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Pythagorean Triangles
''Pythagorean Triangles'' is a book on right triangles, the Pythagorean theorem, and Pythagorean triples. It was originally written in the Polish language by Wacław Sierpiński (titled ''Trójkąty pitagorejskie''), and published in Warsaw in 1954. Indian mathematician Ambikeshwar Sharma translated it into English, with some added material from Sierpiński, and published it in the ''Scripta Mathematica'' Studies series of Yeshiva University (volume 9 of the series) in 1962. Dover Books republished the translation in a paperback edition in 2003. There is also a Russian translation of the 1954 edition. Topics As a brief summary of the book's contents, reviewer Brian Hopkins quotes ''The Pirates of Penzance'': "With many cheerful facts about the square of the hypotenuse." The book is divided into 15 chapters (or 16, if one counts the added material as a separate chapter). The first three of these define the primitive Pythagorean triples (the ones in which the two sides and hypote ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Right Triangle
A right triangle (American English) or right-angled triangle ( British), or more formally an orthogonal triangle, formerly called a rectangled triangle ( grc, ὀρθόσγωνία, lit=upright angle), is a triangle in which one angle is a right angle (that is, a 90- degree angle), i.e., in which two sides are perpendicular. The relation between the sides and other angles of the right triangle is the basis for trigonometry. The side opposite to the right angle is called the '' hypotenuse'' (side ''c'' in the figure). The sides adjacent to the right angle are called ''legs'' (or ''catheti'', singular: '' cathetus''). Side ''a'' may be identified as the side ''adjacent to angle B'' and ''opposed to'' (or ''opposite'') ''angle A'', while side ''b'' is the side ''adjacent to angle A'' and ''opposed to angle B''. If the lengths of all three sides of a right triangle are integers, the triangle is said to be a Pythagorean triangle and its side lengths are collectively known as a '' Pyt ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euler Brick
In mathematics, an Euler brick, named after Leonhard Euler, is a rectangular cuboid whose edges and face diagonals all have integer lengths. A primitive Euler brick is an Euler brick whose edge lengths are relatively prime. A perfect Euler brick is one whose space diagonal is also an integer but such a brick has not yet been found. Definition The definition of an Euler brick in geometric terms is equivalent to a solution to the following system of Diophantine equations: :\begin a^2 + b^2 = d^2\\ a^2 + c^2 = e^2\\ b^2 + c^2 = f^2\end where are the edges and are the diagonals. Properties * If is a solution, then is also a solution for any . Consequently, the solutions in rational numbers are all rescalings of integer solutions. Given an Euler brick with edge-lengths , the triple constitutes an Euler brick as well.Wacław Sierpiński, ''Pythagorean Triangles'', Dover Publications, 2003 (orig. ed. 1962). * Exactly one edge and two face diagonals of a ''primitive'' E ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
1954 Non-fiction Books
Events January * January 1 – The Soviet Union ceases to demand war reparations from West Germany. * January 3 – The Italian broadcaster RAI officially begins transmitting. * January 7 – Georgetown-IBM experiment: The first public demonstration of a machine translation system is held in New York, at the head office of IBM. * January 10 – BOAC Flight 781, a de Havilland Comet jet plane, disintegrates in mid-air due to metal fatigue, and crashes in the Mediterranean near Elba; all 35 people on board are killed. * January 12 – Avalanches in Austria kill more than 200. * January 15 – Mau Mau leader Waruhiu Itote is captured in Kenya. * January 17 – In Yugoslavia, Milovan Đilas, one of the leading members of the League of Communists of Yugoslavia, is relieved of his duties. * January 20 – The US-based National Negro Network is established, with 46 member radio stations. * January 21 – The first nuclear-powered submarine, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics Books
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 t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Association Of America
The Mathematical Association of America (MAA) is a professional society that focuses on mathematics accessible at the undergraduate level. Members include university, college, and high school teachers; graduate and undergraduate students; pure and applied mathematicians; computer scientists; statisticians; and many others in academia, government, business, and industry. The MAA was founded in 1915 and is headquartered at 1529 18th Street, Northwest in the Dupont Circle neighborhood of Washington, D.C. The organization publishes mathematics journals and books, including the ''American Mathematical Monthly'' (established in 1894 by Benjamin Finkel), the most widely read mathematics journal in the world according to records on JSTOR. Mission and Vision The mission of the MAA is to advance the understanding of mathematics and its impact on our world. We envision a society that values the power and beauty of mathematics and fully realizes its potential to promote human flourishi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Number Theory
The ''Journal of Number Theory'' (''JNT'') is a bimonthly peer-reviewed scientific journal covering all aspects of number theory. The journal was established in 1969 by R.P. Bambah, P. Roquette, A. Ross, A. Woods, and H. Zassenhaus (Ohio State University). It is currently published monthly by Elsevier and the editor-in-chief is Dorian Goldfeld ( Columbia University). According to the '' Journal Citation Reports'', the journal has a 2020 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a scientometric index calculated by Clarivate that reflects the yearly mean number of citations of articles published in the last two years in a given journal, as i ... of 0.72. References External links * Number theory Mathematics journals Publications established in 1969 Elsevier academic journals Monthly journals English-language journals {{math-journal-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Reviews
