Nonlinear Tessellations

Construction

Step 3, part 2 proof

The triangle AQB is right isosceles, so the angle AQB = 45.

Consider the segment MN tangent to W at Q.

Because AQ is a radius of W, the angle AQM = 90.

Now angle OQM + angle MQA + angle AQB = 180, so angle OQM = 45.

Therefore the hyperbolic angle OQR = 45.

Because angle OQP = 90 and angle OQR = 45, the arc RQ bisects the angle OQP.

Return to Step 3.