Menu for hyperbolic geometry.

    Download  hyperbol.men (55K for Windows)

    After downloading the above file reset its file type (if necessary) to .men 
    Open this menu file from within Cabri itself.
    The standard Cabri menu bar is augmented on the right by four new pull down menu icons.

    The Menu Bar

    The  four new pull down icons on the menu bar each provide a number of commands of a similar nature.
    The four sections can be roughly categorised as follows;
    • Figures ; commands for drawing lines, line segments (or arcs), and standard figures in the disc.
    • Constructed lines and points ; perpendiculars, midpoints etc.
    • Reflections ; reflection (or inversion) of figures about a disc line.
    • Measurements ; non Euclidean distance between points, angles and triangle sums.

    Help, using the standard Cabri menu item,  is available for each of the commands.

    Drawing in H2

    The menu commands are for the Poincaré disc model of hyperbolic space H2. Hence all constructions start with a circle drawn to a convenient size. There are two ways of doing this.
    circle (Cabri menu item) 
    Using the standard Cabri command to draw a circle choose the centre point and a point on the circumference.  All further reference is then to this circle, called variously the disc circle, the disc boundary or the disc horizon. All points and figures in use should be kept inside this circle.
    Another method for drawing the circle of the fundamental disc is to use the unit disc command (the first item in the rightmost pull down menu.)
    unit disc (Measurements menu) 
    This command  is used whenever non Euclidean distances are to be measured.  Two points are chosen, the centre and then a point on the positive x-axis that is to be one unit (in Euclidean distance) from the centre. The result is the unit disc (the boundary is called the horizon for this macro) with the axes shown in grey. Note that the unit disc can be drawn over an existing disc circle, so that non Euclidean distances can then be measured. To overlay this unit disc choose the centre of the existing circle and then a point on its circumference.
    figure menu