Companion encyclopedia of the history and philosophy of the by Ivor Grattan-Guinness

By Ivor Grattan-Guinness

Arithmetic is likely one of the most simple -- and such a lot historic -- forms of wisdom. but the main points of its historic improvement stay imprecise to all yet a number of experts. The two-volume better half Encyclopedia of the historical past and Philosophy of the Mathematical Sciences recovers this mathematical background, bringing jointly the various world's best historians of arithmetic to check the historical past and philosophy of the mathematical sciences in a cultural context, tracing their evolution from precedent days to the 20 th century.In 176 concise articles divided into twelve components, participants describe and examine the range of difficulties, theories, proofs, and methods in all components of natural and utilized arithmetic, together with chance and information. This vital reference paintings demonstrates the ongoing value of arithmetic and its use in physics, astronomy, engineering, laptop technological know-how, philosophy, and the social sciences. additionally addressed is the heritage of upper schooling in arithmetic. conscientiously illustrated, with annotated bibliographies of assets for every article, The significant other Encyclopedia is a necessary examine device for college kids and lecturers in all branches of mathematics.Contents of quantity 1: -Ancient and Non-Western Traditions -The Western heart a long time and the Renaissance -Calculus and Mathematical research -Functions, sequence, and techniques in research -Logic, Set Theories, and the rules of arithmetic -Algebras and quantity TheoryContents of quantity 2: -Geometries and Topology -Mechanics and Mechanical Engineering -Physics, Mathematical Physics, and electric Engineering -Probability, facts, and the Social Sciences -Higher schooling andInstitutions -Mathematics and tradition -Select Bibliography, Chronology, Biographical Notes, and Index

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Extra info for Companion encyclopedia of the history and philosophy of the mathematical sciences, Volume 2

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He considered a line 1, and a point O not on it, and looked at all the lines through O. Let the points P1 and P2 lie on such a line that meets 1 at Q. The conchoid is composed of the points P1 and P2 for which P1Q=QP2=a fixed distance a (Figure 3). Yet another solution was proposed by Diocles. This curve, called the cissoid, was obtained as follows (Figure 4). Let AB and CD be perpendicular diameters of a circle, and let EB and BF be equal arcs. Draw FH perpendicular to CD and let it meet EC at P.

Coxeter in 1930. It was previously missed by geometers because they assumed—with no logical basis—that if the faces of an Archimedean polyhedron are arranged around a vertex in a certain way, no other Archimedean polyhedron can be formed with this arrangement of faces. During the last century, isogonal polyhedra have been studied without restriction to those with regular faces. The convex ones among them have the interesting property that each is isomorphic to one of the uniform polyhedra; this holds even for the more general class of those not necessarily convex isogonal polyhedra which are topologically equivalent to a solid Page 875 Figure 7 Two distinct Archimedean polyhedra with the same arrangement of faces around each vertex: (a) the rhombicuboctahedron and (b) the pseudorhombicuboctahedron; (a) is uniform, (b) is not sphere.

4 COORDINATE TRANSFORMATIONS Although there is no such subject as advanced coordinate geometry, there is a mainstream development of Descartes’s ideas that fills university courses and is a staple technique of both pure and applied mathematics: coordinate transformations. 12). Changing the origin of the coordinate system or moving the coordinate axes changes the equation of the curve, opening the prospect of finding a simplest possible equation for a curve. For this reason, in the Page 858 Figure 10 Kummer’s quartic surface with 16 double points nineteenth century there was developed a powerful theory for describing coordinate transformations in the language of vector spaces, as Hawkins (1975, 1977) has described.

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