Poincare Model Worksheet

Worksheet:[br]As you go throughout this worksheet keep in mind what a line segment in the Poincaré model is. It is NOT a straight line like in Euclidean geometry. It is the arc of a circle. Refer back to "What is the Poincaré Model" for more information

Step 1:

Using the applet below create 4 points within the circle. Place the points in such a that it looks like they form a rectangle if you were able to connect them with straight lines.

Step 2:

Using the hyperbolic line tool, connect the 4 points so that they form a quadrilateral shape.

Step 3:

Using the hyperbolic midpoint tool find the midpoints of each line segment.

Step 4:

Using the hyperbolic line tool connect the diagonal midpoints.

This is an example of the diagonals of the midpoints being connected in normal Euclidean Geometry. Notice that the quadrilateral made from the midpoints is a parallelogram.

Step 5:

Observe the quadrilateral that you made in the Poincare Model of Hyperbolic geometry.[br]

What shape is the quadrilateral that you formed?

Is it a parallelogram? How do you know?

Can rectangles be made in the Poincare Model?