UnivHypGeom26: Trigonometric laws in hyperbolic geometry using Geometer's Sketchpad

[EmptySpaceEnterprise]

njwildberger, this forum post was the point of departure that led me to your channel.

alienscientist(dot)com/forum/s­howthread.php?1646-Thoughts-on­-the-4th-Dimension

[EmptySpaceEnterprise]

Introduction @00:11 ;

Quadrance @02:09 ;

Spreads @04:37 ;

Dual triangle @07:10 ; perpendicularity;

Pythagoras' theorem @09:26 ;

Triple quad formula @12:12 ;

The Spread law @15:16 ;

The Cross law @16:17 ;

[capibaby1]

For people who have been taught this subject in the classical hyperbolic geometry sense, it might be important to spend more time explaining how to see how to extend their metrical notions outside the circle, and why the algebraic forms of the metric are more fundamental than the transcendental ones in terms of log, sinh, sin etc. I'm personally curious about the relationship between the two, also.

[njwildberger]

@capibaby1 Yes that is possibly a good idea. I will explain the relationship later at some point, when I summarize classical hyperbolic geometry and how it fits into the Universal approach. For a beginner though, I want to emphasize that this treatment here is completely independent of, any much simpler than, the classical one.