustive deductive reasoning that establish logical certainty, to be distinguished from empirical evidence, empirical arguments or non-exhaustive inductive reasoning that establish "reasonable expectation". Presenting many cases in which the statement holds is not enough for a proof, which must demonstrate that the statement is true in ''all'' possible cases. A proposition that has not been proved but is believed to be true is known as a conjecture, or a hypothesis if frequently used as an assumption for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rouse Ball
Walter William Rouse Ball (14 August 1850 – 4 April 1925), known as W. W. Rouse Ball, was a British mathematician, lawyer, and fellow at Trinity College, Cambridge, from 1878 to 1905. He was also a keen amateur magician, and the founding president of the Cambridge Pentacle Club in 1919, one of the world's oldest magic societies. Life Born 14 August 1850 in Hampstead, London, Ball was the son and heir of Walter Frederick Ball, of 3, St John's Park Villas, South Hampstead, London. Educated at University College School, he entered Trinity College, Cambridge, in 1870, became a scholar and first Smith's Prizeman, and gained his BA in 1874 as second Wrangler. He became a Fellow of Trinity in 1875, and remained one for the rest of his life. He died on 4 April 1925 in Elmside, Cambridge, and is buried at the Parish of the Ascension Burial Ground in Cambridge. He is commemorated in the naming of the small pavilion, now used as changing rooms and toilets, on Jesus Green in Cam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Édouard Lucas
__NOTOC__ François Édouard Anatole Lucas (; 4 April 1842 – 3 October 1891) was a French mathematician. Lucas is known for his study of the Fibonacci sequence. The related Lucas sequences and Lucas numbers are named after him. Biography Lucas was born in Amiens and educated at the École Normale Supérieure. He worked in the Paris Observatory and later became a professor of mathematics at the Lycée Saint Louis and the Lycée Charlemagne in Paris. Lucas served as an artillery officer in the French Army during the Franco-Prussian War of 1870–1871. In 1875, Lucas posed a challenge to prove that the only solution of the Diophantine equation :\sum_^ n^2 = M^2\; with ''N'' > 1 is when ''N'' = 24 and ''M'' = 70. This is known as the cannonball problem, since it can be visualized as the problem of taking a square arrangement of cannonballs on the ground and building a square pyramid out of them. It was not until 1918 that a proof (using elliptic functions) was found for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polyhedra
In geometry, a polyhedron (: polyhedra or polyhedrons; ) is a three-dimensional figure with flat polygonal faces, straight edges and sharp corners or vertices. The term "polyhedron" may refer either to a solid figure or to its boundary surface. The terms solid polyhedron and polyhedral surface are commonly used to distinguish the two concepts. Also, the term ''polyhedron'' is often used to refer implicitly to the whole structure formed by a solid polyhedron, its polyhedral surface, its faces, its edges, and its vertices. There are many definitions of polyhedron. Nevertheless, the polyhedron is typically understood as a generalization of a two-dimensional polygon and a three-dimensional specialization of a polytope, a more general concept in any number of dimensions. Polyhedra have several general characteristics that include the number of faces, topological classification by Euler characteristic, duality, vertex figures, surface area, volume, interior lines, Dehn invari ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Group Theory
In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field (mathematics), fields, and vector spaces, can all be seen as groups endowed with additional operation (mathematics), operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right. Various physical systems, such as crystals and the hydrogen atom, and Standard Model, three of the four known fundamental forces in the universe, may be modelled by symmetry groups. Thus group theory and the closely related representation theory have many important applications in physics, chemistry, and materials science. Group theory is also cen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Benjamin Peirce
Benjamin Peirce (; April 4, 1809 – October 6, 1880) was an American mathematician who taught at Harvard University for approximately 50 years. He made contributions to celestial mechanics, statistics, number theory, algebra, and the philosophy of mathematics. Early life He was born in Salem, Massachusetts, the son of first cousins Benjamin Peirce (1778–1831), later librarian of Harvard, and Lydia Ropes Nichols Peirce (1781–1868). After graduating from Harvard University in 1829, he taught mathematics for two years at the Round Hill School in Northampton, and in 1831 was appointed professor of mathematics at Harvard. He added astronomy to his portfolio in 1842, and remained as Harvard professor until his death. In addition, he was instrumental in the development of Harvard's science curriculum, served as the college librarian, and was director of the United States Coast Survey from 1867 to 1874. In 1842, he was elected as a member of the American Philosophical Society ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plagiarism
