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John Pardon
John Vincent Pardon (born June 1989) is an American mathematician who works on geometry and topology. He is primarily known for having solved Gromov's problem on distortion of knots, for which he was awarded the 2012 Morgan Prize. He is currently a full professor of mathematics at Princeton University. Education and accomplishments Pardon's father, William Pardon, is a mathematics professor at Duke University, and when Pardon was a high school student at the Durham Academy he also took classes at Duke. He was a three-time gold medalist at the International Olympiad in Informatics, in 2005, 2006, and 2007. In 2007, Pardon placed second in the Intel Science Talent Search competition, with a generalization to rectifiable curves of the carpenter's rule problem for polygons. In this project, he showed that every rectifiable Jordan curve in the plane can be continuously deformed into a convex curve without changing its length and without ever allowing any two points of the curve to get ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alan T
Alan may refer to: People *Alan (surname), an English and Turkish surname *Alan (given name), an English given name **List of people with given name Alan ''Following are people commonly referred to solely by "Alan" or by a homonymous name.'' *Alan (Chinese singer) (born 1987), female Chinese singer of Tibetan ethnicity, active in both China and Japan *Alan (Mexican singer) (born 1973), Mexican singer and actor * Alan (wrestler) (born 1975), a.k.a. Gato Eveready, who wrestles in Asistencia AsesorÃa y Administración *Alan (footballer, born 1979) (Alan Osório da Costa Silva), Brazilian footballer *Alan (footballer, born 1998) (Alan Cardoso de Andrade), Brazilian footballer *Alan I, King of Brittany (died 907), "the Great" *Alan II, Duke of Brittany (c. 900–952) * Alan III, Duke of Brittany(997–1040) *Alan IV, Duke of Brittany (c. 1063–1119), a.k.a. Alan Fergant ("the Younger" in Breton language) *Alan of Tewkesbury, 12th century abbott *Alan of Lynn (c. 1348–1423), 15th ce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Durham Academy, North Carolina
Durham Academy is an independent, coeducational, day school in Durham, North Carolina, whose 1,237 students range from pre-kindergarten to grade 12. The school has four divisions, each with its own director: Preschool (Pre-kindergarten/Kindergarten), Lower School (grades 1–4), Middle School (grades 5–8) and Upper School (grades 9–12). These are arrayed on three campuses that comprise four acres. Thirty-eight percent of Durham Academy's students are people of color, as are 17 percent of teachers. In 2019–20, Durham Academy awarded more than $2,200,000 in financial aid (not including tuition remission and need-based financial aid for faculty and staff); the average award was $14,682. History Durham Academy was founded in 1933, as the Calvert Method School, by George Watts Hill and his wife. The couple established the school as a private, independent school to educate their children. The school's teaching philosophy (and its name) were based on the Calvert ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Annals Of Mathematics
The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study. History The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as the founding editor-in-chief. It was "intended to afford a medium for the presentation and analysis of any and all questions of interest or importance in pure and applied Mathematics, embracing especially all new and interesting discoveries in theoretical and practical astronomy, mechanical philosophy, and engineering". It was published in Des Moines, Iowa, and was the earliest American mathematics journal to be published continuously for more than a year or two. This incarnation of the journal ceased publication after its tenth year, in 1883, giving as an explanation Hendricks' declining health, but Hendricks made arrangements to have it taken over by new management, and it was continued from March 1884 as the ''Annals of Mathematics''. The n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Torus Knot
In knot theory, a torus knot is a special kind of knot that lies on the surface of an unknotted torus in R3. Similarly, a torus link is a link which lies on the surface of a torus in the same way. Each torus knot is specified by a pair of coprime integers ''p'' and ''q''. A torus link arises if ''p'' and ''q'' are not coprime (in which case the number of components is gcd(''p, q'')). A torus knot is trivial (equivalent to the unknot) if and only if either ''p'' or ''q'' is equal to 1 or −1. The simplest nontrivial example is the (2,3)-torus knot, also known as the trefoil knot. Geometrical representation A torus knot can be rendered geometrically in multiple ways which are topologically equivalent (see Properties below) but geometrically distinct. The convention used in this article and its figures is the following. The (''p'',''q'')-torus knot winds ''q'' times around a circle in the interior of the torus, and ''p'' times around its axis of rotational symmetry.. If ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Embedding
In mathematics, an embedding (or imbedding) is one instance of some mathematical structure contained within another instance, such as a group that is a subgroup. When some object X is said to be embedded in another object Y, the embedding is given by some injective and structure-preserving map f:X\rightarrow Y. The precise meaning of "structure-preserving" depends on the kind of mathematical structure of which X and Y are instances. In the terminology of category theory, a structure-preserving map is called a morphism. The fact that a map f:X\rightarrow Y is an embedding is often indicated by the use of a "hooked arrow" (); thus: f : X \hookrightarrow Y. (On the other hand, this notation is sometimes reserved for inclusion maps.) Given X and Y, several different embeddings of X in Y may be possible. In many cases of interest there is a standard (or "canonical") embedding, like those of the natural numbers in the integers, the integers in the rational numbers, the rational n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Knot (mathematics)
