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This course examines point reflections in hyperbolic geometry, including null reflections and the preservation of perpendicularity and lines. It also develops straightedge constructions for side midpoints and defines vertex bisectors, highlighting cases where midpoints may not exist or may be non-unique.
Syllabus
Introduction
Definition of reflection of a general point
Null reflection theorem
Matrix perpendicularity theorem
Reflection preserves perpendicularity theorem
Reflection preserves lines theorem
Midpoint between 2 points
Geometrical construction of midpoints 1a
Geometrical construction of midpoints 1b
Geometrical construction of midpoints 2
Not all sides have midpoints; side/vertex midpoints/bisectors
Taught by
Insights into Mathematics