''Mathematical Reviews'' is a journal published by the American Mathematical Society (AMS) that contains brief synopses, and in some cases evaluations, of many articles in mathematics, statistics, and theoretical computer science. The AMS also publishes an associated online bibliographic database called MathSciNet which contains an electronic version of ''Mathematical Reviews'' and additionally contains citation information for over 3.5 million items as of 2018. Reviews Mathematical Reviews was founded by Otto E. Neugebauer in 1940 as an alternative to the German journal ''Zentralblatt für Mathematik'', which Neugebauer had also founded a decade earlier, but which under the Nazis had begun censoring reviews by and of Jewish mathematicians. The goal of the new journal was to give reviews of every mathematical research publication. As of November 2007, the ''Mathematical Reviews'' database contained information on over 2.2 million articles. The authors of reviews are volunteer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ZbMATH
zbMATH Open, formerly Zentralblatt MATH, is a major reviewing service providing reviews and abstracts for articles in pure and applied mathematics, produced by the Berlin office of FIZ Karlsruhe – Leibniz Institute for Information Infrastructure GmbH. Editors are the European Mathematical Society, FIZ Karlsruhe, and the Heidelberg Academy of Sciences. zbMATH is distributed by Springer Science+Business Media. It uses the Mathematics Subject Classification codes for organising reviews by topic. History Mathematicians Richard Courant, Otto Neugebauer, and Harald Bohr, together with the publisher Ferdinand Springer, took the initiative for a new mathematical reviewing journal. Harald Bohr worked in Copenhagen. Courant and Neugebauer were professors at the University of Göttingen. At that time, Göttingen was considered one of the central places for mathematical research, having appointed mathematicians like David Hilbert, Hermann Minkowski, Carl Runge, and Felix Klein, t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Eric Stephen Barnes
Eric Stephen Barnes (1924–2000), was an Australian pure mathematician. He was awarded the Thomas Ranken Lyle Medal in 1959, and was (Sir Thomas) Elder Professor of Mathematics at the University of Adelaide. He was elected a Fellow of the Australian Academy of Science The Fellowship of the Australian Academy of Science is made up of about 500 Australian scientists. Scientists judged by their peers to have made an exceptional contribution to knowledge in their field may be elected to Fellowship of the Academy ... in 1954.Eric Stephen Barnes, 1924–2000 Australian Academy of ScienceEric Stephen Barnes, 1924� ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boolean Pythagorean Triples Problem
The Boolean Pythagorean triples problem is a problem from Ramsey theory about whether the positive integers can be colored red and blue so that no Pythagorean triples consist of all red or all blue members. The Boolean Pythagorean triples problem was solved by Marijn Heule, Oliver Kullmann and Victor W. Marek in May 2016 through a computer-assisted proof. Statement The problem asks if it is possible to color each of the positive integers either red or blue, so that no Pythagorean triple of integers ''a'', ''b'', ''c'', satisfying a^2+b^2=c^2 are all the same color. For example, in the Pythagorean triple 3, 4 and 5 (3^2+4^2=5^2), if 3 and 4 are colored red, then 5 must be colored blue. Solution Marijn Heule, Oliver Kullmann and Victor W. Marek showed that such a coloring is only possible up to the number 7824. The actual statement of the theorem proved is There are possible coloring combinations for the numbers up to 7825. These possible colorings were logically and algorithm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heronian Tetrahedron
A Heronian tetrahedron (also called a Heron tetrahedron or perfect pyramid) is a tetrahedron whose edge lengths, face areas and volume are all integers. The faces must therefore all be Heronian triangles. Every Heronian tetrahedron can be arranged in Euclidean space so that its vertex coordinates are also integers. Examples An example known to Leonhard Euler is a Heronian birectangular tetrahedron, a tetrahedron with a path of three edges parallel to the three coordinate axes and with all faces being right triangles. The lengths of the edges on the path of axis-parallel edges are 153, 104, and 672, and the other three edge lengths are 185, 680, and 697, forming four right triangle faces described by the Pythagorean triples (153,104,185), (104,672,680), (153,680,697), and (185,672,697). Eight examples of Heronian tetrahedra were discovered in 1877 by Reinhold Hoppe. 117 is the smallest possible length of the longest edge of a perfect tetrahedron with integral edge lengths. Its othe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tetrahedron
In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all the ordinary convex polyhedra and the only one that has fewer than 5 faces. The tetrahedron is the three-dimensional case of the more general concept of a Euclidean simplex, and may thus also be called a 3-simplex. The tetrahedron is one kind of pyramid, which is a polyhedron with a flat polygon base and triangular faces connecting the base to a common point. In the case of a tetrahedron the base is a triangle (any of the four faces can be considered the base), so a tetrahedron is also known as a "triangular pyramid". Like all convex polyhedra, a tetrahedron can be folded from a single sheet of paper. It has two such nets. For any tetrahedron there exists a sphere (called the circumsphere) on which all four vertices lie, and anot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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