Tessellating with Hyperbolic Triangles?
Follow my instructions to attempt to construct 6 tessellating equilateral (regular) triangles starting from segment AB to attempt form a regular hexagon.
Here's a summary of the directions:
- Create Hyperbolic Circle with center A and radius B. Rename it e (if needed).
- Create Hyperbolic Circle with center B and radius A. Rename it f (if needed).
- Intersect the circles with code Intersect(e,f,1) . Rename the point C (if needed).
- Create Hyperbolic Segment from B to C. Rename it g (if needed).
- Create Hyperbolic Circle with center C and radius A. Rename it h (f needed).
- Intersect the new circle with the first circle with code Intersect(e,h,1) . Rename the point D (if needed).
- Create Hyperbolic Segment from C to D. Rename it k (if needed).
- Repeat the process 4 more times producing 4 more points and 4 more segments.
Be sure to produce point H (a 7th point on circle e).
Questions:
Did it work?
What fact of Geometry are we relying on to be confident this construction works?
What happens when you zoom into your final vertex?