Exercise 1

Look at the Parabola-figure. Open the GeoScript-file and change the data entries
for the object e[8] so that the figure shows the graph of the function

.

Save the GeoScript- and HTML-file in the "excercise"-folder under "e1_function.script"
and "e1_function.html". Use this name scheme in the following exercises, too.

Exercise 2

Develop a figure, which shows the graph of an ellipse with the equation

x = a cos t
y = b sin t

and t Î [0, 2p]. Save the GeoScript- and HTML-file in the "excercise"-folder under "e2_ellipse.script" and "e2_ellipse.html".

Exercise 3

Develop a figure, which shows the graph of a cycloide with the equation

x = rt – a sin t
y = r – a cos t

and t Î [–2p, 2p].

Exercise 4

Choose an arbitrary function or parametric curve on your own and
describe the graph in GeoScript like in exercise 1-3.

Exercise 5

Look at the figure Non-Affin Mapping with the mapping f(x, y) = (|x|, 3|y|).

Develop a similar figure where a triangle ABC is mapped to A'B'C' with f(x, y) = (–x, –y).

Exercise 6

Change the figure Non-Affin Mapping like in exercise 5,
but choose a mapping f(x, y) on your own.

Exercise 7

a) Change the response analysis in figure Algebra of Sets,
that (S1) becomes to ((A + B) Ç C) \ A = {P}.

b) Choose an equation on your own and construct an according figure
with response analysis.

Exercise 8

a) Change the response analysis in figure Image vector seeked that f(x, y): = (–y, x).

b) Choose a function f(x, y) equation on your own and construct an according figure
with response analysis.

Exercise 9

Take the figure from exercise 8 b) and extend it, so that the starting points are randomized.
You find an example in Image vector seeked (randomized).

Exercise 10

Change the figure Vectoraddition. Choose the start values for a and b and the equation
for c on your own.

Exercise 11

The response analysis in Coefficients of mapping seeked checks the values of the
controllers. Develop a similar figure with A'B'C' as the image of a reflection of ABC on
the straight line g: y = x. (Hint: a₁ = 0, a₂ = 1, b₁ = 1, b₂ = 0.)