Plagiarism is the representation of another person's language, thoughts, ideas, or expressions as one's own original work.From the 1995 ''Random House Dictionary of the English Language, Random House Compact Unabridged Dictionary'': use or close imitation of the language and thoughts of another author and the representation of them as one's own original work qtd. in From the Oxford English Dictionary: The action or practice of taking someone else's work, idea, etc., and passing it off as one's own; literary theft. Although precise definitions vary depending on the institution, in many countries and cultures plagiarism is considered a violation of academic integrity and journalistic ethics, as well as of social norms around learning, teaching, research, fairness, respect, and responsibility. As such, a person or Legal Entity, entity that is determined to have committed plagiarism is often subject to various punishments or sanctions, such as Suspension (punishment), suspension, Expul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Michel Reiss
Michel Reiss (23 July 1805 in Frankfurt – 27 January 1869 in Frankfurt) was a German mathematician who introduced the Reiss relation. References * Biography in Allgemeine Deutsche Biographie (ADB; ) is one of the most important and comprehensive biographical reference works in the German language. It was published by the Historical Commission of the Bavarian Academy of Sciences between 1875 and 1912 in 56 volumes, printed in Lei ... ( Wikisource copy) 1805 births 1869 deaths 19th-century German mathematicians {{Germany-mathematician-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jakob Steiner
Jakob Steiner (18 March 1796 – 1 April 1863) was a Swiss mathematician who worked primarily in geometry. Life Steiner was born in the village of Utzenstorf, Canton of Bern. At 18, he became a pupil of Heinrich Pestalozzi and afterwards studied at Heidelberg. Then, he went to Berlin, earning a livelihood there, as in Heidelberg, by tutoring. Here he became acquainted with A. L. Crelle, who, encouraged by his ability and by that of Niels Henrik Abel, then also staying at Berlin, founded his famous '' Journal'' (1826). After Steiner's publication (1832) of his ''Systematische Entwickelungen'' he received, through Carl Gustav Jacob Jacobi, who was then professor at Königsberg University, and earned an honorary degree there; and through the influence of Jacobi and of the brothers Alexander and Wilhelm von Humboldt a new chair of geometry was founded for him at Berlin (1834). This he occupied until his death in Bern on 1 April 1863. He was described by Thomas Hirst as follo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pasch Configuration
In mathematics, specifically in incidence geometry and especially in projective geometry, a complete quadrangle is a system of geometric objects consisting of any four Point (geometry), points in a Plane (geometry), plane, no three of which are Collinearity, on a common line, and of the six Line (geometry), lines connecting the six pairs of points. Duality (projective geometry), Dually, a ''complete quadrilateral'' is a system of four lines, no three of which pass through the same point, and the six points of Line–line intersection, intersection of these lines. The complete quadrangle was called a tetrastigm by , and the complete quadrilateral was called a tetragram; those terms are occasionally still used. The complete quadrilateral has also been called a Pasch configuration, especially in the context of Steiner triple systems. Diagonals The six lines of a complete quadrangle meet in pairs to form three additional points called the ''diagonal points'' of the quadrangle. Si ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert Richard Anstice
Robert Richard Anstice (1813–1853) was an English clergyman and mathematician who wrote two remarkable papers on combinatorics, published the same year he died in the Cambridge and Dublin Mathematical Journal. He pioneered the use of primitive roots in this field, anticipating the work of Eugen Netto on Steiner's triplets. Anstice studied at Christ Church, Oxford, where he graduated in 1835, receiving a Master's in 1837. Nothing is known about his life in the next ten years. In 1846, he was ordained priest, and in the following year he became rector of Wigginton, Hertfordshire Wigginton (''Wigentone'' - 1086) is a large village and civil parish running north–south and perched at on the edge of the Chiltern Hills and aside the border with Buckinghamshire. It is part of Dacorum district in the county of Hertfordsh ...., MacTutor History of Mathematics. He died there in 1853 References Bibliography * * * External links * {{DEFAULTSORT:Anstice, Robert ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
