Portal talk:Mathematics/Archive2020
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Duplicate "Did you know"
Number 34 and Number 43 in “Did you know” of Mathematics Portal are the same. — Preceding unsigned comment added by AshrithSagar (talk • contribs) 08:22, 5 June 2020 (UTC)
WP:RECOG discussion
dcljr, what do you think about automating the "Selected article" section using {{Transclude list item excerpts as random slideshow}}? This can be done after JL-Bot populates the section #Recognized content above. For an example of how it works, see Portal:Sports and its list of articles populated by the bot. —andrybak (talk) 18:14, 8 June 2020 (UTC)
- Have not had a chance to look into this. Hang on… - dcljr (talk) 07:22, 10 June 2020 (UTC)
- Dcljr, JL-Bot has updated the section above. 48 featured and good articles in total. Perhaps, more templates and categories could be added to the current list, which I made from Wikipedia:WikiProject_Council/Directory/Science#Mathematics. —andrybak (talk) 16:38, 18 June 2020 (UTC)
- The bot output has been moved to Portal:Mathematics/Recognized content. —andrybak (talk) 15:12, 5 November 2020 (UTC)
- Here's a demo of how this would look like:
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Image 1The derivative is a fundamental tool of calculus that quantifies the sensitivity of change of a function's output with respect to its input. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. The tangent line is the best linear approximation of the function near that input value. For this reason, the derivative is often described as the instantaneous rate of change, the ratio of the instantaneous change in the dependent variable to that of the independent variable. The process of finding a derivative is called differentiation.
There are multiple different notations for differentiation, two of the most commonly used being Leibniz notation and prime notation. Leibniz notation, named after Gottfried Wilhelm Leibniz, is represented as the ratio of two differentials, whereas prime notation is written by adding a prime mark. Higher order notations represent repeated differentiation, and they are usually denoted in Leibniz notation by adding superscripts to the differentials, and in prime notation by adding additional prime marks. The higher order derivatives can be applied in physics; for example, while the first derivative of the position of a moving object with respect to time is the object's velocity, how the position changes as time advances, the second derivative is the object's acceleration, how the velocity changes as time advances. (Full article...) -
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In the mathematical theory of minimal surfaces, the double bubble theorem states that the shape that encloses and separates two given volumes and has the minimum possible surface area is a standard double bubble: three spherical surfaces meeting at angles of 120° on a common circle. The double bubble theorem was formulated and thought to be true in the 19th century, and became a "serious focus of research" by 1989, but was not proven until 2002.
The proof combines multiple ingredients. Compactness of rectifiable currents (a generalized definition of surfaces) shows that a solution exists. A symmetry argument proves that the solution must be a surface of revolution, and it can be further restricted to having a bounded number of smooth pieces. Jean Taylor's proof of Plateau's laws describes how these pieces must be shaped and connected to each other, and a final case analysis shows that, among surfaces of revolution connected in this way, only the standard double bubble has locally-minimal area. (Full article...) -
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The 17-animal inheritance puzzle is a mathematical puzzle involving unequal but fair allocation of indivisible goods, usually stated in terms of inheritance of a number of large animals (17 camels, 17 horses, 17 elephants, etc.) which must be divided in some stated proportion among a number of beneficiaries.
Despite often being framed as a puzzle, it is more an anecdote about a curious calculation than a problem with a clear mathematical solution. Beyond recreational mathematics and mathematics education, the story has been repeated as a parable with varied metaphorical meanings. (Full article...) -
Image 4In algebraic geometry and theoretical physics, mirror symmetry is a relationship between geometric objects called Calabi–Yau manifolds. The term refers to a situation where two Calabi–Yau manifolds look very different geometrically but are nevertheless equivalent when employed as extra dimensions of string theory.
Early cases of mirror symmetry were discovered by physicists. Mathematicians became interested in this relationship around 1990 when Philip Candelas, Xenia de la Ossa, Paul Green, and Linda Parkes showed that it could be used as a tool in enumerative geometry, a branch of mathematics concerned with counting the number of solutions to geometric questions. Candelas and his collaborators showed that mirror symmetry could be used to count rational curves on a Calabi–Yau manifold, thus solving a longstanding problem. Although the original approach to mirror symmetry was based on physical ideas that were not understood in a mathematically precise way, some of its mathematical predictions have since been proven rigorously. (Full article...) -
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Open-source licenses are software licenses that allow content to be used, modified, and shared. They facilitate free and open-source software (FOSS) development. Intellectual property (IP) laws restrict the modification and sharing of creative works. Free and open-source licenses use these existing legal structures for an inverse purpose. They grant the recipient the rights to use the software, examine the source code, modify it, and distribute the modifications. These criteria are outlined in the Open Source Definition.
