# Geometry ## with an Introduction to COSMIC TOPOLOGY

The files listed below run with The Geometer’s Sketchpad. These files, made by the author using Sketchpad v. 4.05, offer dynamic constructions with comments that complement content in the text.

• Text Tools.
• Chapter 1
• Exercise 1.3.5 – Coneland (coneland.gsp )
• Chapter 3
• Inversion (inversion_intro.gsp)
• Theorem 3.2.10 – Inversion preserves angle magnitudes (inversion_conformal.gsp)
• Theorem 3.4.8 – The Fundamental Theorem of Mobius Transformations (Mob1_0_infinity.gsp)
• Type I and II clines (typeIandII.gsp)
• Mobius transformations determined by 2 inversions (mobtwoinversions.gsp)
• Chapter 5
• hyperbolic translation (hyperbolictranslation.gsp)
• hyperbolic rotation (hyperbolicrotation.gsp)
• parallalel displacement (paralleldisplacement.gsp)
• Example 5.1.8 - Moving an “M” around in the hyperbolic plane (Move_the_M.gsp)
• Definition 5.2.10 - Constructing a hyperbolic circle (hypcircle.gsp)
• The hyperbolic circle through 3 points, perhaps - Figure 5.3.13 (hypcirclethrough3pts.gsp)
• Exercise 5.4.4 - All ideal triangles are congruent (ideal_triangle.gsp)
• Theorem 5.4.21 - Right angled hexagons (rightanglehexagon.gsp)
• Chapter 6
• A look at antipodal points (antipodal_points.gsp)
• Figures in elliptic space (elliptic_figures.gsp)
• Chapter 7
• Example 7.7.9 and Exercise 7.7.1 - H1 as a quotient of the Euclidean plane, with Dirichlet domains (H1Dirichlet.gsp)
• Section 7.7 – The space C2 as a quotient of the Euclidean plane (C2quotient.gsp)
• Exercise 7.7.2 - C3 as a quotient of the hyperbolic plane, with Dirichlet   (C3Dirichlet.gsp)
• Exercise 7.7.4 – The Dirichlet domain of an observer in C2 varies from point to point (C2Dirichlet.gsp)