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Strong Law Of Small Numbers
In mathematics, the "strong law of small numbers" is the humorous law that proclaims, in the words of Richard K. Guy (1988): In other words, any given small number appears in far more contexts than may seem reasonable, leading to many apparently surprising coincidences in mathematics, simply because small numbers appear so often and yet are so few. Earlier (1980) this "law" was reported by Martin Gardner. Guy's subsequent 1988 paper of the same title gives numerous examples in support of this thesis. (This paper earned him the MAA Lester R. Ford Award.) Second strong law of small numbers Guy gives Moser's circle problem as an example. The number of and . The first five terms for the number of regions follow a simple sequence, broken by the sixth term. Guy also formulated a second strong law of small numbers: Guy explains this latter law by the way of examples: he cites numerous sequences for which observing the first few members may lead to a wrong guess about the gener ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Coincidence
A mathematical coincidence is said to occur when two expressions with no direct relationship show a near-equality which has no apparent theoretical explanation. For example, there is a near-equality close to the round number 1000 between powers of 2 and powers of 10: :2^ = 1024 \approx 1000 = 10^3. Some mathematical coincidences are used in engineering when one expression is taken as an approximation of another. Introduction A mathematical coincidence often involves an integer, and the surprising feature is the fact that a real number arising in some context is considered by some standard as a "close" approximation to a small integer or to a multiple or power of ten, or more generally, to a rational number with a small denominator. Other kinds of mathematical coincidences, such as integers simultaneously satisfying multiple seemingly unrelated criteria or coincidences regarding units of measurement, may also be considered. In the class of those coincidences that are of a pure ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1988 In Science
The year 1988 in science and technology involved many significant events, some listed below. Astronomy and space exploration * September 29 – NASA resumes Space Shuttle flights, grounded after the ''Challenger'' disaster. * November 15 – In the Soviet Union, the uncrewed Shuttle ''Buran'' is launched by an Energia rocket on her maiden orbital spaceflight (this was the first and last space flight for the shuttle). * Canadian astronomers Bruce Campbell, G. A. H. Walker and Stephenson Yang publish radial-velocity observations suggesting that an extrasolar planet orbits the star Gamma Cephei, although its existence is not confirmed until 2003. * Asteroid 3994 Ayashi is discovered by Masahiro Koishikawa. * 4407 Taihaku is discovered. * 4539 Miyagino is discovered. Climatology * NASA climate scientist James Hansen uses the term ''global warming'' in testimony to the United States Congress bringing it to public attention. * The Intergovernmental Panel on Climate Change (IPCC) i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1988 Documents
File:1988 Events Collage.png, From left, clockwise: The oil platform Piper Alpha explodes and collapses in the North Sea, killing 165 workers; The USS Vincennes (CG-49) mistakenly shoots down Iran Air Flight 655; Australia celebrates its Bicentennial on January 26; The 1988 Summer Olympics are held in Seoul, South Korea; Soviet troops begin their withdrawal from Afghanistan, which is completed the next year; The 1988 Armenian earthquake kills between 25,000-50,000 people; The 8888 Uprising in Myanmar, led by students, protests the Burma Socialist Programme Party; A bomb explodes on Pan Am Flight 103, causing the plane to crash down on the town of Lockerbie, Scotland- the event kills 270 people., 300x300px, thumb rect 0 0 200 200 Piper Alpha rect 200 0 400 200 Iran Air Flight 655 rect 400 0 600 200 Australian Bicentenary rect 0 200 300 400 Pan Am Flight 103 rect 300 200 600 400 1988 Summer Olympics rect 0 400 200 600 8888 Uprising rect 200 400 400 600 1988 Armenian earthquake rect 400 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Humor
A mathematical joke is a form of humor which relies on aspects of mathematics or a stereotype of mathematicians. The humor may come from a pun, or from a double meaning of a mathematical term, or from a lay person's misunderstanding of a mathematical concept. Mathematician and author John Allen Paulos in his book ''Mathematics and Humor'' described several ways that mathematics, generally considered a dry, formal activity, overlaps with humor, a loose, irreverent activity: both are forms of "intellectual play"; both have "logic, pattern, rules, structure"; and both are "economical and explicit". Some performers combine mathematics and jokes to entertain and/or teach math. Humor of mathematicians may be classified into the esoteric and exoteric categories. Esoteric jokes rely on the intrinsic knowledge of mathematics and its terminology. Exoteric jokes are intelligible to the outsiders, and most of them compare mathematicians with representatives of other disciplines or with commo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics Papers
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Daniel Kahneman
