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The Resource Axiomatic Approach to Geometry : Geometric Trilogy I

Axiomatic Approach to Geometry : Geometric Trilogy I

Label
Axiomatic Approach to Geometry : Geometric Trilogy I
Title
Axiomatic Approach to Geometry
Title remainder
Geometric Trilogy I
Creator
Subject
Language
eng
Summary
This volume's historical focus, with fully worked solutions to all the famous problems in classical geometry, demonstrates the profound influence of axiomatic geometry, over more than three millennia, on the evolution of mathematics as an academic discipline
Cataloging source
MiAaPQ
Literary form
non fiction
Nature of contents
dictionaries
Axiomatic Approach to Geometry : Geometric Trilogy I
Label
Axiomatic Approach to Geometry : Geometric Trilogy I
Link
http://libproxy.rpi.edu/login?url=https://ebookcentral.proquest.com/lib/rpi/detail.action?docID=1592340
Publication
Copyright
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Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
  • An Axiomatic Approach to Geometry -- Preface -- The Geometric Trilogy -- Contents -- Chapter 1: Pre-Hellenic Antiquity -- 1.1 Prehistory -- 1.2 Egypt -- 1.3 Mesopotamia -- 1.4 Problems -- 1.5 Exercises -- Chapter 2: Some Pioneers of Greek Geometry -- 2.1 Thales of Miletus -- 2.2 Pythagoras and the Golden Ratio -- 2.3 Trisecting the Angle -- 2.4 Squaring the Circle -- 2.5 Duplicating the Cube -- 2.6 Incommensurable Magnitudes -- 2.7 The Method of Exhaustion -- 2.8 On the Continuity of Space -- 2.9 Problems -- 2.10 Exercises -- Chapter 3: Euclid's Elements -- 3.1 Book 1: Straight Lines -- 3.2 Book 2: Geometric Algebra -- 3.3 Book 3: Circles -- 3.4 Book 4: Polygons -- 3.5 Book 5: Ratios -- 3.6 Book 6: Similarities -- 3.7 Book 7: Divisibility in Arithmetic -- 3.8 Book 8: Geometric Progressions -- 3.9 Book 9: More on Numbers -- 3.10 Book 10: Incommensurable Magnitudes -- 3.11 Book 11: Solid Geometry -- 3.12 Book 12: The Method of Exhaustion -- 3.13 Book 13: Regular Polyhedrons -- 3.14 Problems -- 3.15 Exercises -- Chapter 4: Some Masters of Greek Geometry -- 4.1 Archimedes on the Circle -- 4.2 Archimedes on the Number pi -- 4.3 Archimedes on the Sphere -- 4.4 Archimedes on the Parabola -- 4.5 Archimedes on the Spiral -- 4.6 Apollonius on Conical Sections -- 4.7 Apollonius on Conjugate Directions -- 4.8 Apollonius on Tangents -- 4.9 Apollonius on Poles and Polar Lines -- 4.10 Apollonius on Foci -- 4.11 Heron on the Triangle -- 4.12 Menelaus on Trigonometry -- 4.13 Ptolemy on Trigonometry -- 4.14 Pappus on Anharmonic Ratios -- 4.15 Problems -- 4.16 Exercises -- Chapter 5: Post-Hellenic Euclidean Geometry -- 5.1 Still Chasing the Number pi -- 5.2 The Medians of a Triangle -- 5.3 The Altitudes of a Triangle -- 5.4 Ceva's Theorem -- 5.5 The Trisectrices of a Triangle -- 5.6 Another Look at the Foci of Conics -- 5.7 Inversions in the Plane
  • 5.8 Inversions in Solid Space -- 5.9 The Stereographic Projection -- 5.10 Let us Burn our Rulers! -- 5.11 Problems -- 5.12 Exercises -- Chapter 6: Projective Geometry -- 6.1 Perspective Representation -- 6.2 Projective Versus Euclidean -- 6.3 Anharmonic Ratio -- 6.4 The Desargues and the Pappus Theorems -- 6.5 Axiomatic Projective Geometry -- 6.6 Arguesian and Pappian Planes -- 6.7 The Projective Plane over a Skew Field -- 6.8 The Hilbert Theorems -- Step 1. Borrowing our Intuition from the Euclidean Case -- Step 2. The System of Coordinates -- Step 3. Addition on K -- Step 4. The Zero Element -- Step 5. The Opposites -- Step 6. Commutativity of Addition -- Step 7. Associativity of Addition -- Step 8. Multiplication on K -- Step 9. The Zero and the Unit for the Multiplication -- Step 10. Associativity of Multiplication -- Step 11. The Inverses -- Step 12. The Distributivity Laws -- Step 13. The Equation of a Line -- Step 14. The Homogeneous Coordinates -- 6.9 Problems -- 6.10 Exercises -- Chapter 7: Non-Euclidean Geometry -- 7.1 Chasing Euclid's Fifth Postulate -- 7.2 The Saccheri Quadrilaterals -- 7.3 The Angles of a Triangle -- 7.4 The Limit Parallels -- 7.5 The Area of a Triangle -- 7.6 The Beltrami-Klein and Poincaré Disks -- 7.7 Problems -- 7.8 Exercises -- Chapter 8: Hilbert's Axiomatization of the Plane -- 8.1 The Axioms of Incidence -- 8.2 The Axioms of Order -- 8.3 The Axioms of Congruence -- 8.4 The Axiom of Continuity -- 8.5 The Axioms of Parallelism -- 8.6 Problems -- 8.7 Exercises -- Appendix A: Constructibility -- A.1 The Minimal Polynomial -- A.2 The Eisenstein Criterion -- A.3 Ruler and Compass Constructibility -- A.4 Constructibility Versus Field Theory -- Appendix B: The Classical Problems -- B.1 Duplicating the Cube -- B.2 Trisecting the Angle -- B.3 Squaring the Circle -- Appendix C: Regular Polygons
  • C.1 What the Greek Geometers Knew -- C.2 The Problem in Algebraic Terms -- C.3 Fermat Primes -- C.4 Elements of Modular Arithmetic -- C.5 A Flavour of Galois Theory -- C.6 The Gauss-Wantzel Theorem -- References and Further Reading -- Index
http://library.link/vocab/cover_art
https://contentcafe2.btol.com/ContentCafe/Jacket.aspx?Return=1&Type=S&Value=9783319017303&userID=ebsco-test&password=ebsco-test
Dimensions
unknown
http://library.link/vocab/discovery_link
{'f': 'http://opac.lib.rpi.edu/record=b4390126'}
Edition
1st ed.
Extent
1 online resource (410 pages)
Form of item
online
Isbn
9783319017303
Media category
computer
Media MARC source
rdamedia
Media type code
c
Sound
unknown sound
Specific material designation
remote

Library Locations

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