|
Rule Of 3 (mathematics)
In mathematics, specifically in elementary arithmetic and elementary algebra, given an equation between two fractions or rational expressions, one can cross-multiply to simplify the equation or determine the value of a variable. The method is also occasionally known as the "cross your heart" method because lines resembling a heart outline can be drawn to remember which things to multiply together. Given an equation like : \frac a b = \frac c d, where and are not zero, one can cross-multiply to get : ad = bc \quad \text \quad a = \fracd. In Euclidean geometry the same calculation can be achieved by considering the ratios as those of similar triangles. Procedure In practice, the method of cross-multiplying means that we multiply the numerator of each (or one) side by the denominator of the other side, effectively crossing the terms over: : \frac a b \nwarrow \frac c d, \quad \frac a b \nearrow \frac c d. The mathematical justification for the method is from the followin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), Mathematical analysis, analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of mathematical object, abstract objects that consist of either abstraction (mathematics), abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to proof (mathematics), prove properties of objects, a ''proof'' consisting of a succession of applications of in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Charles Darwin
Charles Robert Darwin ( ; 12 February 1809 – 19 April 1882) was an English Natural history#Before 1900, naturalist, geologist, and biologist, widely known for his contributions to evolutionary biology. His proposition that all species of life have descended from a Common descent, common ancestor is now generally accepted and considered a fundamental scientific concept. In a joint presentation with Alfred Russel Wallace, he introduced his scientific theory that this Phylogenetics, branching pattern of evolution resulted from a process he called natural selection, in which the struggle for existence has a similar effect to the artificial selection involved in selective breeding.. Darwin has been described as one of the most influential figures in human history and was honoured by Burials and memorials in Westminster Abbey, burial in Westminster Abbey. Darwin's early interest in nature led him to neglect his medical education at the University of Edinburgh Medical Schoo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unitary Method
In elementary algebra, the unitary method is a problem-solving technique taught to students as a method for solving word problems involving proportionality and units of measurement. It consists of first finding the value or proportional amount of a single unit, from the information given in the problem, and then multiplying the result by the number of units of the same kind, given in the problem, to obtain the result. As a simple example, to solve the problem: "A man walks 7 miles in 2 hours. How far does he walk in 7 hours?", one could first calculate how far the man walks in a single hour, as the ratio of the first two givens. 7 miles divided by 2 hours is 3 miles per hour. Then, multiplying by the third given, 7 hours, gives the answer as 24 miles. The same method can also be used as a step in more complicated problems, such as those involving the division of a good into different proportions. When used in this way, the value of a single unit, found in the unitary method, ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Turn (angle)
The turn (symbol tr or pla) is a unit of plane angle measurement that is the measure of a complete angle—the angle subtended by a complete circle at its center. One turn is equal to radians, 360 degrees or 400 gradians. As an angular unit, one turn also corresponds to one cycle (symbol cyc or c) or to one revolution (symbol rev or r). Common related units of frequency are '' cycles per second'' (cps) and '' revolutions per minute'' (rpm). The angular unit of the turn is useful in connection with, among other things, electromagnetic coils (e.g., transformers), rotating objects, and the winding number of curves. Divisions of a turn include the half-turn and quarter-turn, spanning a straight angle and a right angle, respectively; metric prefixes can also be used as in, e.g., centiturns (ctr), milliturns (mtr), etc. In the ISQ, an arbitrary "number of turns" (also known as "number of revolutions" or "number of cycles") is formalized as a dimensionless ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trairāśika
Trairāśika is the Sanskrit term used by Indian astronomers and mathematicians of the pre-modern era to denote what is known as the " rule of three" in elementary mathematics and algebra. In the contemporary mathematical literature, the term "rule of three" refers to the principle of cross-multiplication which states that if \tfrac=\tfrac then ad=bc or a=\tfrac. The antiquity of the term ''trairāśika'' is attested by its presence in the Bakhshali manuscript, a document believed to have been composed in the early centuries of the Common Era. The ''trairāśika'' rule Basically ''trairāśika'' is a rule which helps to solve the following problem: :"If p produces h what would i produce?" Here p is referred to as ''pramāṇa'' ("argument"), h as ''phala'' ("fruit") and i as ''ichcā'' ("requisition"). The ''pramāṇa'' and ''icchā'' must be of the same denomination, that is, of the same kind or type like weights, money, time, or numbers of the same objects. ''Phala'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Odds Ratio
An odds ratio (OR) is a statistic that quantifies the strength of the association between two events, A and B. The odds ratio is defined as the ratio of the odds of event A taking place in the presence of B, and the odds of A in the absence of B. Due to symmetry, odds ratio reciprocally calculates the ratio of the odds of B occurring in the presence of A, and the odds of B in the absence of A. Two events are independent if and only if the OR equals 1, i.e., the odds of one event are the same in either the presence or absence of the other event. If the OR is greater than 1, then A and B are associated (correlated) in the sense that, compared to the absence of B, the presence of B raises the odds of A, and symmetrically the presence of A raises the odds of B. Conversely, if the OR is less than 1, then A and B are negatively correlated, and the presence of one event reduces the odds of the other event occurring. Note that the odds ratio is symmetric in the two events, and no causa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cross-ratio