Daniel Kahneman (; he, דניאל כהנמן; born March 5, 1934) is an Israeli-American psychologist and economist notable for his work on the psychology of judgment and decision-making, as well as behavioral economics, for which he was awarded the 2002 Nobel Memorial Prize in Economic Sciences (shared with Vernon L. Smith). His empirical findings challenge the assumption of human rationality prevailing in modern economic theory. With Amos Tversky and others, Kahneman established a cognitive basis for common human errors that arise from heuristics and biases, and developed prospect theory. In 2011 he was named by '' Foreign Policy'' magazine in its list of top global thinkers. In the same year his book ''Thinking, Fast and Slow'', which summarizes much of his research, was published and became a best seller. In 2015, ''The Economist'' listed him as the seventh most influential economist in the world. He is professor emeritus of psychology and public affairs at Princeton U ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Amos Tversky
Amos Nathan Tversky ( he, עמוס טברסקי; March 16, 1937 – June 2, 1996) was an Israeli cognitive and mathematical psychologist and a key figure in the discovery of systematic human cognitive bias and handling of risk. Much of his early work concerned the foundations of measurement. He was co-author of a three-volume treatise, ''Foundations of Measurement''. His early work with Daniel Kahneman focused on the psychology of prediction and probability judgment; later they worked together to develop prospect theory, which aims to explain irrational human economic choices and is considered one of the seminal works of behavioral economics. Six years after Tversky's death, Kahneman received the 2002 Nobel Memorial Prize in Economic Sciences for the work he did in collaboration with Amos Tversky. (The prize is not awarded posthumously.) Kahneman told ''The New York Times'' in an interview soon after receiving the honor: "I feel it is a joint prize. We were twinned for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jean-Pierre Serre
Jean-Pierre Serre (; born 15 September 1926) is a French mathematician who has made contributions to algebraic topology, algebraic geometry, and algebraic number theory. He was awarded the Fields Medal in 1954, the Wolf Prize in 2000 and the inaugural Abel Prize in 2003. Biography Personal life Born in Bages, Pyrénées-Orientales, France, to pharmacist parents, Serre was educated at the Lycée de Nîmes and then from 1945 to 1948 at the École Normale Supérieure in Paris. He was awarded his doctorate from the Sorbonne in 1951. From 1948 to 1954 he held positions at the Centre National de la Recherche Scientifique in Paris. In 1956 he was elected professor at the Collège de France, a position he held until his retirement in 1994. His wife, Professor Josiane Heulot-Serre, was a chemist; she also was the director of the Ecole Normale Supérieure de Jeunes Filles. Their daughter is the former French diplomat, historian and writer Claudine Monteil. The French mathematician Denis S ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Representativeness Heuristic
The representativeness heuristic is used when making judgments about the probability of an event under uncertainty. It is one of a group of heuristics (simple rules governing judgment or decision-making) proposed by psychologists Amos Tversky and Daniel Kahneman in the early 1970s as "the degree to which n event(i) is similar in essential characteristics to its parent population, and (ii) reflects the salient features of the process by which it is generated". Heuristics are described as "judgmental shortcuts that generally get us where we need to go – and quickly – but at the cost of occasionally sending us off course." Heuristics are useful because they use effort-reduction and simplification in decision-making. When people rely on representativeness to make judgments, they are likely to judge wrongly because the fact that something is more representative does not actually make it more likely. The representativeness heuristic is simply described as assessing similarity of ob ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pigeonhole Principle
In mathematics, the pigeonhole principle states that if items are put into containers, with , then at least one container must contain more than one item. For example, if one has three gloves (and none is ambidextrous/reversible), then there must be at least two right-handed gloves, or at least two left-handed gloves, because there are three objects, but only two categories of handedness to put them into. This seemingly obvious statement, a type of counting argument, can be used to demonstrate possibly unexpected results. For example, given that the population of London is greater than the maximum number of hairs that can be present on a human's head, then the pigeonhole principle requires that there must be at least two people in London who have the same number of hairs on their heads. Although the pigeonhole principle appears as early as 1624 in a book attributed to Jean Leurechon, it is commonly called Dirichlet's box principle or Dirichlet's drawer principle after an 1834 t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Law Of Large Numbers
In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials should be close to the expected value and tends to become closer to the expected value as more trials are performed. The LLN is important because it guarantees stable long-term results for the averages of some random events. For example, while a casino may lose money in a single spin of the roulette wheel, its earnings will tend towards a predictable percentage over a large number of spins. Any winning streak by a player will eventually be overcome by the parameters of the game. Importantly, the law applies (as the name indicates) only when a ''large number'' of observations are considered. There is no principle that a small number of observations will coincide with the expected value or that a streak of one value will immediately be "balanced ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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