After 1980, the United States began to treat software as a literary work covered by copyright law. Richard Stallman founded the free software movement in response to the rise of proprietary software. The term "open source" was used by the Open Source Initiative (OSI), founded by free software developers Bruce Perens and Eric S. Raymond. "Open source" emphasizes the strengths of the open development model rather than software freedoms. While the goals behind the terms are different, open-source licenses and free software licenses describe the same thing. (Full article...) -
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In computer science, the clique problem is the computational problem of finding cliques (subsets of vertices, all adjacent to each other, also called complete subgraphs) in a graph. It has several different formulations depending on which cliques, and what information about the cliques, should be found. Common formulations of the clique problem include finding a maximum clique (a clique with the largest possible number of vertices), finding a maximum weight clique in a weighted graph, listing all maximal cliques (cliques that cannot be enlarged), and solving the decision problem of testing whether a graph contains a clique larger than a given size.
The clique problem arises in the following real-world setting. Consider a social network, where the graph's vertices represent people, and the graph's edges represent mutual acquaintance. Then a clique represents a subset of people who all know each other, and algorithms for finding cliques can be used to discover these groups of mutual friends. Along with its applications in social networks, the clique problem also has many applications in bioinformatics, and computational chemistry. (Full article...) -
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An actuary is a professional with advanced mathematical skills who deals with the measurement and management of risk and uncertainty. The name of the corresponding field is actuarial science which covers rigorous mathematical calculations in areas of life expectancy and life insurance. These risks can affect both sides of the balance sheet and require asset management, liability management, and valuation skills. Actuaries provide assessments of financial security systems, with a focus on their complexity, their mathematics, and their mechanisms.
While the concept of insurance dates to antiquity, the concepts needed to scientifically measure and mitigate risks have their origins in the 17th century studies of probability and annuities. Actuaries of the 21st century require analytical skills, business knowledge, and an understanding of human behavior and information systems to design and manage programs that control risk. The actual steps needed to become an actuary are usually country-specific; however, almost all processes share a rigorous schooling or examination structure and take many years to complete. (Full article...) -
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In graph theory, a book embedding is a generalization of planar embedding of a graph to embeddings in a book, a collection of half-planes all having the same line as their boundary. Usually, the vertices of the graph are required to lie on this boundary line, called the spine, and the edges are required to stay within a single half-plane. The book thickness of a graph is the smallest possible number of half-planes for any book embedding of the graph. Book thickness is also called pagenumber, stacknumber or fixed outerthickness. Book embeddings have also been used to define several other graph invariants including the pagewidth and book crossing number.
Every graph with n vertices has book thickness at most , and this formula gives the exact book thickness for complete graphs. The graphs with book thickness one are the outerplanar graphs. The graphs with book thickness at most two are the subhamiltonian graphs, which are always planar; more generally, every planar graph has book thickness at most four. All minor-closed graph families, and in particular the graphs with bounded treewidth or bounded genus, also have bounded book thickness. It is NP-hard to determine the exact book thickness of a given graph, with or without knowing a fixed vertex ordering along the spine of the book. Testing the existence of a three-page book embedding of a graph, given a fixed ordering of the vertices along the spine of the embedding, has unknown computational complexity: it is neither known to be solvable in polynomial time nor known to be NP-hard. (Full article...) -
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Pytest is a Python testing framework that originated from the PyPy project. It can be used to write various types of software tests, including unit tests, integration tests, end-to-end tests, and functional tests. Its features include parametrized testing, fixtures, and assert re-writing.
Pytest fixtures provide the contexts for tests by passing in parameter names in test cases; its parametrization eliminates duplicate code for testing multiple sets of input and output; and its rewritten assert statements provide detailed output for causes of failures. (Full article...) -
Image 10The small set expansion hypothesis or small set expansion conjecture in computational complexity theory is an unproven computational hardness assumption. Under the small set expansion hypothesis it is assumed to be computationally infeasible to distinguish between a certain class of expander graphs called "small set expanders" and other graphs that are very far from being small set expanders. This assumption implies the hardness of several other computational problems, and the optimality of certain known approximation algorithms.
The small set expansion hypothesis is related to the unique games conjecture, another unproven computational hardness assumption according to which accurately approximating the value of certain games is computationally infeasible. If the small set expansion hypothesis is true, then so is the unique games conjecture. (Full article...) -
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The demographic history of Scotland includes all aspects of population history in what is now Scotland. The earliest surviving archaeological evidence of human settlement is of Mesolithic hunter-gatherer encampments. These suggest a highly mobile boat-using people, probably with a very low density of population. Neolithic farming brought permanent settlements dating from 3500 BC, and greater concentrations of population. Evidence of hillforts and other buildings suggest a growing settled population. Changes in the scale of woodland indicates that the Roman invasions from the first century AD had a negative impact on the native population.
