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Englisch
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Beschreibung
The principle aim of this unique text is to illuminate the beauty of the subject both with abstractions like proofs and mathematical text, and with visuals, such as abundant illustrations and diagrams. With few mathematical prerequisites, geometry is presented through the lens of linear fractional transformations. The exposition is motivational and the well-placed examples and exercises give students ample opportunity to pause and digest the material. The subject builds from the fundamentals of Euclidean geometry, to inversive geometry, and, finally, to hyperbolic geometry at the end. Throughout, the author aims to express the underlying philosophy behind the definitions and mathematical reasoning. This text may be used as primary for an undergraduate geometry course or a freshman seminar in geometry, or as supplemental to instructors in their undergraduate courses in complex analysis, algebra, and number theory. There are elective courses that bring together seemingly disparate topics and this text would be a welcome accompaniment.
The principle aim of this unique text is to illuminate the beauty of the subject both with abstractions like proofs and mathematical text, and with visuals, such as abundant illustrations and diagrams. With few mathematical prerequisites, geometry is presented through the lens of linear fractional transformations. The exposition is motivational and the well-placed examples and exercises give students ample opportunity to pause and digest the material. The subject builds from the fundamentals of Euclidean geometry, to inversive geometry, and, finally, to hyperbolic geometry at the end. Throughout, the author aims to express the underlying philosophy behind the definitions and mathematical reasoning. This text may be used as primary for an undergraduate geometry course or a freshman seminar in geometry, or as supplemental to instructors in their undergraduate courses in complex analysis, algebra, and number theory. There are elective courses that bring together seemingly disparate topics and this text would be a welcome accompaniment.
Über den Autor
Arseniy (Senia) Sheydvasser is a postdoctoral researcher in the department of mathematics at the Technion. His interests include algebraic number theory, additive number theory, and logic.
Zusammenfassung
Highly visual and beautifully illustrated
Exercises are organized into sections pertaining to various topics
Assumed little mathematical knowledge
Inhaltsverzeichnis
Motivation.- I Euclidean and Inversive Geometry.- Euclidean Isometries and Similarities.- Inversive Geometry.- Applications of Inversive Geometry.- II Non-Euclidean Geometry.- Spherical Geometry.- Appendix: Set Theory.
Details
| Erscheinungsjahr: | 2023 |
|---|---|
| Fachbereich: | Geometrie |
| Genre: | Mathematik, Medizin, Naturwissenschaften, Technik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Inhalt: |
xv
231 S. 10 s/w Illustr. 96 farbige Illustr. 231 p. 106 illus. 96 illus. in color. |
| ISBN-13: | 9783031250019 |
| ISBN-10: | 303125001X |
| Sprache: | Englisch |
| Einband: | Gebunden |
| Autor: | Sheydvasser, Arseniy |
| Hersteller: |
Springer Nature Switzerland
Springer International Publishing |
| Verantwortliche Person für die EU: | Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com |
| Maße: | 241 x 160 x 19 mm |
| Von/Mit: | Arseniy Sheydvasser |
| Erscheinungsdatum: | 17.04.2023 |
| Gewicht: | 0,586 kg |
Über den Autor
Arseniy (Senia) Sheydvasser is a postdoctoral researcher in the department of mathematics at the Technion. His interests include algebraic number theory, additive number theory, and logic.
Zusammenfassung
Highly visual and beautifully illustrated
Exercises are organized into sections pertaining to various topics
Assumed little mathematical knowledge
Inhaltsverzeichnis
Motivation.- I Euclidean and Inversive Geometry.- Euclidean Isometries and Similarities.- Inversive Geometry.- Applications of Inversive Geometry.- II Non-Euclidean Geometry.- Spherical Geometry.- Appendix: Set Theory.
Details
| Erscheinungsjahr: | 2023 |
|---|---|
| Fachbereich: | Geometrie |
| Genre: | Mathematik, Medizin, Naturwissenschaften, Technik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Inhalt: |
xv
231 S. 10 s/w Illustr. 96 farbige Illustr. 231 p. 106 illus. 96 illus. in color. |
| ISBN-13: | 9783031250019 |
| ISBN-10: | 303125001X |
| Sprache: | Englisch |
| Einband: | Gebunden |
| Autor: | Sheydvasser, Arseniy |
| Hersteller: |
Springer Nature Switzerland
Springer International Publishing |
| Verantwortliche Person für die EU: | Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com |
| Maße: | 241 x 160 x 19 mm |
| Von/Mit: | Arseniy Sheydvasser |
| Erscheinungsdatum: | 17.04.2023 |
| Gewicht: | 0,586 kg |
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