1.

Record Nr.

UNINA9910141013703321

Autore

Smith James T

Titolo

Methods of geometry / / James T. Smith

Pubbl/distr/stampa

New York, : John Wiley & Sons, 2000

ISBN

9786613813619

9781282242494

1282242490

9781118032787

1118032780

9781118031032

1118031032

Descrizione fisica

1 online resource (506 p.)

Disciplina

516

Soggetti

Geometry

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

"A Wiley-Interscience publication"--t.p.

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

Methods of Geometry; Contents; Preface; About the author; 1 Introduction; 1.1 Episodes; 1.2 Advanced geometry; 1.3 This book; 1.4 Reading about geometry; 1.5 Projects; 2 Foundations; 2.1 Geometry as applied mathematics; 2.2 Need for rigor; 2.3 Axiomatic method; 2.4 Euclid's Elements; 2.5 Coordinate geometry; 2.6 Foundation problem; 2.7 Parallel axiom; 2.8 Firm foundations; 2.9 Geometry as pure mathematics; 2.10 Exercises and projects; 3 Elementary Euclidean geometry; 3.1 Incidence geometry; 3.2 Ruler axiom and its consequences; 3.3 Pasch's axiom and the separation theorems

3.4 Angles and the protractor axioms3.5 Congruence; 3.6 Perpendicularity; 3.7 Parallel axiom and related theorems; 3.8 Area and Pythagoras' theorem; 3.9 Similarity; 3.10 Polyhedral volume; 3.11 Coordinate geometry; 3.12 Circles and spheres; 3.13 Arcs and trigonometric functions; 3.14 π; 4 Exercises on elementary geometry; 4.1 Exercises on the incidence and ruler axioms; 4.2 Exercises related to Pasch's axiom; 4.3 Exercises on congruence and perpendicularity; 4.4 Exercises involving the parallel axiom; 4.5 Exercises on similarity and Pythagoras' theorem



4.6 Exercises on circles and spheres, part 14.7 Exercises on area; 4.8 Exercises on volume; 4.9 Exercises on circles and spheres, part 2; 4.10 Exercises on coordinate geometry; 5 Some triangle and circle geometry; 5.1 Four concurrence theorems; 5.2 Menelaus' theorem; 5.3 Desargues' theorem; 5.4 Ceva's theorem; 5.5 Trigonometry; 5.6 Vector products; 5.7 Centroid; 5.8 Orthocenter; 5.9 Incenter and excenters; 5.10 Euler line and Feuerbach circle; 5.11 Exercises; 6 Plane isometrles and similarities; 6.1 Transformations; 6.2 Isometries; 6.3 Reflections; 6.4 Translations; 6.5 Rotations

6.6 Structure theorem6.7 Glide reflections; 6.8 Isometries and orthogonal matrices; 6.9 Classifying isometries; 6.10 Similarities; 6.11 Exercises; 7 Three dimensional isometries and similarities; 7.1 Isometries; 7.2 Reflections; 7.3 Translations and rotations; 7.4 Glide and rotary reflections; 7.5 Classifying isometries; 7.6 Similarities; 7.7 Exercises; 8 Symmetry; 8.1 Polygonal symmetry; 8.2 Friezes; 8.3 Wallpaper ornaments; 8.4 Polyhedra; 8.5 Exercises; Appendix A Equivalence relations; Appendix B Least upper bound principle; Appendix C Vector and matrix algebra; Bibliography; Index

Sommario/riassunto

A practical, accessible introduction to advanced geometry Exceptionally well-written and filled with historical and bibliographic notes, Methods of Geometry presents a practical and proof-oriented approach. The author develops a wide range of subject areas at an intermediate level and explains how theories that underlie many fields of advanced mathematics ultimately lead to applications in science and engineering. Foundations, basic Euclidean geometry, and transformations are discussed in detail and applied to study advanced plane geometry, polyhedra, isometries, similarities, and symmetry. An



2.

Record Nr.

UNINA9911026003103321

Autore

Dangler Jean

Titolo

Edging toward Iberia / / Jean Dangler

Pubbl/distr/stampa

Toronto : , : University of Toronto Press, , [2018]

©2017

ISBN

1-4875-1276-7

1-4875-1275-9

Descrizione fisica

1 online resource (vii, 170 pages)

Collana

Toronto Iberic

Classificazione

cci1icc

coll13

Disciplina

936.6/01

Soggetti

LITERARY CRITICISM / European / Spanish & Portuguese

Electronic books.

Iberian Peninsula Antiquities Historiography

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di contenuto

Periodization and geography -- Network theory and world-systems analysis -- The Islamicate trade network -- Non-modern Iberian travel and the Islamicate travel network -- Feudalism, "slavery," and poverty -- Politics -- Identity and culture.

Sommario/riassunto

"Nonmodern Iberia was a fluid space of shifting political kingdoms and culturally diverse communities. Scholars have long used a series of obsolete investigative frameworks such as the Reconquista, along with modern ideas of nation-states, periodization, and geography that are inadequate to the study of Iberia's complex heterogeneity. In Edging Toward Iberia Jean Dangler argues that new tools and frameworks for research are needed. She proposes a combination of network theory by Manuel Castells and World-Systems Analysis as devised by Immanuel Wallerstein to show how network and system principles can be employed to conceptualize and analyze nonmodern Iberia in more comprehensive ways. Network principles are applied to the well-known themes of medieval trade and travel, along with the socioeconomic conditions of feudalism, slavery, and poverty to demonstrate how questions of power and temporal-historical change may be addressed through system tenets. Edging Toward Iberia challenges current



historical and literary research methods and brings a fresh perspective on the examination of politics, identity, and culture."--