Popular Lectures in Mathematics PLM – serie
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4 produkter
4 produkter
247 kr
Skickas inom 5-8 vardagar
In this book, I. Ya. Bakel'man introduces inversion transformations in the Euclidean plane and discusses the interrelationships among more general mathematical concepts. The author begins by defining and giving examples of the concept of a transformation in the Euclidean plane, and then explains the "point of infinity" and the "stereographic projection" of the sphere onto the plane. With this preparation, the student is capable of applying the theory of inversions to classical construction problems in the plane. The author also discusses the theory of pencils of circles, and he uses the acquired techniques in a proof of Ptolemy's theorem. In the final chapter, the idea of a group is introduced with applications of group theory to geometry. The author demonstrates the group-theoretic basis for the distinction between Euclidean and Lobachevskian geometry.
247 kr
Skickas inom 5-8 vardagar
In contrast to the vast literature on Euclidean geometry as a whole, little has been published on the relatively recent developments in the field of combinatorial geometry. Boltyanskii and Gohberg's book investigates this area, which has undergone particularly rapid growth in the last thirty years. By restricting themselves to two dimensions, the authors make the book uniquely accessible to interested high school students while maintaining a high level of rigor. They discuss a variety of problems on figures of constant width, convex figures, coverings, and illumination. The book offers a thorough exposition of the problem of cutting figures into smaller pieces. The central theorem gives the minimum number of pieces into which a figure can be divided so that all the pieces are of smaller diameter than the original figure. This theorem, which serves as a basis for the rest of the material, is proved for both the Euclidean plane and Minkowski's plane.
231 kr
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This volume describes the relationship between systems of linear inequalities and the geometry of convex polygons, examines solution sets for systems of linear inequalities in two and three unknowns (extension of the processes introduced to systems in any number of unknowns is quite simple), and examines questions of the consistency or inconsistency of such systems. Finally, it discusses the field of linear programming, one of the principal applications of the theory of systems of linear inequalities. A proof of the duality theorem of linear programming is presented in the last section.
247 kr
Skickas inom 5-8 vardagar
N. N. Vorob'ev's Criteria for Divisibility introduces the high school or early college student to a specific number-theoretic topic and explains the general mathematical structures which underlie the particular concepts discussed. Vorob'ev discusses the ideas of well-ordered sets, partial and linear orderings, equivalence relations, equivalence classes, algorithms, and the relationship between the determinability of algorithms defined on the integers and the well-ordering principle. All this is done comprehensively with the help of a unique plan for study which encourages the student to skip large sections of the book on first reading and return to them later. The more general and conceptually challenging material appears in small print, so that the student must have a good grasp of the number-theoretic concepts on which the generalizations are based before making the step to generalization. The booklet provides both specific knowledge in a particular field of mathematical investigation and a fine basis on which to continue studies in mathematics.