There are almost no written sources from which to reconstruct the demography of early medieval Scotland. This was probably a high fertility, high mortality society, similar to developing countries in the modern world. The population may have grown from half a million to a million by the mid-fourteenth century when the Black Death reached the country. It may then have fallen to as low as half a million by the end of the fifteenth century. Roughly half lived north of the River Tay and perhaps 10 per cent in the burghs that grew up in the later medieval period. Inflation in prices, indicating greater demand, suggests that the population continued to grow until the late sixteenth century, when it probably levelled off. It began to grow again in the relative stability of the late seventeenth century. The earliest reliable evidence suggests a population of 1.2 million in 1681. This was probably reduced by the "seven ill years" of the 1690s, which caused severe famine and depopulation, particularly in the north. The first national census was conducted in 1755, and showed the population of Scotland as 1,265,380. By then four towns had populations of over 10,000, with the capital, Edinburgh, the largest with 57,000 inhabitants. (Full article...) -
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Srinivasa Ramanujan
(22 December 1887 – 26 April 1920) was an Indian mathematician. Though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions, including solutions to mathematical problems then considered unsolvable.
Ramanujan initially developed his own mathematical research in isolation. According to Hans Eysenck, "he tried to interest the leading professional mathematicians in his work, but failed for the most part. What he had to show them was too novel, too unfamiliar, and additionally presented in unusual ways; they could not be bothered". Seeking mathematicians who could better understand his work, in 1913 he began a postal correspondence with the English mathematician G. H. Hardy at the University of Cambridge, England. Recognising Ramanujan's work as extraordinary, Hardy arranged for him to travel to Cambridge. In his notes, Hardy commented that Ramanujan had produced groundbreaking new theorems, including some that "defeated me completely; I had never seen anything in the least like them before", and some recently proven but highly advanced results. (Full article...) -
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Josiah Willard Gibbs (/ɡɪbz/; February 11, 1839 – April 28, 1903) was an American scientist who made significant theoretical contributions to physics, chemistry, and mathematics. His work on the applications of thermodynamics was instrumental in transforming physical chemistry into a rigorous deductive science. Together with James Clerk Maxwell and Ludwig Boltzmann, he created statistical mechanics (a term that he coined), explaining the laws of thermodynamics as consequences of the statistical properties of ensembles of the possible states of a physical system composed of many particles. Gibbs also worked on the application of Maxwell's equations to problems in physical optics. As a mathematician, he created modern vector calculus (independently of the British scientist Oliver Heaviside, who carried out similar work during the same period) and described the Gibbs phenomenon in the theory of Fourier analysis.
In 1863, Yale University awarded Gibbs the first American doctorate in engineering. After a three-year sojourn in Europe, Gibbs spent the rest of his career at Yale, where he was a professor of mathematical physics from 1871 until his death in 1903. Working in relative isolation, he became the earliest theoretical scientist in the United States to earn an international reputation and was praised by Albert Einstein as "the greatest mind in American history." In 1901, Gibbs received what was then considered the highest honor awarded by the international scientific community, the Copley Medal of the Royal Society of London, "for his contributions to mathematical physics." (Full article...) -
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The Matchbox Educable Noughts and Crosses Engine (sometimes called the Machine Educable Noughts and Crosses Engine or MENACE) was a mechanical computer made from 304 matchboxes designed and built by artificial intelligence researcher Donald Michie in 1961. It was designed to play human opponents in games of noughts and crosses (tic-tac-toe) by returning a move for any given state of play and to refine its strategy through reinforcement learning.
Michie did not have a computer readily available, so he worked around this restriction by building it out of matchboxes. The matchboxes used by Michie each represented a single possible layout of a noughts and crosses grid. When the computer first played, it would randomly choose moves based on the current layout. As it played more games, through a reinforcement loop, it disqualified strategies that led to losing games, and supplemented strategies that led to winning games. Michie held a tournament against MENACE in 1961, wherein he experimented with different openings. (Full article...) -
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In the mathematics of circle packing, a Doyle spiral is a pattern of non-crossing circles in the plane in which each circle is surrounded by a ring of six tangent circles. These patterns contain spiral arms formed by circles linked through opposite points of tangency, with their centers on logarithmic spirals of three different shapes.
Doyle spirals are named after mathematician Peter G. Doyle, who made an important contribution to their mathematical construction in the late 1980s or early 1990s. However, their study in phyllotaxis (the mathematics of plant growth) dates back to the early 1900s. (Full article...)
Unfinished selected pictures
dcljr, please see the added captions:
If that's enough, I'll remove the disclaimer and add these pictures to the rotation on the portal's page. —andrybak (talk) 13:29, 5 November 2020 (UTC)