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Hyperbolic Lines
This figure shows hyperbolic lines AB, PQ and XY.
Note. The points A, P, X, B, Q and Y lie on C,
so do not belong to the geometry.
You can vary the lines by moving any of these points.
By experimenting, you should convince yourself of
the following facts
- A hyperbolic line which passes through the centre O
is a euclidean segment, i.e. a diameter of C.
- Two hyperbolic lines meet at most once.
- Two hyperbolic lines which share a boundary point
make zero angle (since each is orthogonal to C).
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Hyperbolic Triangles
The figure shows a hyperbolic triangle PQR
You can move any of the vertices, P, Q and R,
but if any point is dragged outside the circle C,
the associated hyperbolic segments vanish.
By experimenting, you should convince yourself of
the following facts
- If the points are moved so that a segment passes
through O, the segment is a line segment.
- When a vertex is close to O,
the associated segments are almost straight
Due to a bug, the segments vanish if a vertex is at O
- When a vertex is close to the boundary C,
the angle betwen the segments is close to zero.
You should look at cases where O is inside
and outside the triangle, and observe the shapes.
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