In geometry, the cross-ratio, also called the double ratio and anharmonic ratio, is a number associated with a list of four collinear points, particularly points on a projective line. Given four points , , , on a line, their cross ratio is defined as : (A,B;C,D) = \frac where an orientation of the line determines the sign of each distance and the distance is measured as projected into Euclidean space. (If one of the four points is the line's point at infinity, then the two distances involving that point are dropped from the formula.) The point is the harmonic conjugate of with respect to and precisely if the cross-ratio of the quadruple is , called the ''harmonic ratio''. The cross-ratio can therefore be regarded as measuring the quadruple's deviation from this ratio; hence the name ''anharmonic ratio''. The cross-ratio is preserved by linear fractional transformations. It is essentially the only projective invariant of a quadruple of collinear points; this underlies ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sylvie And Bruno
''Sylvie and Bruno'', first published in 1889, and its second volume ''Sylvie and Bruno Concluded'' published in 1893, form the last novel by Lewis Carroll published during his lifetime. Both volumes were illustrated by Harry Furniss. The novel has two main plots: one set in the real world at the time the book was published (the Victorian era), the other in the fantasy world of Fairyland. While the latter plot is a fairy tale with many nonsense elements and poems, similar to Carroll's ''Alice'' books, the story set in Victorian Britain is a social novel, with its characters discussing various concepts and aspects of religion, society, philosophy and morality. Origin Two short pieces, "Fairy Sylvie" and "Bruno's Revenge", originally appeared in '' Aunt Judy's Magazine'' in 1867. Some years later, in 1873 or 1874, Carroll had the idea to use these as the core for a longer story. Much of the rest of the novel he compiled from notes of ideas and dialogue which he had collected over ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Mad Gardener's Song
"The Mad Gardener's Song" is a poem by Lewis Carroll that appears in his two linked novels: ''Sylvie and Bruno'' and Sylvie and Bruno Concluded, ''Sylvie and Bruno Concluded'' (published in 1889 and 1893 respectively). "And what a wild being it was who sang these wild words! A Gardener he seemed to be—yet surely a mad one, by the way he brandished his rake—madder, by the way he broke, ever and anon, into a frantic jig—maddest of all, by the shriek in which he brought out the last words of the stanza!" (''Sylvie and Bruno'', Chapter V). Structure The poem consists of nine stanzas, each of six lines. Each stanza contains alternating lines in iambic tetrameter and iambic trimeter, and the three trimetric lines rhyme with each other. The verses are scattered throughout the novels, eight verses in ''Sylvie and Bruno'' and one in ''Sylvie and Bruno Concluded'', as follows: From ''Sylvie and Bruno:'' Verse 1—Chapter V. A Beggar's Palace. Verse 2—Chapter VI. The Magic Lo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lewis Carroll
Charles Lutwidge Dodgson (27 January 1832 – 14 January 1898), better known by his pen name Lewis Carroll, was an English author, poet, mathematician, photographer and reluctant Anglicanism, Anglican deacon. His most notable works are ''Alice's Adventures in Wonderland'' (1865) and its sequel ''Through the Looking-Glass'' (1871). He was noted for his facility with word play, logic, and fantasy. His poems ''Jabberwocky'' (1871) and ''The Hunting of the Snark'' (1876) are classified in the genre of literary nonsense. Some of Alice's nonsensical wonderland logic reflects his published work on mathematical logic. Carroll came from a family of high-church Anglicanism, Anglicans, and pursued his clerical training at Christ Church, Oxford, where he lived for most of his life as a scholar, teacher and (necessarily for his academic fellowship at the time) Anglican deacon. Alice Liddell – a daughter of Henry Liddell, the Dean of Christ Church, Oxford, Dean of Christ Church – is wide ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Biometrika
''Biometrika'' is a peer-reviewed scientific journal published by Oxford University Press for the Biometrika Trust. The editor-in-chief is Paul Fearnhead (Lancaster University). The principal focus of this journal is theoretical statistics. It was established in 1901 and originally appeared quarterly. It changed to three issues per year in 1977 but returned to quarterly publication in 1992. History ''Biometrika'' was established in 1901 by Francis Galton, Karl Pearson, and Raphael Weldon to promote the study of biometrics. The history of ''Biometrika'' is covered by Cox (2001). The name of the journal was chosen by Pearson, but Francis Edgeworth insisted that it be spelt with a "k" and not a "c". Since the 1930s, it has been a journal for statistical theory and methodology. Galton's role in the journal was essentially that of a patron and the journal was run by Pearson and Weldon and after Weldon's death in 1906 by Pearson alone until he died in 1936. In the early days, the Ameri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Karl Pearson
Karl Pearson (; born Carl Pearson; 27 March 1857 – 27 April 1936) was an English biostatistician and mathematician. He has been credited with establishing the discipline of mathematical statistics. He founded the world's first university statistics department at University College London in 1911, and contributed significantly to the field of biometrics and meteorology. Pearson was also a proponent of Social Darwinism and eugenics, and his thought is an example of what is today described as scientific racism. Pearson was a protégé and biographer of Sir Francis Galton. He edited and completed both William Kingdon Clifford's ''Common Sense of the Exact Sciences'' (1885) and Isaac Todhunter's ''History of the Theory of Elasticity'', Vol. 1 (1886–1893) and Vol. 2 (1893), following their deaths. Early life and education Pearson was born in Islington, London, into a Quaker family. His father was William Pearson QC of the Inner Temple, and his mother Fanny (née Smit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
