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Math 161 Suggested Syllabus Text: Geometry with Geometry Explorer, M. Hvidsten, UCI Custom Reprint. Lecture 1 2 3 4 5 Section 1.1, 1.2 1.4, 1.5 1.6 2.1 2.2 6 2.4, 2.5 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 2.6 3.1, 3.2 3.4, 3.5 3.6 ----4.1 4.3 7.1 7.2 7.3 7.3 7.4, 7.5 7.6 7.8 ----9.1, 9.2 9.3 9.5 9.6 9.8 --- Topic Introduction to Geometry Axiomatic Method, Properties of Axiomatic Systems Euclid’s Axiomatic Geometry Angles, Lines and Parallels Congruent Triangles and Pasch’s Axiom Measurement and Area in Euclidean Geometry, Similar Triangles Circle Geometry Cartesian Coordinate System, Vector Geometry Angles in Coordinate Geometry, The Complex Plane Birkhos Axiomatic System for Analytic Geometry Review Midterm # 1 Euclidean Constructions Constructibility Background and History of Non-Euclidean Geometry Models of Hyperbolic Geometry Basic Results in Hyperbolic Geometry cont. Saccheri Quadrilateral, Lambert Quadrilateral and triangles Area in Hyperbolic Geometry Models and Isomorphism Review Midterm # 2 Introduction to Fractal Geometry, Self-Similarity Similarity Dimension Contraction Mappings and the Space of Fractals Fractal Dimension Algorithmic Geometry Review * Note: Instructors may choose to replace the Fractals topic with either the Symmetry or Transformational Geometry chapters. In addition, if time permits 2-3 lectures about Knot Theory may be added to the course (from instructor notes).