2D-Geometry And 2D-Graphs, Version 7
Short description
This programme is intended to enrich the mathematical education in secondary
schools.
Not only teachers will benefit from this programme in their preparations
of lessons but also students will profit by exploring, testing, constructing,
calculating and visualizing geometrical objects.
This version of the programme contains many elements of an „interactive
geometry“. In many cases objects can be moved or resized with the
mouse. Depending objects, like images of a transformation, are adapted
during the movement.
All objects are shown in a 2d-coordinate-system with numerous options
either with equidistant or individual scales.
The offered geometrical objects are the following:
Point, line segment, vector, half-line, straight line, angle, triangle,
rectangle, polygon, circular sector, circle, sector of an ellipse, ellipse.
These objects can be changed by various options and they can be moved
with the mouse (if not achored). Especially with triangles you can find
even more options: It is possible to draw mid-perpendicular, bisectrix
of angle, median and height as well as incircle and circumcircle. In addition
squares over all sides can be drawn and there are special options for
rectangular triangles. For example, a shear animation can be started,
visualizing the proof of the theorem of Pythagoras.
Also the options of ellipses have been enhanced. Now the focus points
and the focal radii can be shown and changes of semi-axes, rotation and
translation with the mouse have been implemented.
You can input tables of values and calculate approximations by functions.
New to version 7 is the option to generate a Bézier curve along
control-points (with or without weights). Moving the control-points will
adapt the curve automatically.
You can calculate distances and intersections for many combinations of
objects.
The most important geometrical objects can be mapped by affine transformations:
Here too, the principle of interactive geometry has been put into practice.
If, for example, a point acting as centre of scaling is moved, all corresponding
images are adapted during the movement.
Additionally the programme offers the opportunity of drawing functional
graphs. This works with functions of one variable and with parametric
functions (x(t);y(t)). You can find several options like the calculation
of zeroes, extremes and integrals. Also the intersection of functional
graphs can be calculated.
Furthermore you can draw the Mandelbrot set and Julia sets. Interesting
regions of these sets can be zoomed in by selecting an appropriate rectangle.
The results of calculations are usually shown in the resizable text window.
This contents can be saved together with the graphical data or sent to
a printer.
It is also possible to save the graphical scene as an enhanced metafile
(*.emf), in postscript format (*.eps) or as a bitmap (*.bmp, *.jpg, *.png).
This way you can import the saved files into word processing software
to produce worksheets or educational material.
A big emphasis has been laid on a fluent operability. Accessing the options
of an object by right clicking on it is one example of this.
