College geometry : a unified approach /: a unified approach. (2011)

• Record Type: Book
• Further Information: Note: David Kay.
• Other Names: Kay, David C, 1933-
• Contents: Lines, Distance, Segments, and Rays; Intended Goals; Axioms of Alignment; A Glimpse at Finite Geometry; Metric Geometry; Eves’ 25-Point Affine Geometry: A Model for Axioms 0–4; Distance and Alignment; Properties of Betweenness: Segments and Rays; Coordinates for Rays; Geometry and the Continuum; Segment Construction Theorems Angles, Angle Measure, and Plane Separation; Angles and Angle Measure; Plane Separation; Consequences of Plane Separation: The Postulate of Pasch; The Interior of an Angle: The Angle Addition Postulate; Angle Construction Theorems; Consequences of a Finite Metric Unified Geometry: Triangles and Congruence; Congruent Triangles: SAS Hypothesis; A Metric for City Centers; The SAS Postulate and the ASA and SSS Theorems; Euclid’s Superposition Proof: An Alternative to Axiom 12; Locus, Perpendicular Bisectors, and Symmetry; The Exterior Angle Inequality; Inequalities for Triangles; Further Congruence Criteria; Special Segments Associated with Triangles Quadrilaterals, Polygons, and Circles; Quadrilaterals; Congruence Theorems for Convex Quadrilaterals; The Quadrilaterals of Saccheri and Lambert; Polygons; Circles in Unified Geometry Three Geometries; Parallelism in Unified Geometry and the Influence of α; Elliptic Geometry: Angle-Sum Theorem; Pole-Polar Theory for Elliptic Geometry; Angle Measure and Distance Related: Archimedes’ Method; Hyperbolic Geometry: Angle-Sum Theorem; A Concept for Area: AAA Congruence; Parallelism in Hyperbolic Geometry; Asymptotic Triangles in Hyperbolic Geometry; Euclidean Geometry: Angle-Sum Theorem; Median of a Trapezoid in Euclidean Geometry; Similar Triangles in Euclidean Geometry; Pythagorean Theorem Inequalities for Quadrilaterals: Unified Trigonometry; An Inequality Concept for Unified Geometry; Ratio Inequalities for Trapezoids; Ratio Inequalities for Right Triangles; Orthogonal Projection and "Similar" Triangles in Unified Geometry; Unified Trigonometry: The Functions c(θ) and s(θ); Trigonometric Identities; Classical Forms for c(θ) and s(θ); Lambert Quadrilaterals and the Function C(u); Identities for C(u); Classical Forms for C(u); The Pythagorean Relation for Unified Geometry; Classical Unified Trigonometry Beyond Euclid: Modern Geometry; Directed Distance: Stewart’s Theorem and the Cevian Formula; Formulas for Special Cevians; Circles: Power Theorems and Inscribed Angles; Using Circles in Geometry; Cross Ratio and Harmonic Conjugates; The Theorems of Ceva and Menelaus; Families of Mutually Orthogonal Circles Transformations in Modern Geometry; Projective Transformations; Affine Transformations; Similitudes and Isometries; Line Reflections: Building Blocks for Isometries and Similitudes; Translations and Rotations; Circular Inversion Non-Euclidean Geometry: Analytical Approach; Law of Sines and Cosines for Unified Geometry; Unifying Identities for Unified Trigonometry; Half-Angle Identities for Unified Geometry; The Shape of a Triangle in Unified Geometry: Cosine Inequality; The Formulas of Gauss: Area of a Triangle; Directed Distance: Theorems of Menelaus and Ceva; Poincarè’s Model for Hyperbolic Geometry; Other Models: Surface Theory; Hyperbolic Parallelism and Bolyai’s Ideal Points Appendix A: Sketchpad Experiments; Appendix B: Intuitive Spherical Geometry; Appendix C: Proof in Geometry; Appendix D: The Real Numbers and Least Upper Bound; Appendix E: Floating Triangles/Quadrilaterals; Appendix F: Axiom Systems for Geometry Solutions to Selected Problems Bibliography Index
• Publisher Details: Place of publication not identified : CRC Press
• Publication Date: 2011
• Extent: 1 online resource (652 pages), (22 illustrations)
• Subjects: 516; Geometry
• Languages: English
• ISBNs: 9781439895221; 1439895228
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.