## At A Glance

### UnivHypGeom12: Null points and null lines

Null points and null lines are central in universal hyperbolic geometry. By definition a null point is just a point which lies on its dual line, and dually a null line is just a line which passes through its dual point. We extend the rational parametrization of the unit circle to the projective parametrization of null points and null lines. And we determine the joins of null points and meets of null lines using these coordinates.CONTENT SUMMARY: pg 1: @00:09 Null points and null lines; definitions;pg 2: @5:37 Rationalparametrization of unit (null) circle; fix exceptional point; moving to projective parameterization;?pg 3: @10:21 Projective parametrization of the unit circle; dual statement (projective parametrization of null lines);pg 4: @14:42 remarks to connect parametrization with linear algebra;? mention of chromogeometry; pg 5: @18:12 Join of null points theorem; proof 1; pg 6: @23:31 Join of null points theorem; proof 2; pg 7: @27:40 Meet of null lines theorem; pg 8: @32:31 Introduction of Standard Triangle #2 (st2); A triply nill triangle;(THANKS to EmptySpaceEnterprise)
Length: 36:20

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