|
15 Schoolgirl Problem
Kirkman's schoolgirl problem is a problem in combinatorics proposed by Rev. 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 numbe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorics
Combinatorics is an area of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many applications ranging from logic to statistical physics and from evolutionary biology to computer science. Combinatorics is well known for the breadth of the problems it tackles. Combinatorial problems arise in many areas of pure mathematics, notably in algebra, probability theory, topology, and geometry, as well as in its many application areas. Many combinatorial questions have historically been considered in isolation, giving an ''ad hoc'' solution to a problem arising in some mathematical context. In the later twentieth century, however, powerful and general theoretical methods were developed, making combinatorics into an independent branch of mathematics in its own right. One of the oldest and most accessible parts of combinatorics is gra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
RHF Denniston
RHF may refer to: * Regional health authority (Norway), Regional health authority or ''Regionalt helseforetak'', of Norway * Ice Hockey Federation of Russia (Russian Hockey Federation) * Residence Hall Federation at Virginia Tech campus#Residence Hall Federation, Virginia Tech campus * Royal Highland Fusiliers * Right heart failure#Right-sided failure, Right heart failure or Right-sided heart failure * RHF Productions, owners of brand Red Hot TV (UK) * Rhythm Heaven Fever See also * * * RHFS (other) {{disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lu Jiaxi (mathematician)
Lu Jiaxi (; June 10, 1935 – October 31, 1983) was a self-taught Chinese mathematician who made important contributions in combinatorial design theory. He was a high school physics teacher in a remote city and worked in his spare time on the problem of large sets of disjoint Steiner triple systems. Biography Background Lu Jiaxi was born in a poor family in Shanghai. His father was a seller of soy sauce concentrate. His parents had four children, but the three older children all died early from illness, and Lu Jiaxi was the only surviving child. When he was in junior middle school, his father died from an illness that the family could not afford to treat, so he started working after finishing junior middle school in 1949 to earn a living. He served an apprenticeship at an automobile hardware firm in Shanghai. In October 1951, he was admitted to a statistics training course in Shenyang offered by the administration for electrical equipment industry of Northeast China, and he fi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Henry Seely White
Henry Seely White (May 20, 1861 – May 20, 1943) was an Americans, American mathematician. He was born in Cazenovia, New York to parents Aaron White and Isadore Maria Haight. He matriculated at Wesleyan University in Connecticut and graduated with honors in 1882 at the age of twenty-one. White excelled at Wesleyan in astronomy, ethics, Latin, logic, mathematics, and philosophy. At the university, John Monroe Van Vleck taught White mathematics and astronomy. Later, Van Vleck persuaded White to continue to study mathematics at the graduate level. Subsequently, White studied at the University of Göttingen under Felix Klein, Klein, and received his doctorate in 1891. White was Mathematics Department Chair at Northwestern University. He left Northwestern to be near his ill mother and became Chairman of the Mathematics Department at Vassar College. He "attributed his interest in geometry both to his work at Wesleyan and Goettingen and to summers spent working on his grandfather's fa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Henry Dudeney
Henry Ernest Dudeney (10 April 1857 – 23 April 1930) was an English author and mathematician who specialised in logic puzzles and mathematical games. He is known as one of the country's foremost creators of mathematical puzzles. Early life Dudeney was born in the village of Mayfield, East Sussex, England, one of six children of Gilbert and Lucy Dudeney. His grandfather, John Dudeney, was well known as a self-taught mathematician and shepherd; his initiative was much admired by his grandson. Dudeney learned to play chess at an early age, and continued to play frequently throughout his life. This led to a marked interest in mathematics and the composition of puzzles. Chess problems in particular fascinated him during his early years. Career Although Dudeney spent his career in the Civil Service, he continued to devise various problems and puzzles. Dudeney's first puzzle contributions were submissions to newspapers and magazines, often under the pseudonym of "Sphinx." Much of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wilhelm Ahrens
Wilhelm Ahrens (3 March 1872 – 23 May 1927) was a German mathematician and writer on recreational mathematics. Biography Ahrens was born in Lübz at the Elde in Mecklenburg and studied from 1890 to 1897 at the University of Rostock, Humboldt University of Berlin, and the University of Freiburg. In 1895 at the University of Rostock he received his Promotion (Ph.D.), ''summa cum laude'', under the supervision of Otto Staude with dissertation entitled ''Über eine Gattung n-fach periodischer Functionen von n reellen Veränderlichen''. From 1895 to 1896 he taught at the German school in Antwerp and then studied another semester under Sophus Lie in Leipzig. In 1897 Ahrens was a teacher in Magdeburg at the Baugewerkeschule, from 1901 at the engineering school. Inspired by Sophus Lie, he wrote "On transformation groups, all of whose subgroups are invariant" (''Hamburger Math Society'' Vol 4, 1902). He worked a lot on the history of mathematics and mathematical games (recreational mat ... [...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 Ca ... [...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 t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polyhedra
In geometry, a polyhedron (plural polyhedra or polyhedrons; ) is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices. A convex polyhedron is the convex hull of finitely many points, not all on the same plane. Cubes and pyramids are examples of convex polyhedra. A polyhedron is a 3-dimensional example of a polytope, a more general concept in any number of dimensions. Definition Convex polyhedra are well-defined, with several equivalent standard definitions. However, the formal mathematical definition of polyhedra that are not required to be convex has been problematic. Many definitions of "polyhedron" have been given within particular contexts,. some more rigorous than others, and there is not universal agreement over which of these to choose. Some of these definitions exclude shapes that have often been counted as polyhedra (such as the self-crossing polyhedra) or include shapes that are often not considered as valid polyhed ... [...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 ce ... [...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 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 U.S. Coast Survey from 1867 to 1874. In 1842, he was elected as a member of the American Philosophical Society. He was elected a Foreig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plagiarism
Plagiarism is the fraudulent representation of another person's language, thoughts, ideas, or expressions as one's own original work.From the 1995 '' 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. While precise definitions vary, depending on the institution, such representations are generally considered to violate academic integrity and journalistic ethics as well as social norms of learning, teaching, research, fairness, respect and responsibility in many cultures. It is subject to sanctions such as penalties, suspension, expulsion from school or work, substantial fines and even imprisonment. Plagiarism is typically not in itself a crime, but like counterfeiting, fraud can be punished in a court f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
