Laboratory on Mathematics and Mathematics Education/DGS

Task 1: Exploring Dynamic Geometry Systems!

1. Download GeoGebra. If you are not allowed to install software on your system, I will give you GeoGebra on a flash.
2. Try to construct the perpendicular bisector of two points on at least three different ways.
3. Try to create the construction which "proofs" Thales' Theorem.
4. Show that the sum of a triangle's angles is always 180°.
5. Show that in a circle the angle at the center is double of the angle at the circumference.
6. Given a triangle, show that its perpendicular bisectors always intersect in one single point, the circumcenter. Do this also for its median lines (centroid) and for the heights of its sides (orthocenter). Afterwards, show that these three points always are on one line (Euler line)
7. Construct a regular hexagon.
8. "Proof" some other geometric theorems. If you can't remember one, select on from the following list.

Task 2: Dynamic aspects of functions

1. Invent a bathtube story for a given a "bathtube graph".
2. Create filling graphs for a given jar (and vice versa).
3. How could the EIS principle be realized in this context? Collect ideas!

1. Show how the unit circle is connected to the sinus curve in GeoGebra.
2. Do the same for the graphs of cosine and tangent.
3. Show the effects of functional parameters on graphs of different functions (for example, quadratic functions in different representations, (co)sine, exponential functions, ...). Create dynamic worksheets using sliders!
4. Show that the loci of points which have the same distance from a given point and line are on a parabola. Are all parabolas graphics of a function?