The Java Applet that is the central feature of this website is an interactive implementation of the
Poincaré model for
the Lobachevskian Plane. When you start the applet (by clicking on the image of the airplane
on the home page), you should get a window that looks like the one at the right. (If the window is not maximized
when it appears, click on the maximize button at the upper right.)
The large area at the upper-left of the window is the actual "interactive drawing pad" on which you can construct figures that represent figures in the Lobachevskian Plane. The small region at the bottom-left provides prompts for actions to guide you in constructing your drawing, plus messages about mistakes. The large area to the right records the responses to querys about measurements of figures. At the bottom-center of the screen is a small "redraw" button, that allows you to refresh the drawing at any time, and a small box that reports the current percentage of the entire model shown.
You begin any drawing by point-and-click placement of points. The applet automatically labels the points as they are added. Once two or more points have been placed, you can draw a geometric object determined by a pair of points: a segment, ray or line, or a circle centered at one point and passing through another. To do so, select the desired construction from the Construct menu and click on the desired points.
Once an object or several objects are drawn, more construction possibilities are enabled, corresponding to the wider range of geometric possibilities. You can construct a point on a pre-existing object, construct the point(s) of intersection of two objects, construct a perpendicular, a midpoint, or an angle bisector. Also, you can extend any segment, or copy any segment or angle.
From the Measure menu, you can choose to measure the distance between any two points, the measure of any angle, or the defect of any polygon (up to six-sided, provided it does not intersect itself).
Options on the Edit menu allow you to undo previous constructions -- serially, in reverse order -- and then to redo them, if you again change your mind. You also have total control over the point labels: you can suppress all labels, show all labels, or selectively show some and hide others. In addition, you can move the label on any point (to produce a cleaner figure, with labels not superimposed on objects). The zoom in and zoom out selections decrease or increase the portion of the model visible; zooming all the way out shows the entire disk.
Finally, any figure can be "morphed" by moving a point. When a point is moved, any objects that were constructed dependent on that point also move, and points or objects in turn dependent on these move accordingly. Points constructed in the "free" point mode (e.g., not as midpoints, or points of intersection), can be moved freely; points constructed "on" an object can be moved elsewhere on that object, but cannot be removed from the object; and points constructed otherwise (e.g., as the foot of a perpendicular) cannot be moved directly.
For detailed information on how each construction is accomplished, or how to measure something, or how to rearrange the labels or move points, see the detailed information accessible from the Help menu.