Analytic Geometry, Version 7.1
Short description
The programme Analytic Geometry,
Version 7.1, is a flexible system
for presenting geometrical objects with hidden surfaces (on an OpenGL-Basis)
in a rotatable 3D-coordinate system. This new version introduces the concepts
of interactive Geometry in the 3rd dimension. So most of the objects
are easily rotated or translated with the mouse in combination with certain
keys on your keyboard.
You may select parallel or central projection.
Beside the known objects of the 2d-world like point, vector, line segment,
straight line, circle, circular disk, ellipse the programme also supports
solids like rectangular solid, regular tetrahedron, pyramid, prism, sphere,
cone, cylinder and torus.
You can calculate distances and intersections of the most often occurring
object combinations. Here too, you can find the concept of Interactive
Geometry. All objects that are the result of distance or intersection
calculations are automatically recalculated during translation or rotation
of participating objects.
You can find special options with spheres: You can define points on the
surface, translate them on the surface and connect them by great circles.
Additionally you can switch on or off a grid of longitudes and latitudes.
Every sphere can be endowed with an own rotation. Also distances between
points (as segments of a great circle) on the sphere can be calculated.
We have also implemented chapters from elementary courses in geometry.
So it is possible to test 2 vectors on collinearity or 3 vectors on linear
dependency. Also linear combinations of vectors can be drawn.
As a very powerful improvement we mention animations of points and spheres.
The flexibility comes through general functions in parametric form, that
can be assigned to these objects. These functions can be defined relative
to a reference object (point or sphere). So you can easily define the
movement of planets including satellites.
If necessary all data of a point, sphere or line segment can be watched
in an inspection window - even while they move e.g. during an animation.
This new version of the programme includes affine tansformations. This
- together with animations - offers a great bandwidth of effects.
Also the graphs of functions of 2 variables f(x,y) and those of functions
in parametric form can be drawn in the scene (including families of functions).
The palette of programme features is completed by the presentation of
Bézier curves, defined by a set of control points, where weights
are accepted.
It is possible to show the object data in an always visible and sizable
text window.
You can certainly save, load or print the scene or export it as graphic
to be included in word processing projects.
This programme can be used in various ways in the mathematical education
in secondary or higher schools of all types and even in colleges of higher
education.
Also individuals interested in mathematics outside of educational institutions
may enjoy this programme and benefit from it.
The emphases of this programme with interactive geometry are high quality
graphical representation of the constructed scene, calculations of distances
and intersections as well as animations.