In mathematics, a knot is an embedding of the circle into three-dimensional Euclidean space, (also known as ). Often two knots are considered equivalent if they are ambient isotopic, that is, if there exists a continuous deformation of which takes one knot to the other. A crucial difference between the standard mathematical and conventional notions of a knot is that mathematical knots are closed — there are no ends to tie or untie on a mathematical knot. Physical properties such as friction and thickness also do not apply, although there are mathematical definitions of a knot that take such properties into account. The term ''knot'' is also applied to embeddings of in , especially in the case . The branch of mathematics that studies knots is known as knot theory and has many relations to graph theory. Formal definition A knot is an embedding of the circle () into three-dimensional Euclidean space (), or the 3-sphere (), since the 3-sphere is compact. Two knots are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Knot Theory
In the mathematical field of topology, knot theory is the study of knot (mathematics), mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined so it cannot be undone, Unknot, the simplest knot being a ring (or "unknot"). In mathematical language, a knot is an embedding of a circle in 3-dimensional Euclidean space, \mathbb^3 (in topology, a circle is not bound to the classical geometric concept, but to all of its homeomorphisms). Two mathematical knots are equivalent if one can be transformed into the other via a deformation of \mathbb^3 upon itself (known as an ambient isotopy); these transformations correspond to manipulations of a knotted string that do not involve cutting it or passing through itself. Knots can be described in various ways. Using different description methods, there may be more than one description of the same knot. For example, a common method of descr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transactions Of The American Mathematical Society
The ''Transactions of the American Mathematical Society'' is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society. It was established in 1900. As a requirement, all articles must be more than 15 printed pages. See also * ''Bulletin of the American Mathematical Society'' * '' Journal of the American Mathematical Society'' * ''Memoirs of the American Mathematical Society'' * ''Notices of the American Mathematical Society'' * ''Proceedings of the American Mathematical Society'' External links * ''Transactions of the American Mathematical Society''on JSTOR JSTOR (; short for ''Journal Storage'') is a digital library founded in 1995 in New York City. Originally containing digitized back issues of academic journals, it now encompasses books and other primary sources as well as current issues of j ... American Mathematical Society academic journals Mathematics journals Publications established in 1900 {{math-journal-st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Science News
''Science News (SN)'' is an American bi-weekly magazine devoted to articles about new scientific and technical developments, typically gleaned from recent scientific and technical journals. History ''Science News'' has been published since 1922 by Society for Science & the Public, a non-profit organization founded by E. W. Scripps in 1920. American chemist Edwin Slosson served as the publication's first editor. From 1922 to 1966, it was called ''Science News Letter''. The title was changed to ''Science News'' with the March 12, 1966 issue (vol. 89, no. 11). Tom Siegfried was the editor from 2007 to 2012. In 2012, Siegfried stepped down, and Eva Emerson became the Editor in Chief of the magazine. In 2017, Eva Emerson stepped down to become the editor of a new digital magazine, Annual Reviews. On February 1, 2018 Nancy Shute became the Editor in Chief of the magazine. In April 2008, the magazine changed from a weekly format to the current biweekly format, and the website was ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convex Curve
In geometry, a convex curve is a plane curve that has a supporting line through each of its points. There are many other equivalent definitions of these curves, going back to Archimedes. Examples of convex curves include the convex polygons, the boundaries of convex sets, and the graphs of convex functions. Important subclasses of convex curves include the closed convex curves (the boundaries of bounded convex sets), the smooth curves that are convex, and the strictly convex curves, which have the additional property that each supporting line passes through a unique point of the curve. Combinations of these properties have also been considered. Bounded convex curves have a well-defined length, which can be obtained by approximating them with polygons, or from the average length of their projections onto a line. The maximum number of grid points that can belong to a single curve is controlled by its length. The points at which a convex curve has a unique supporting line are dens ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jordan Curve
In mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight. Intuitively, a curve may be thought of as the trace left by a moving point. This is the definition that appeared more than 2000 years ago in Euclid's ''Elements'': "The urvedline is €¦the first species of quantity, which has only one dimension, namely length, without any width nor depth, and is nothing else than the flow or run of the point which €¦will leave from its imaginary moving some vestige in length, exempt of any width." This definition of a curve has been formalized in modern mathematics as: ''A curve is the image of an interval to a topological space by a continuous function''. In some contexts, the function that defines the curve is called a ''parametrization'', and the curve is a parametric curve. In this article, these curves are sometimes called ''topological curves'' to distinguish them from more constrained curves such a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Carpenter's Rule Problem
The carpenter's rule problem is a discrete geometry problem, which can be stated in the following manner: ''Can a simple planar polygon be moved continuously to a position where all its vertices are in convex position, so that the edge lengths and simplicity are preserved along the way?'' A closely related problem is to show that any non-self-crossing polygonal chain can be straightened, again by a continuous transformation that preserves edge distances and avoids crossings. Both problems were successfully solved by . Combinatorial proof Subsequently to their work, Ileana Streinu provided a simplified combinatorial proof formulated in the terminology of robot arm motion planning. Both the original proof and Streinu's proof work by finding non-expansive motions of the input, continuous transformations such that no two points ever move towards each other. Streinu's version of the proof adds edges to the input to form a pointed pseudotriangulation, removes one added convex hull edge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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