"Teaching basic concepts in Analysis with dynamical geometry programs"

Stefan Welke*
Beethoven-Gymnasium Bonn
Stefan Welke, In der Wehrhecke 29, D-53125 Bonn
D-53125 Bonn
Germany
E-mail:Spwelke@aol.com



Modern software technology allows new paths in teaching concepts. Dynamical geometry programs like Cabri Geometre offer the
opportunity to demonstrate the concept of Derivative by visualizing the limit
                  delta y 
            lim ------------- 
                   delta x 
      delta x -> 0
as a dynamical change of a geometric figure. So the student can see what really happens in the limiting case: We magnify the characteristic
triangle and we can observe that the ratio, that defines the slope of the secants, attains a definite value, the slope of the tangent. 
Utilizing geometric ideas of I. Newton, this access to the subject is demonstrated in detail by the example of trigonometric and inverse
trigonometric functions.