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 80.
Σελίδα xi
... Note to Instructors I have found that incorporating geometric explorations and fractal geometry in the courses I teach makes them more rewarding for both my students and myself . I sincerely hope that materials in this text will be ...
... Note to Instructors I have found that incorporating geometric explorations and fractal geometry in the courses I teach makes them more rewarding for both my students and myself . I sincerely hope that materials in this text will be ...
Σελίδα 6
... note that accepting fewer statements without proof leaves more statements to be proved . For this reason the axiomatic systems used in secondary - school geometry are seldom independent . The verification that an axiomatic system is ...
... note that accepting fewer statements without proof leaves more statements to be proved . For this reason the axiomatic systems used in secondary - school geometry are seldom independent . The verification that an axiomatic system is ...
Σελίδα 10
... Note that the word " incident " has been used in place of the undefined term " on " in this axiom system , since " incident " is commonly used in the study of general projective planes . 1 5 4 2 3 The consistency of this axiomatic 10 1 ...
... Note that the word " incident " has been used in place of the undefined term " on " in this axiom system , since " incident " is commonly used in the study of general projective planes . 1 5 4 2 3 The consistency of this axiomatic 10 1 ...
Σελίδα 11
... Note that Models P.1 and P.2 depict a projective plane of order 2 and both have exactly three points on each line , but there are projective planes with more than three points on a line as shown by the next model . Model P.3 Points A ...
... Note that Models P.1 and P.2 depict a projective plane of order 2 and both have exactly three points on each line , but there are projective planes with more than three points on a line as shown by the next model . Model P.3 Points A ...
Σελίδα 19
... Note that the vector for any given point contains exactly three l's , so in the language of coding theory , we say that each vector has weight 3. Fol- lowing a brief introduction to the area of coding theory , we shall see that these ...
... Note that the vector for any given point contains exactly three l's , so in the language of coding theory , we say that each vector has weight 3. Fol- lowing a brief introduction to the area of coding theory , we shall see that these ...
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