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Transformationsgeometrie: Eine Einführung in die Symmetrie (Bachelor-Texte in...-
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Standort: Morgantown, West Virginia, USA
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eBay-Artikelnr.:376585490414
Artikelmerkmale
- Artikelzustand
- Release Year
- 1982
- Book Title
- Transformation Geometry: An Introduction to Symmetry (Undergra...
- ISBN
- 9780387906362
Über dieses Produkt
Product Identifiers
Publisher
Springer New York
ISBN-10
0387906363
ISBN-13
9780387906362
eBay Product ID (ePID)
145574
Product Key Features
Number of Pages
Xii, 240 Pages
Language
English
Publication Name
Transformation Geometry : an Introduction to Symmetry
Subject
Geometry / General, Transformations, Physics / General
Publication Year
1982
Type
Textbook
Subject Area
Mathematics, Science
Series
Undergraduate Texts in Mathematics Ser.
Format
Hardcover
Dimensions
Item Weight
42 Oz
Item Length
9.2 in
Item Width
6.1 in
Additional Product Features
Intended Audience
Scholarly & Professional
Number of Volumes
1 vol.
Illustrated
Yes
Table Of Content
1 Introduction.- 1.1 Transformations and Collineations.- 1.2 Geometric Notation.- 1.3 Exercises.- 2 Properties of Transformations.- 2.1 Groups of Transformations.- 2.2 Involutions.- 2.3 Exercises.- 3 Translations and Halfturns.- 3.1 Translations.- 3.2 Halfturns.- 3.3 Exercises.- 4 Reflections.- 4.1 Equations for a Reflection.- 4.2 Properties of a Reflection.- 4.3 Exercises.- 5 Congruence.- 5.1 Isometries as Products of Reflections.- 5.2 Paper Folding Experiments and Rotations.- 5.3 Exercises.- 6 The Product of Two Reflections.- 6.1 Translations and Rotations.- 6.2 Fixed Points and Involutions.- 6.3 Exercises.- 7 Even Isometries.- 7.1 Parity.- 7.2 The Dihedral Groups.- 7.3 Exercises.- 8 Classification of Plane Isometries.- 8.1 Glide Reflections.- 8.2 Leonardo's Theorem.- 8.3 Exercises.- 9 Equations for Isometries.- 9.1 Equations.- 9.2 Supplementary Exercises (Chapter 1-8).- 9.3 Exercises.- 10 The Seven Frieze Groups.- 10.1 Frieze Groups.- 10.2 Frieze Patterns.- 10.3 Exercises.- 11 The Seventeen Wallpaper Groups.- 11.1 The Crystallographic Restriction.- 11.2 Wallpaper Groups and Patterns.- 11.3 Exercises.- 12 Tessellations.- 12.1 Tiles.- 12.2 Reptiles.- 12.3 Exercises.- 13 Similarities on the Plane.- 13.1 Classification of Similarities.- 13.2 Equations for Similarities.- 13.3 Exercises.- 14 Classical Theorems.- 14.1 Menelaus, Ceva, Desargues, Pappus, Pascal.- 14.2 Euler, Brianchon, Poncelet, Feuerbach.- 14.3 Exercises.- 15 Affine Transformations.- 15.1 Collineations.- 15.2 Linear Transformations.- 15.3 Exercises.- 16 Transformations on Three-space.- 16.1 Isometries on Space.- 16.2 Similarities on Space.- 16.3 Exercises.- 17 Space and Symmetry.- 17.1 The Platonic Solids.- 17.2 Finite Symmetry Groups on Space.- 17.3 Exercises.- Hints and Answers.- Notation Index.
Synopsis
Transformation geometry is a relatively recent expression of the successful venture of bringing together geometry and algebra. The name describes an approach as much as the content. Our subject is Euclidean geometry. Essential to the study of the plane or any mathematical system is an under- standing of the transformations on that system that preserve designated features of the system. Our study of the automorphisms of the plane and of space is based on only the most elementary high-school geometry. In particular, group theory is not a prerequisite here. On the contrary, this modern approach to Euclidean geometry gives the concrete examples that are necessary to appreciate an introduction to group theory. Therefore, a course based on this text is an excellent prerequisite to the standard course in abstract algebra taken by every undergraduate mathematics major. An advantage of having nb college mathematics prerequisite to our study is that the text is then useful for graduate mathematics courses designed for secondary teachers. Many of the students in these classes either have never taken linear algebra or else have taken it too long ago to recall even the basic ideas. It turns out that very little is lost here by not assuming linear algebra. A preliminary version of the text was written for and used in two courses-one was a graduate course for teachers and the other a sophomore course designed for the prospective teacher and the general mathematics major taking one course in geometry., Transformation geometry is a relatively recent expression of the successful venture of bringing together geometry and algebra. The name describes an approach as much as the content. Our subject is Euclidean geometry. Essential to the study of the plane or any mathematical system is an under standing of the transformations on that system that preserve designated features of the system. Our study of the automorphisms of the plane and of space is based on only the most elementary high-school geometry. In particular, group theory is not a prerequisite here. On the contrary, this modern approach to Euclidean geometry gives the concrete examples that are necessary to appreciate an introduction to group theory. Therefore, a course based on this text is an excellent prerequisite to the standard course in abstract algebra taken by every undergraduate mathematics major. An advantage of having nb college mathematics prerequisite to our study is that the text is then useful for graduate mathematics courses designed for secondary teachers. Many of the students in these classes either have never taken linear algebra or else have taken it too long ago to recall even the basic ideas. It turns out that very little is lost here by not assuming linear algebra. A preliminary version of the text was written for and used in two courses-one was a graduate course for teachers and the other a sophomore course designed for the prospective teacher and the general mathematics major taking one course in geometry.
LC Classification Number
QA440-699
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Welo's Resales
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Angemeldet als privater VerkäuferDaher finden verbraucherschützende Vorschriften, die sich aus dem EU-Verbraucherrecht ergeben, keine Anwendung. Der eBay-Käuferschutz gilt dennoch für die meisten Käufe. Mehr erfahrenMehr erfahren
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- z***8 (8)- Bewertung vom Käufer.Letzter MonatBestätigter KaufGreat experience purchasing this backpack! It is as described, in great condition, and was sold for a reasonable price. My husband was surprised to hear it wasn’t a brand new item! Shipping was extremely fast, which is always an exciting surprise. The packaging was also well done. Overall, very pleased with my purchase and shopping experience! Thank you!
- 1***x (16)- Bewertung vom Käufer.Letzte 6 MonateBestätigter KaufShipping was very fast, came as described, great packaging and the value was great. Goated seller 10/10 👍
- a***- (3)- Bewertung vom Käufer.Letzte 6 MonateBestätigter KaufShipped on time. Product was as described and expected. I don’t like paying more in shipping than on the actual product. But I needed this item quickly and was thankful it was shipped quickly and in perfect condition. Bubble wrap was even included in packaging to ensure my product made in to me unharmed.