A Course in Modern GeometriesSpringer Science & Business Media, 9 Μαρ 2013 - 441 σελίδες A Course in Modern Geometries is designed for a junior-senior level course for mathematics majors, including those who plan to teach in secondary school. Chapter 1 presents several finite geometries in an axiomatic framework. Chapter 2 continues the synthetic approach as it introduces Euclid's geometry and ideas of non-Euclidean geometry. In Chapter 3, a new introduction to symmetry and hands-on explorations of isometries precedes the extensive analytic treatment of isometries, similarities and affinities. A new concluding section explores isometries of space. Chapter 4 presents plane projective geometry both synthetically and analytically. The extensive use of matrix representations of groups of transformations in Chapters 3-4 reinforces ideas from linear algebra and serves as excellent preparation for a course in abstract algebra. The new Chapter 5 uses a descriptive and exploratory approach to introduce chaos theory and fractal geometry, stressing the self-similarity of fractals and their generation by transformations from Chapter 3. Each chapter includes a list of suggested resources for applications or related topics in areas such as art and history. The second edition also includes pointers to the web location of author-developed guides for dynamic software explorations of the Poincaré model, isometries, projectivities, conics and fractals. Parallel versions of these explorations are available for "Cabri Geometry" and "Geometer's Sketchpad". Judith N. Cederberg is an associate professor of mathematics at St. Olaf College in Minnesota. |
Αναζήτηση στο βιβλίο
Αποτελέσματα 1 - 5 από τα 53.
Σελίδα viii
... Reflections 3.2 * Exploring Rotations and Finite Symmetry Groups 3.3 * Exploring Translations and Frieze Pattern Symmetries 3.4 * Exploring Plane Tilings 3.11 * 3.14 Exploring 3 - D Isometries * Indicates web supplements using dynamic ...
... Reflections 3.2 * Exploring Rotations and Finite Symmetry Groups 3.3 * Exploring Translations and Frieze Pattern Symmetries 3.4 * Exploring Plane Tilings 3.11 * 3.14 Exploring 3 - D Isometries * Indicates web supplements using dynamic ...
Σελίδα ix
... reflections , rotations , translations and glide reflections are ex- plored before the analytic model is set up and used to confirm properties of these transformations . ( 2 ) The early introduction of these transformations necessitates ...
... reflections , rotations , translations and glide reflections are ex- plored before the analytic model is set up and used to confirm properties of these transformations . ( 2 ) The early introduction of these transformations necessitates ...
Σελίδα x
Judith N. Cederberg. products of reflections has been restated to spell out the exact products involved . ( 3 ) Vectors are now used in the definition of translations , glide reflections , and dilations . ( 4 ) The particu- lar linear ...
Judith N. Cederberg. products of reflections has been restated to spell out the exact products involved . ( 3 ) Vectors are now used in the definition of translations , glide reflections , and dilations . ( 4 ) The particu- lar linear ...
Σελίδα xviii
... Reflections * 103 3.3 Exploring Rotations and Finite Symmetry Groups * 108 3.4 Exploring Translations and Frieze Pattern Symmetries * 116 3.5 An Analytic Model of the Euclidean Plane 121 3.6 Transformations of the Euclidean Plane 129 ...
... Reflections * 103 3.3 Exploring Rotations and Finite Symmetry Groups * 108 3.4 Exploring Translations and Frieze Pattern Symmetries * 116 3.5 An Analytic Model of the Euclidean Plane 121 3.6 Transformations of the Euclidean Plane 129 ...
Σελίδα 103
Έχετε φτάσει το όριο προβολής για το συγκεκριμένο βιβλίο.
Έχετε φτάσει το όριο προβολής για το συγκεκριμένο βιβλίο.
Περιεχόμενα
1 | |
5 | |
17 | |
Geometric Transformations of the Euclidean Plane | 99 |
4 | 116 |
6 | 128 |
7 | 135 |
13 | 175 |
Projective Geometry | 213 |
10 | 269 |
Appendices | 389 |
Geometry | 399 |
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
AABC affine transformation algebra analytic angle sum APQR assume asymptotic triangles axiomatic system axis collineation congruent Construct contains Corollary corresponding Definition determined dimension direct isometry distance distinct points elements elliptic geometry equation equilateral triangle Euclid's Euclidean geometry Euclidean plane exactly Exercise fifth postulate FIGURE Find the matrix fractal frieze group frieze pattern glide reflection H(AB homogeneous coordinates homogeneous parameters hyperbolic geometry ideal points incident invariant points label maps Mathematics matrix representation midpoint non-Euclidean geometry Note P₁ pair parallel lines pencil of points pencils of lines perpendicular perspective plane of order Playfair's axiom point conic point set points and lines polar projective geometry Proof Let proof of Theorem properties prototile Prove Theorem real numbers result rotation Saccheri quadrilateral segment self-similarity sensed parallel set of points sides Sierpinski triangle similar straight lines symmetry groups tiling translation ultraparallel unique vector verify vertices