Hyperbolic Geometry Exploration NonEuclid is a Java program,
written by Joel Castellanos, for doing geometry in hyperbolic
space. Go to the NonEuclid page and run the applet. It should
display a large black circle - that's the Poincaré disk. The
program opens with a sample drawing. To clear the disk, choose
"New" under the File menu. This will leave you in "Draw Line
Segment" mode, as shown in the upper left corner. Draw some line
segments. - What do lines that go through the center of the disk
look like? Clear your drawing, and draw a triangle. On the Edit
menu, choose "Move Point". Now you can drag the corners of your
triangle and see how it changes. On the Measurements menu,
select "Measure Triangle", and click the three corners of your
triangle. You should see the side and angle measurements of the
triangle in the box on the left. Go back to "Move Point" mode.
Move your triangle around to get a feel for the lengths of its
sides and the sum of its angles. - Draw a triangle which appears
large but really ha