## At A Glance

### UnivHypGeom9: Duality and perpendicularity

Perpendicularity in universal hyperbolic geometry is defined in terms of duality. One big difference with classical HG is that points can also be perpendicular, not just lines. Once we have perpendicularity, we can define altitudes. We also state the collinear points theorem and concurrent lines theorem, using homogeneous coordinates and determinants.CONTENT SUMMARY: pg1: @00:04pg2: examples of viewing plane (good for study) @02:44pg3: exercises: point duality theorem line duality theorem @09:03pg4: proof (of point duality theorem) @10:14pg5: Perpendicularity: lines and points @11:48pg6: examples of perpendicular points and perpendicular lines @13:48pg7: Altitudes of triangles @20:22pg8: Concurrent lines theorem and proof @27:48pg9: Collinear? points theorem @30:09 (THANKS to EmptySpaceEnterprise)
Length: 33:11

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