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"Geometry Of Conics deals with the properties of conics (plane curves of second degree) that can be formulated and proved using only elementary geometry. Starting with the well-known optical properties of conics, this book moves to less trivial results, both classical and contemporary. It demonstrates the advantage of purely geometric methods of studying conics."--Publisher's website.
Plane geometry is developed from its basic objects and their properties and then moves to conics and basic solids, including the Platonic solids and a proof of Euler's polytope formula. Particular care is taken to explain symmetry groups, including the description of ornaments and the classification of isometries.
This book, first published in 2004, is an example based and self contained introduction to Euclidean geometry with numerous examples and exercises.
This textbook provides an introduction to Euclidean geometry. While developing geometry for its own sake, the book also emphasizes the links between geometry and other branches of pure and applied mathematics.
This volume presents an accessible, self-contained survey of topics in Euclidean and non-Euclidean geometry. It includes plentiful illustrations and exercises in support of the thoroughly worked-out proofs. The author's emphasis on the connections between Euclidean and non-Euclidean geometry unifies the range of topics covered.The text opens with a brief review of elementary geometry before proceeding to advanced material. Topics covered include advanced Euclidean and non-Euclidean geometry, division ratios and triangles, transformation geometry, projective geometry, conic sections, and hyperbolic and absolute geometry. Topics in Geometry includes over 800 illustrations and extensive exercises of varying difficulty.
The usefulness of matrix theory as a tool in disciplines ranging from quantum mechanics to psychometrics is widely recognized, and courses in matrix theory are increasingly a standard part of the undergraduate curriculum. This outstanding text offers an unusual introduction to matrix theory at the undergraduate level. Unlike most texts dealing with the topic, which tend to remain on an abstract level, Dr. Eves' book employs a concrete elementary approach, avoiding abstraction until the final chapter. This practical method renders the text especially accessible to students of physics, engineering, business and the social sciences, as well as math majors. Although the treatment is fundamental — no previous courses in abstract algebra are required — it is also flexible: each chapter includes special material for advanced students interested in deeper study or application of the theory. The book begins with preliminary remarks that set the stage for the author's concrete approach to matrix theory and the consideration of matrices as hypercomplex numbers. Dr. Eves then goes on to cover fundamental concepts and operations, equivalence, determinants, matrices with polynomial elements, similarity and congruence. A final optional chapter considers matrix theory from a generalized or abstract viewpoint, extending it to arbitrary number rings and fields, vector spaces and linear transformations of vector spaces. The author's concluding remarks direct the interested student to possible avenues of further study in matrix theory, while an extensive bibliography rounds out the book. Students of matrix theory will especially appreciate the many excellent problems (solutions not provided) included in each chapter, which are not just routine calculation exercises, but involve proof and extension of the concepts and material of the text. Scientists, engineers, economists and others whose work involves this important area of mathematics, will welcome the variety of special types of matrices and determinants discussed, which make the book not only a comprehensive introduction to the field, but a valuable resource and reference work.
Algebraic curves are the graphs of polynomial equations in two variables. This book fills the gap between the familiar subject of analytic geometry and the general study of algebraic curves, by explaining complex topics in an elementary fashion through a focus on lines, conics, and cubics. 148 illus.